It included this graphic, perhaps the most often shared on gerrymandering, and I'm told it's even used in classrooms:

One big problem with that: it's misinformation. It looks and feels educational, it seems intended to be educational, but it unquestionably promotes the same myth about “how gerrymandering works” that partisan liars use to claim things like “New England is extremely gerrymandered.” I'll explain.

What Gerrymandering Is

Gerrymandering is defined as the drawing of political territories - usually House Districts - in a way that favors a particular political party.1

What Gerrymandering Is Not

A certain percentage of votes not yielding a similar percentage of Representatives for a given state or region.

The most common posts circulated on the subject treat gerrymandering as above - an “expected value” calculation.

That is: given 5 Representatives in a state that votes 40% Republican, how many seats should Republicans receive (implicitly, in a fair state that does not gerrymander)?

40% of 5 seats is 2; therefore, a “fair” calculation is considered 2. Whether gerrymandering is explained this way is not my opinion. This so-called best explanation of gerrymandering literally called this perfect representation.

To be perfectly clear, this is not just an oversimplification - it is wrong. Explaining gerrymandering this way would be analogous to “explaining” the Electoral College by invoking the National Popular Vote: your opinion of what is “fair” is irrelevant to how the system works.

The United States does not proportionally allocate House seats based on statewide votes, nor does it allocate Electors based on National Popular Vote. Stating what would be “fair” in a system we do not have is not an explanation of anything. It is a strawman. And in the context of “explaining gerrymandering” it is misinformation.

The public is confused, and I'm once again pissed off about misinformation coming from sources that should know better.

It is the exact same reasoning used by right wing accounts, when they share graphics like this:

According to this meme, given 36% of the vote, 0 seats in a state like Massachusetts with NINE representatives must be gerrymandering (or, at minimum, “is unfair”).

It's just this:

And that has nothing to do with what gerrymandering is, isn't, or how it works.

The Gerrymandering Test

Assuming you know what gerrymandering is: drawing lines to favor a particular political party, and what it is not - deviation from proportional statewide representation - how can we explain or teach to the public what is and isn't gerrymandering?

This is a calculation that can be done for every state. I'll show you how.

Here is the rationale:

Without considering political or demographic data at all (i.e. the complete absence of any possibility of gerrymandering) how many seats would a party be expected to win?

The findings will be called the expectation.

To illustrate how it works, first consider the following map. It may look familiar.

There are two rules that all districts must follow:

1. Contiguous (all districts touch another part of the district)

2. All districts are the same size

Given those two rules, there are a few thousand possible configurations (4,006, I think). There are only so many shapes you can make when each district contains just 5 equidistant units, but here are a few examples of what a valid map might look like:

Remember, each of these maps were drawn with zero consideration to political affiliation. The proportion of red to blue in any district is purely chance - none of them can possibly be “gerrymandered” by any definition. More on this map in a moment. But first, note:

There's exactly one map that results in blue controlling all 5 districts: it's pretty easy to see in this layout.

Myth debunked:

“Gerrymandering is when funny lines”

It's approximately impossible that this map would be selected by chance. The absence of weird shapes does not mean the map isn't gerrymandered. In real life, communities of interest don't always reside within neat shapes. Weird shapes are a red flag, not a checkered flag: suspicious, not conclusive.

Whether or not the above 5-0 map is “fair” simply isn't relevant to the topic of gerrymandering. The question of gerrymandering requires asking: was it map drawn neutral of political consideration? With a probability of 4,005/4,006 (~99.98%) - no.

A brief exploration of this map teaches a few important lessons.

Map # 1: Clustered

Given this exact “clustered” configuration of red and blue, in the total absence of any possible gerrymandering, here is the range and probability of possible outcomes:

Blue probably gets 3 seats. Maybe 4. Simple enough. That's exactly what you would have thought! Where's the misinformation, Carl?!

Well first, remember, the old “explanation” described maps as fair or unfair based on the outcome, not whether the maps were gerrymandered. Also, there's about a 1/4 chance that maps that are drawn with zero political bias result in blue not having 3 seats.

At the risk of this turning into a lesson on probability (you can bookmark this as your next read, if you like), it's perfectly fine to say:

For this map, blue has an expectation of 3 seats.

Foreshadowing, “60% Blue and 40% Red” isn't the only relevant variable. It's not even the most important one!

Map #2: Dispersed

Surprise! Count the dots if you want - it's still 60% Blue and 40% Red. And yet, in this scenario, it is very hard for blue not to have a majority in at least four out of five districts!

Here's the percentage of non-gerrymandered outcomes:

Maps 1 and 2 have the same exact percentage of red and blue: the only thing that has changed is where they live. With that alone, the expectation has gone from 3/5 seats to 4/5 seats. Not just that, but Blue’s chances of controlling 5/5 districts is higher in the “dispersed” configuration than it was of controlling 4/5 districts in the “clustered” configuration!

Map #3: Dispersed Threshold

At 60% of the vote, the expectation for Blue (where red is dispersed) is about 4/5 seats.

At 64%, that expectation becomes 5/5. And it's not particularly close.

The reason for the unintuitive threshold is this:

In a winner-take-all system, every district has a winner and a loser. A loser may receive 49% of the votes, but they don’t get 49% of a seat - they get 0. This nonlinear relationship between votes-to-seats doesn’t cease to exist simply by zooming out to the state level.

And that’s where the misunderstanding comes from.

The calculation of “fairness” in (for lack of a better descriptor) non-Carl graphics assumes a linear relationship of statewide votes to seats: 50% of the vote yielding 50% of the seats, 60% of the vote yielding 60% of the seats, and so on. That is simply not correct. This is not my opinion, this is the provable mathematical reality.

Without considering how “spread out” voters are, seat percentage to statewide popular vote percentage will follow a sigmoid shape, like this:

Going from, say, 55% (z =1) to 60% (z=2) of the popular vote in a given state has a highly disproportionate impact on seat expectations because there become far fewer permutations of districts within which the majority party doesn't get at least 50%. This is represented by the steep middle of the chart.

Going from 65% to 85% (z= 3 to z = 7) would be much smaller, if not negligible, despite a larger gross change - illustrated where the curve becomes asymptotic/flat. If that explanation is too many words, don't sweat it, there are more charts to illustrate.

Map #4: Dispersed Dominance

If you ask someone how many seats is “fair” for a party that receives 28% of votes statewide, given 5 seats, the answer will probably be “one.”

But that outcome is impossible to achieve except with gerrymandering.

I'll repeat:

For the map above, the only way for Red to get even one seat is to consider partisan affiliation and then draw the maps specially to ensure it: reverse gerrymandering.

Not what you expected? Blue winning 5/5 seats isn't just the expectation anymore. Anything else would require special treatment for Red.

Real World Application: “Blue States”

1. The percentage of voters who support a party statewide matters somewhat for expected seats per state. But when it comes to how many districts are won under the rules in the United States (Single Member, most-votes-wins), how those voters are dispersed matters at least as much, if not more! This is because of the concept I illustrated above called “spatial nonlinearity.”

   In the Northeast, where Democrats hold a comfortable majority in most states, rural voters are extremely dispersed and make up a smaller percentage of the population than, for example, in the Midwest.

2. Even without spatial nonlinearity (clustered vs. dispersed) - which is a huge variable - the relationship between votes to seats is also not linear.

Put these two facts together, and you can understand why “60% of the votes → 60% of the seats = fair” makes no sense: it has nothing to do with the system we actually have, nor anything to do with “gerrymandering.”

If someone wants to argue about what type of system we should have, great. You can talk about proportionality or multi-member districts or even look at my article on Uruguay’s neat system if you want. If you're really itching to learn more about the difference between US-style and the many other European systems, and how we forecast probabilities within them, check out this article from .

But you don't get to draw a map that shows your opinion of what a fair map would look like, and claim any deviation from it is “gerrymandering.”

Now that we’ve disproven the “New England gerrymandered!” lie, let’s look at how where people live impacts red states.

Map #5: Blue Minority, Clustered

This 60-40 Red scenario is designed to look like a state that is relatively Red statewide, but has Blue “big cities.” That is, a nonrandom geographical cluster that mirrors reality.

Look at the expectation for Red in this scenario:

And compare that to the 60% Blue map presented earlier in which Red is dispersed - as is the case in most “Blue” states:

Well I'll be damned. These are the same percentages, only in a different configuration!

This difference is entirely attributable to spatial nonlinearity where people freaking live.

Now, to be clear, this is not to say blue states don't gerrymander or red states don't gerrymander - I'll get to that.

This is to say in the total absence of any possibility of gerrymandering, where people live (clustered versus dispersed) makes this much difference. This has nothing to do with “fairness.” It only has to do with math. Quote me.

Map #6: Red Dominant Clustered

If you're anything like the people I've presented this to, your mind is probably already kind of blown by how different the expectations are for those 60-40 maps. I'm not finished yet.

Earlier, I defined “dominance” as 72%. While shrinking states down to 25 dots loses some nuance, it is certainly not an oversimplification to illustrate the impact of geography on the chances of reaching a majority in a district.

And here’s the punchline:

Even at 72% dominance, the expectation for Red is barely four seats. Compare that to:

That collective gasp you heard was the people who created the “fair” graphics acknowledging that those graphics have nothing to do with gerrymandering.

Do I need to say it again? Distribution matters.

One final map before I give an overview of how gerrymandering works and what it looks like.

Map #7 : Red WTF clustered

This Reagan 1984-looking map features an extreme version of what actually exists in the deepest-red states: a Blue-majority city packed densely within a sea of Red.

It would be quite easy, if Red gets to draw the map, to deny Blue any representation. But it would be done explicitly for that purpose. That transitions nicely into what “Representatives” are for, and how gerrymandering is actually done.

Why the House of Representatives exists

Without getting into the “shoulds” and “fairs” of the matter, Congress was designed to balance possibly competing interests: “big states” and “small states” - and perhaps big cities vs rural areas.

Since all states - regardless of population - receive two Senators, there's a highly disproportionate impact of voting power-to-population in the Senate. California gets two senators - a maximum of two votes in the Senate - as do states with less than a fiftieth of their population, like Wyoming.

As a trade-off, Representatives are allocated based on population. As the population grows but the number of Representatives stays the same, that ratio changes. In any case, the trade-off is that Representatives represent districts within states, not states as a whole. As such, invoking a state’s voting preference in discussions of Representives is again a red herring: we already have elected officials for that office. It's called the Senate.

How Gerrymandering Works:

There are two simple concepts that are required to understand gerrymandering, that are required to be present in any real gerrymandering:

1. Packing

2. Cracking

“Packing” is intentionally putting likely supporters of a political party into a single district.

“Cracking” is intentionally splitting likely supporters of a political party in close geographic proximity into multiple districts.

Notably, packing is done almost exclusively to put a party at a disadvantage statewide. Cracking, on the other hand, can be done to give your party an advantage or to put another party at a disadvantage.

To borrow a chart from the Gerrymandering Project, a great visual:

On the left, Purple is packed mostly into one district, giving Green a big advantage. On the right, purple strategically “cracked” their own cluster of voters, spreading them into several districts.

The math behind both strategies is simple:

In a winner-take-all district, winning 60% of the vote (a pretty comfortable margin in itself) yields exactly as many seats as winning 99% of the vote in that district would. Strategically, every vote beyond what is already a comfortable margin of victory can be described as wasted votes. A good gerrymanderer wants to:

1. Waste as few votes as possible

2. Make your opponent waste as many as possible

Now, you might describe any votes beyond the 50.01% to guarantee victory as “wasted” and that's kind of true, but only with the benefit of hindsight. The best (honest) predictive modelers will only get you to +/- 5% for the next election - and maps are supposed to be in effect for several elections. Without getting into the weeds - maybe another article - it’s probability and risk tolerance.

Given just 25 units and only a few valid shapes (compared to real life where any shapes are possible) it's harder to illustrate packing and cracking - but it can be done. Consider the following:

And here's the corresponding range of outcomes:

In the absence of gerrymandering, there's still a 1/3 chance that Red holds a majority of seats, despite not receiving a majority of the vote.

But look at the entirely plausible maps that could be drawn if Blue or Red were in power:

What's important to understand, is that with advanced models that are now sensitive down to the street level (seriously), aggressive gerrymanderers can choose their voters. This scenario above isn't an exception, it's the norm.

“Gerrymandering is when politicians choose their voters, instead of voters choosing their politicians”

- (unknown source)

Almost no one likes gerrymandering - except when it benefits their side. Even then, it feels dirty. How could we eliminate gerrymandering, in the event we get bipartisan agreement? Well, getting bipartisan agreement will probably require a mutual understanding of what gerrymandering is. Republicans demanding a reverse-gerrymander of states like Massachusetts in the name of “fairness” seems problematic.

In the event there is an agreement to end gerrymandering, “how” is a big unanswered question. I'm skeptical of elected or unelected commissions because it's an inherently political job where those ideas of “fairness” and bias tend to interfere. Though, don't get me wrong - far better than the free-for-all we currently have.

I have some ideas (though you probably won't like it). But no matter what - remember:

In order to get rid of gerrymandering, we first have to properly define it. Misleading people into believing that any deviation from our opinion about what is fair is “gerrymandering” won't get us closer to that goal…and it also happens to be bad for education, which isn't cool.

Best Explanation Ever?

If you liked this article, please share it. You are welcome to use it or any portion in a classroom setting - a comment or tag on social media would be appreciated (@RealCarlAllen). I am also available for speaking engagements.

If you found this article accessible and insightful, consider buying my book The Polls Weren't Wrong, which irrefutably debunks the pervasively accepted myth that polls “underestimated” Trump in 2016, that polls “missed” regarding Brexit, among other interesting topics. It offers readers of all backgrounds the ability to understand poll data for what it means - not be misled by analysts who assert how much someone is “up by” is the primary (or only) variable of relevance.

You can also follow my forecasting for US Midterms and beyond (along with other thoughts and analysis) by subscribing.

Oh, and scroll around on my Substack for lots of science and statistics-related analysis.

Subscribe now

As you probably know, in addition to teaching people how polls work (and don't work) I am pretty passionate about fighting misinformation in science and statistics.

Recently, I've done some posts on anti-vaxxers, gun homicides, and fructose for some reason.

What you may not know, is my weird ascent as an expert in the field of political polling exists because of my well-calibrated bullshit detector.

Most people who are elite performers in scientific fields are very smart, they can elaborate with great detail all the supporting evidence for their field's findings, and they do not trouble themselves with the simpletons who debate what they have proven.

While experts can identify misinformation and misuse of statistics, they rarely understand how to combat it. This leaves an enormous (and growing) expert-to-public gap that is increasingly filled by ideologues who weaponize oversimplifications to push political, social, cultural, and/or financial agendas.

The result is a public discourse where truth is often overshadowed by confidence and confirmation bias - and expert knowledge never reaches who needs it most.

This article will directly address how to combat misinformation.

Pseudoscience

To be brief (because we all want to know what I think about what Elon thinks about what makes a Real Woman): pseudoscience throughout all of history follows a surprisingly predictable pattern.

It starts with a hypothesis, usually one that just makes sense (Flat Earth, Stationary Earth, Creationism, Heavy Objects Fall Faster) or has supporting data that could feasibly fool a nonexpert (Anti-Vax, Climate Change denial, Accurate Polls should Predict Election Margin)…

As someone who does science, I'll remind you that, scientifically, there is nothing wrong with any of the above hypotheses. The first step of the scientific method is brilliantly summarized by Feynman: “first, we guess it.”

But when evidence is presented to contradict or outright falsify those beliefs, that's when science versus pseudoscience is revealed. In pseudoscience, the hypothesis is not revised. Instead, the standards for evidence are shifted, and reasons for accepting the belief modified. Apologetics are invoked (what they really meant was..) and auxillary assumptions added - known as ad hoc reasoning - to protect the initial hypothesis.

Which leads me to…

Is Sex Binary?

This is a hot “debate” right now. Not because of any scientific breakthrough or unresolved problem…but because some people need someone to hate for no reason* and transgender people are easy targets right now.

*to distract from far more important and consequential issues

Of course, transgender is a social and psychological construct, not really relevant to the biological definition of sex, but you wouldn't confuse most of these people with intellectuals - or logicians.

For most, “biology” is just a useful excuse to hate someone for being different. Indeed, similar arguments were used against homosexuals and interracial marriage not long ago.

Whether or not sex is binary has nothing to do with transgender rights, participation in sports, and so on. It's a deflection to offer external support for the core belief: “I think it's okay to discriminate against transgender people.”

The question of a sex binary is incredibly complex - more complex than anyone who hasn't studied the topic can comprehend.

Anyone who claims the answer is simple or easily proven is...simply…wrong. Any educated person who does it is doing so because they have something to sell (and a certain crowd is happy to buy), or has an agenda they believe is advanced by saying it.

There are still things we don't know about sexual development, and almost everything we learn uncovers more things we don't.

The right answer to the question is: probably not. But it almost certainly depends on how “sex” is defined. Yes, seriously.

Here, I will honestly represent the best argument in favor of the sex binary:

“There are two gametes: sperm and ova. Sex refers specifically to sexual reproduction, therefore there are only two sexes.”

That creates a few awkward logical problems. There's a bit of motte-and-bailey going on which I'll touch on momentarily, but there's a more glaring issue:

It defines sex by an outcome (gamete production) that many individuals - children, post-menopausal adults, infertile people - do not and may never realize. The category is treated as fundamental, but the criterion is conditional, incomplete, and developmentally contingent.

Very quickly, this definition is shown to be insufficient. You may be able to classify most people by it, but there are lots of people who probably are objectively “male” or “female” not covered by the definition.

In case you think I'm being disingenuous about the position of those who argue in the affirmative for a sex binary, below is a debate I had with one of the field's influencers, who regularly publishes on the topic.

I asked him for evidence that sex is binary, he responded as follows:

Citing a source the way he did (“world's leading experts”) is a common poisoning the well tactic, with a touch of appeal to authority - rarely accepted in rational discourse - rarely needed in scientific discourse.

Nonetheless, I gave him a big benefit of the doubt, and opted to focus on the content of the definition rather than his framing.

You'll note that the definitions were not “should” or “would” or “could” produce certain gametes…but are given in relation to what gametes someone produces.

Testable, falsifiable, definitions that are easily shown as incomplete.

So I asked a simple follow up:

According to these definitions, what is the sex of a person that produces no gametes?

After a nearly instant back-and-forth leading to the above comment, citation, and my question he stopped responding.

For over a year.

Then, a few months ago, he cited my tweet and said this:

See the change?

No longer is world-leading-expert definition sufficient, apparently. He never answered my question regarding a person who produces no gametes, he simply revised the definition to shift the standard of evidence.

Now, people who don't produce gametes can fit. Post-menopausal women: obviously female. And so on.

But now, he's invoking something much harder to test, something subjective: what their anatomy is “organized around.”

That gets into the highly complex nature of sex, requires a lot of criteria that go down to the molecular level, and raises even more questions: is it a “majority rules” situation…can it be represented on a flow chart? The answer is no, not without begging the question.

It gives adherents to the belief, who have gone through the discomfort of having their “produce egg = female, produce sperm = male” proposal disproven, something to cling to - without changing their beliefs. Something that SOUNDS scientific, but provides goalposts slippery enough to: “organized around”

That's because pseudoscience doesn't thrive under honest complexity; it requires dishonest simplification. It reminds me of my teenage years when I pressed creationists on their definition of the word “kind” and they couldn't define it, they just gave examples. It means whatever they want it to mean. Objectively defining it would subject it to unwanted scrutiny.

It's specific enough to sound scientific, and too vague to be disproven by science. The pseudoscience sweet spot.

Normally, someone less experienced at dealing with these types of people (and myself, when younger) would argue against the new “organized around” definition being subjective, unfalsifiable, or simply point out that it changed.

Then the new topic is how the definition isn't subjective (even if it is) how it isn't unfalsifiable (even if it is) and so on. The topic changed, they are no longer accountable for their original definition, ego protected.

But I've learned some things over the years.

The first step here is to “close” the original debate, not acquiesce to a new one.

Make them admit their previous definition - which was clearly different than this one - was insufficient to classify all males and females, and that it changed.

It doesn't mean conceding their new definition is wrong, or even that the old one was, it just shows a shred of intellectual honesty, integrity, and respect for rational discourse. A respectable scientist would have no problem doing this. And conveniently, it's a very quick way to determine who is worth your time and who isn't.

To be blunt, most people aren't.

Debates of fact, and science, imply adherence to the rules of reason, but as I explained and illustrated here, this deception is intentional. Do not assume someone is willing to adhere to scientific standards merely because they claim a scientific position. You do not need to grant the benefit of the doubt on a fundamentally pivotal - and simple - question, and is it not overly intrusive or rude to confirm it. Though I promise you, very many will act offended as an escape (and coping) mechanism to avoid being pinned down. Pseudoscientists need to feign scientific adherence, but they cannot (intellectually) survive being forced to adhere to scientific standards. The easiest way to determine whether someone is “worth the time” is to ask a question like:

• Is there anything that could change your mind?

• If I prove you wrong, will you admit you're wrong?

Rule Number One (two, and three)

If rule number one is “establish what their position is”

Rule number two goes one of two ways.

2. “Prove it” - if they make the claim they accept the burden of proof.

• 2a - “If I prove you wrong, will you admit you're wrong?”

This is an important step because it will save you a ton of wasted time trying to change the minds of people who are, by definition, irrational. Anyone who doesn't follow “2” or “2a” is conceding that they are not rational. Both of those responses require a direct response - they won't want to give one. Don't let them change the subject.

It doesn't mean they're a bad person, just not suited for rational discourse.

Occasionally, very occasionally, a person will revise their original statement when presented with the possibility that someone could prove it wrong. Sometimes it's a genuine explanation, others a dishonest deflection. In either case, if you insist on engaging with people in matters of fact, follow rule three:

3. Before a new topic is introduced or debated, the previous one must be resolved, closed, or conceded. That means no topic changing, no “what I meant was” - if the original claim is incomplete or insufficient, it must be conceded (that is, they admit it was wrong, incomplete, or insufficient) before a new topic is allowed to be discussed.

This standard allows you to know if the person you're dealing with is engaging honestly. If they're not willing to admit that statement was wrong, it follows that if this one is, they won't admit that either.

I'm working on a more concise flow chart of my own, but this one is very good:

Here, a curious account responded to my post seemingly requesting directly to have a livestreamed debate.

I simply stated the terms under which I would have the debate.

They refused.

When I asked if they would agree to the terms, they went from a direct, inquisitive challenge to…well…

Notice how quickly they went from a confident challenge to angrily name-calling, just by being asked to agree to very simple terms. This is standard in the post-Kirk “debate” era.

Don't get me wrong, debate has long included sophists and eristics - and the practice been rightly criticized as not being a truth-seeking activity.

My approach to exclude people from “debate” who are not seeking truth is very intentional, and a lesson I'm proud to have learned. I'm less proud to have learned that this excludes most people.

In the social media era, where platform size is more important than substance - and vibes more important than valid logic - it's easy to get disheartened by this lack of intellectual curiosity.

Looking at the history of pseudoscience - I've constructed a very helpful visual. Two pyramids, almost identical:

Note the bottom of the pyramid is the same on either side.

On the side of science, there are the truth-seekers: people who will change their minds if evidence justifies it.

On the ideology side, there are “influencers” who give their followers the lines and “sources” to regurgitate as if they are meaningful or profound. Importantly, debunking any of those sources does nothing to change the underlying belief - making it inherently unscientific and irrational.

Musk says Womb = Woman

There are few examples that could possibly be clearer than vibes and “virtue signals” being more important to an ideologue than fact.

Authority is not exclusive to ideologues, science has this problem to an extent. But if Albert Einstein himself proclaimed the Sun revolved around the Earth, that claim survives or fails on its merits, not who said it.

The comment - clearly an effort to establish some objective basis for “sex” - fails on so many levels. The most basic of which is that some women receive hysterectomies, and Musk's position awkwardly asserts that this procedure changes someone's sex.

But remember, Elon has positioned himself at the top of the ideologue pyramid. And it is not permissible in the pseudoscientist ideology to question authority. So the apologetics began:

What he meant was…

And other comments took the form of:

“If you have a womb you are a woman! What's so controversial about that?”

(While conveniently ignoring the very strong qualifier: “otherwise you are not.”)

Apologetics are very common among those trying to preserve unscientific beliefs.

Remember, if you choose to engage with these types of people, that the terms of rational discussion are explicitly stated and agreed to. Anything else will be a massive waste of time, unless you're a sicko like me who does it for batting practice, to prepare to take on actual scientists.

Almost without exception, people like this simply want a platform to state their beliefs - Elon paid billions for that privilege. Ideologues do not genuinely want to gain knowledge or have their understanding challenged, they want to position their opinion as on the same level of your facts.

But this one, for whatever reason, attracts a particular interest among a large group of people - both sports bettors and outsiders - confidently wrong.

There's nothing wrong with being wrong, even confidently so - been there more than once. But when you're corrected (politely or otherwise, for the record) and refuse to acknowledge as such, it becomes willful ignorance.

As it happens, the reasoning underlying the “equal action” belief is perfectly plausible on the surface - like most misconceptions. But the error in reasoning crosses domains: it's not “just” a sports betting problem.

Interestingly, there has been very little published on the topic, so my post will aim to both fill that void and debunk the myth once and for all.

The Reasoning

If sportsbooks get equal action on both sides of a bet, they will make money. This is basically true!

The disconnect - where the myth comes from - is that since this “guaranteed profit” scenario is ideal…

The Hypothesis

Sportsbooks can (and/or do) set lines with the goal or intent of attracting equal action.

There are many avenues to prove this wrong - in theory, practice, and reality. First, a few terms. Then the math.

Important Terms

The most common “juice” or “vig” on a bet is -110 (in American terms). That means you must risk $110 to make a $100 profit on a winning wager. Wagers can be any amount, but the simplest example is: “Risk $110 to win $210.”

A line is a number a bettor can bet either side of: most commonly a point-spread or over/under (aka total). For example, if the spread is “Team A -3” bettors may wager on Team A -3, OR Team B +3.

The final score is adjusted by this handicap to determine the winner: if Team A wins by more than 3, those bettors win. Ties are possible, in which case bets are refunded.

The process for “over/under” bets is similar. The teams’ combined points, goals, etc. determines the result.

A sportsbook (or “book”) is a place that allows people to place wagers. Oddsmakers are the people who decide what line the books will offer.

In simple terms, if two people risk $110 on each side of a bet with -110 odds (assuming it's not a push) the Sportsbook has collected $220, pays out $210, and pockets that sweet $10. Of course, sportsbooks deal with many more zeroes, but the concept holds. The mathematically astute may note that the number doesn't have to be literally equal for the sportsbook to profit, but it needs to be pretty close.

The Math

Sportsbooks are in the business of making money. They built resorts in the desert with that money. As you can imagine, oddsmakers deal in probability, and are tasked with things like “exposure” and “risk management.”

The first and perhaps most important concept that I've found helps people make sense of the “guaranteed profit” myth, is this: sports betting is a portfolio. Each game makes up a percentage of that portfolio.

Similar to a casino, where a game like roulette has a clearly defined “house edge” - the casino doesn't set up the game to attract “equal action” on black and red. Or odd and even.

That would, of course, be the “ideal” scenario but it's simply not possible to enforce.

Sportsbooks, like casinos - because they're in the business of making money - are more concerned with long term good exposure than a “guaranteed profit” in every event: they accept some risk of loss with every spin, every card, every bounce - as long as there's a greater chance of winning.

And this roulette analogy works quite well for the basic “math” section:

If I stumble up to an empty roulette wheel and place a $1,000 wager on “black” do you think they'll announce to their patrons they're offering a better payout on “red” to entice more action? Or turn me away because they don't have anyone else on “red”?

Of course not. There's about a 48% chance I double my money, and a 52% chance I lose. They're perfectly content with that exposure.

For this spin, the casino may lose money. This specific roulette wheel may “lose them money” for hours, days, even weeks. But “this specific roulette wheel” does not make a casino. Because the odds are in their favor, even if only slightly, they will make money in the long run - at this wheel, and across the casino.

Now consider a sportsbook with perfect balance on a game: $10,000 on both sides. A second before the game starts, I try to get my stumbly $1,000 bet on whichever team wears black jerseys, because black is hot, baby. Do they take it? If the goal is balanced books, they could simply turn me away. But they never do. Almost.

Moving Lines!

In sports betting, unlike roulette and other casino games, there's a unique mechanism sportsbooks have at their disposal: they can change the line.

A game that starts at “Team A -3” may move to “Team A -4.” Now, the additional point may inspire more action on Team B +4. Theoretically, this may “balance the books” but this move is also not without risk. If Team A wins by exactly 4 - a probability that can be calculated - they pay out the “-3” bettors, and the “+4” bettors get refunded.

Alternatively, instead of moving the line, sportsbooks may modify the juice on the wager. Instead of Team A -3 at -110, they may change the line to -3 at -120. The corresponding change would allow bettors to take Team B +3 at +100.

Within tight bounds, these moves don't necessarily create bad exposure.

However…

Huge Exposure

What's a sportsbook supposed to do when they take six figures of action on one side?

And the action keeps coming in on that side?

Then they move the line…

And it keeps coming in on that side? Millions of dollars profit or loss riding on the outcome.

It turns out, people who bet for fun (we'll call them casual bettors) make up almost all of the money wagered on any given game. You can't “control” which side they bet on, any more than you can control whether they bet red or black in roulette.

But! Mythholders insist - you can PREDICT it!

That's kind of true, actually. Casual bettors disproportionately bet favorites, and “overs.” And coinflip bettors disproportionately prefer heads.

(Though rarely so drastically).

So the next step of the hypothesis requires asking…how much do you need to move the line in order to attract “equal action” on both sides?

And this is where it breaks down. All because of the dreaded Sharps.

Sharp Bettors

While casual bettors bet for fun, sharp bettors bet because they believe they have an edge. They tend to have deep pockets, discipline, advanced models, and lots of “outs” (places to make bets). Sharps don't just try to identify wagers with edges, they act quickly to compare odds across books, get the best odds, and aggressively wager: lines may “correct” in seconds or minutes. Getting an extra half-point on a spread, or -105 juice instead of -110 makes a remarkable difference in a sharp’s long term profitability.

And here is the main reason the “even money” hypothesis breaks down:

Sharps act as a “check” on bad lines, even if a particular line would have otherwise attracted even money from casual bettors.

Sharps don’t wager on a given game or side just because it's a big game, or they're bored… their wagers are dependent on the line.

Other fields have names for this error of thinking:

Economists have the Lucas Critique: models that treat behavior as fixed break down when in reality people adjust. Setting a line intended to respond to bettor behavior changes bettor behavior.

Goodhart’s Law applies in that if sportsbooks targeted balanced action instead of accurate pricing, the line becomes exploitable - because sharp bettors respond to mispricing, not balance.

The larger, more universal flaw in reasoning is called endogeneity. It means a variable is jointly determined inside the system (dependent), not independently set from the outside.

The mistake:

Treating something that responds to your decision as if it were independent of your decision.

Simply put, the only way to ensure long term profitability is for oddsmakers to set lines with the result in mind. For events with odds around -110, their line needs to result in each side winning close to 50% of the time.

I think I have successfully simplified this:

50-50 Myth Flow Chart

A Fine Hypothesis You Have There

Like all good hypotheses, we have to honestly answer questions like:

• What would we expect to observe if the hypothesis is accurate?

• What would serve as evidence against it?

It follows that if sportsbooks are trying to get 50-50 action, they should (at least) often or usually get it. Likewise, if they're setting lines with regard to outcome, favorites should win around 50% of the time, as should overs.

Some years or decades ago, before sports betting was as easy as a few clicks in an app - it was quite hard to know how much exposure sportsbooks had unless you were an insider. Which is to say, it was kind of forgivable to say that even though my reasoning makes sense, I couldn't really “prove” it.

After all, are sportsbooks really taking six, seven, or even eight figure risks in individual games?!

Yes.

It is literally public information now.

And even people who make the odds aren't shy to talk about “needing a side”

The reality is that they almost never get 50-50 action, or close to it! 75-25 splits are more common.

But guess what they DO achieve?

With regard to the actual result, their lines yield outcomes very close to 50-50.

For any given game - like any spin of the roulette wheel - they may lose money. They may lose a lot. For days, weeks, even months on occasion. But as long as their exposure is good exposure, they know that in the long run they'll make money. Here's a random baseball game today.

The fact is - if sportsbooks are setting lines to “try and get the most action on both sides…”

They will lose money.

If their models don't pick the winner, someone's model will.

From The Makers’ Mouths

If you're not sufficiently convinced by everything I shared above - from the math to the logic to the actual numbers - you don't deserve to keep reading this article. But since it's the only good source I've found that deeply addresses the 50-50 myth, I should share:

From the article:

There is a popular belief that sportsbooks take an equal amount of money on both sides of a game to guarantee a profit.

Is it fact or fiction?

“That’s a fallacy,” former William Hill and Caesars Sportsbook director Nick Bogdanovich said. “It never happens that way. The books always have decisions. That’s the bottom line. And some are bigger than others.”

Red Rock Resort sportsbook director Chuck Esposito:

“It’s somewhat of a myth to be able to divide action equally on every game,” he said. “We’re going to have a vested interest in every game in every sport.”

Westgate SuperBook Vice President Jay Kornegay:

“an urban legend.”

South Point sportsbook director Chris Andrews:

“There’s almost always more money on one side than the other, either naturally or by design.”

Sharps vs Books

Your friendly author with some explanation here - by design? Why would sportsbooks want more money on one side by design?

Well, if their goal was to balance their books - they wouldn't. But you understand now that it's a myth. Still, it's weird to think about sportsbooks effectively gambling on a side. But that often happens.

MGM Resorts director of trading Jeff Stoneback said:

“when professionals get involved, we want to make sure we’re on their side.”

The answer to the question most people have: “why would sportsbooks let someone they know is ‘sharp’ bet with them? Aren't they afraid to lose money?”

Starts to fall into place now.

Andrews, who refers to sharps as “wiseguys” says:

“If I have the wiseguys on one side and the public on the other, I’ll do my best to go in needing the wiseguy’s side to win.”

One of the most commonly cited facts among the mythholders is that lines and odds move, which they conclude supports their “equal action” hypothesis.

Setting aside the fact that lines can change due to player injury reports, weather, and lots of extraneous factors, we can strip all of that away and again follow the direction of line movement according to the money wagered.

If the goal were even money, the line should change to benefit the team or side that has received less money. But that isn't how it works.

Kornegay says:

“A regular house player can bet six figures, and there’s a chance we might not move the line. But there are times a very sharp player bets 10 dimes on something, and we could move it off of their $10,000 bet.

In fact, there are many examples of teams getting a lot of money bet on them, and their line gets worse anyways. It happens so often, there's a name for it: Reverse Line Movement.

For example, if Team A is -3, and has received 80% of bets, the “even money hypothesis” says the line should be moved to -3.5, -4, or higher, to get more action on Team B.

So why does the line sometimes move to -2.5 despite that?

Wiseguys.

This can only make sense if line accuracy > bet distribution

It's not about even action. It's about good exposure and volume. There's a life lesson in there somewhere, probably.

Relating To My Other Work

Traditionally held beliefs are hard to overcome, especially if they're in the majority. Whether it's Nate Silver pushing polls-as-predictions into mainstream prominence, or whatever pseudoscience is popping right now, being able to overcome that bias - changing your mind when presented with correct information - that's how science is done.

In other words:

All models have assumptions. There’s no such thing as a “purely data-driven” model - only models whose assumptions are obvious, and models whose assumptions are hidden or intentionally obfuscated or ignored.

The difference between a good model and a bad one isn’t whether assumptions exist. It’s whether those assumptions are valid, explicit, and aligned with the real-world process being modeled.

The best models don’t pretend to eliminate assumptions - they interrogate them. They ask:

• What must be true for this input to have meaning?

• What mechanism links this variable to the outcome?

• What happens if that mechanism doesn’t hold?

Weak models do the opposite. They inherit assumptions - often unconsciously - because they are standard, convenient, or historically accepted. They optimize for the recent past (so they can say it backtests well) without asking whether the inputs actually measure what they claim to measure.

And in domains with limited, noisy data - like presidential elections - that distinction becomes everything.

Because when the data is sparse, assumptions don’t just support the model…

They are the model.

In most cases, "what happened last time/game/season" is the most basic model. And it's not always the worst. But it does have a ton of assumptions - such that it is NOT always the best model. Sometimes it's not even the best starting point.

Nate Silver's political models did exactly this.

My predictive models for player performance noted the reasoning flaw used by Silver:

And in political applications, Silver’s models were honestly even worse than that.

Silver's Early Models

In 2008, his first public models, he noted that his older versions had “heretofore” assigned undecideds 50:50. (Back to that in a moment)

But he then says he doesn't want a neutral assumption, he wants a predictive one. A nice sentiment, if you can keep it.

In his efforts to be "more predictive" he looks at primary data, how much Obama "overperformed" in each state (by comparing the margin of the poll to the margin of the election)…and uses that to inform his general election undecided allocation.

There is so much wrong with this approach.

The two things most wrong are:

1. It assumes primaries & general elections are similar enough to use in a predictive model

In primaries, it's D vs D. In general elections, it's not.

A voter switching their polled preference from Biden to Obama before the primary (thus causing a poll "overperformance") is far more common and likely than switching from McCain to Obama during the general.

This is a problem I've effectively solved, but apparently still stumps the field's experts, like when they asked “perhaps it is harder to predict the margin when more candidates are
running?”

2. The assumption that this poll “spread” vs election “spread” is a measure of "overperformance."

At some point (I think 2012, certainly by 2016) He realized this "model" was garbage.

Not because he noticed an error in his process, mind you - but because he realized this allocation wasn't predictive.

He reverted to the 50:50 assumption, adding error bars with varying size and tails.

This process highlights a central, and frankly, elementary modeling problem.

The Predictive Modeling Problem

There's a huge correlation-causation problem when it comes to "predictiveness" such that construct validity is absolutely ESSENTIAL to a model's viability.

Modern forecasters copy Silver's approach to using how well polls “predict” some result because they can't fathom of a better approach.

The problem is that metric can appear highly predictive purely by chance, especially in small samples or noisy systems. Because Presidential Elections are four years apart, it feels like going back to, say, 1996 is a long time. The reality is that the sample size from that is eight. Literally eight.

Some (like Silver) believe this can be improved by going back farther…but now you're including far fewer polls with very different methodologies from a far less polarized populace…to get your sample size to, what? Twenty?

There is no fixing the sample size problem in Presidential Elections. And critically: these are not independent, identically distributed (i.i.d.) observations.

Even if you weight by recency, you're just back to the sample size problem. It's circular.

So when analysts say things like:

“Over the last 4 elections, pollsters have had an average error of X”

What they are implicitly assuming is:

• Those 4 elections are comparable

• The underlying error distribution is stable

• The causes of past error will persist in the same way

None of those assumptions are reliably true, some are provably false.

This creates the central problem of “predictive” models:

A poor predictive metric can have a high predictive correlation if your only concern is "does it get the right answer?"

This is PROBABILISTIC reasoning vs DETERMINISTIC reasoning. (Put this in a new tab to read next. This concept is not as intuitive as it seems.)

For example, the alphabetical first name of the Vice Presidential Candidate has successfully predicted the last 14 elections. 14/14. Insane. Does it get the right answer? Better than any system ever.

Doesn't mean it's a valid metric.

That is a more obvious example (probably 0 correlation despite high predictive accuracy) than the relationship of poll leads to election margin of victory: a metric that does have some correlation - but not nearly as high as experts seem to think. And it's still internally invalid.

Analysts around the world are always looking for an undiscovered or underutilized metric that has explanatory value for some outcome.

But laymen like Shane (who have far more in common with the field's experts than you would believe) think "a single realized event" can meaningfully measure "accuracy."

If I say there's a 67% chance that Iowa St. beats Kentucky in the March Madness game tomorrow…

And someone else says 50%…

The game's outcome is irrelevant to the accuracy of each model!

When we talk about uncertain future events with probabilities that are absolutely unknowable, it seems rational to use "closer to result" as a substitute for "true value"

But this is hindsight bias.

If you ask me the odds of rolling a 3, 4, 5, or 6 on a single die, the answer is 4/6 or 2/3

We can call it 67%

Someone who says "nah, either it happens or it doesn't, 50/50" is not validated when the roll happens to be 1 or 2.

Based on this "single realized event" they were "closer to the result" - but this is meaningless.

But there's no way smart experts would do things like this...right?

Welcome To My Hell

Based on a sample size of one election, Silver (and a consensus of experts on poll data around the world)

Believe that, yes, we can say with a remarkable level of precision who the most accurate pollster was based on one election.

Silver and others use this assumption in their models to give more weight to "more accurate" pollsters in future elections 🙃

And, if you could believe it…it's worse than that.

Leading up to the 2012 election, Silver noted that there was “not a single instance in the database where a candidate lost a state when he held a lead of more than 3.5 points in the polling average (in highly polled states) at this point in time.

A 2.4-point lead in the polls, Silver calculated then, amounts to roughly an 80% win probability.

By 2023, they claimed a lead of this size is “little better than tossup”

The reason these calculations continuously fail, is because they're assuming a strong correlation where there is only a small one. All of their calculations, every single one of them - no dispute, no argument, no debate - they all assume that undecideds split 50-50 in every case.

The thing Silver said in 2008 wasn't a good assumption, but then abandoned because he couldn't figure out how primaries and general elections have different underlying variables…

That assumption underpins every single calculation made for poll accuracy. Every single one.

And they use a sample size of "one election" to justify this.

It all starts from the same untested axiom that he (and the rest of the field) has always used: comparing margin of the poll to the margin of the election. The field simply cannot fathom the assumption that "accurate polls will predict the winner and margin of victory" being invalid - despite it being a trivial proof.

Their bias + tradition does not allow them to question the core assumption. A pattern that often repeats itself in scientific history.

To wrap this up with Silver's more recent models:

Yes, his more recent models are "better" in that they model a range of outcomes with appropriate uncertainty.

But I found a hidden variable in his models thanks to a very simple input error that proves he STILL uses this "most recent election" logic to inform that uncertainty calculation.

In 2020, Silver said Trump had a 10% chance to win Maine

This was absolutely baffling, considering Biden had a 53-40 advantage in the poll average. My model (and others) put it at 99% or higher

So why the discrepancy?

2016.

In 2016, it's often claimed Trump "overperformed" his polls. He didn't, really: he won a majority of undecideds and a big chunk of people who said they were going to vote third-party but changed their mind.

This claim of "overperformance" was a case study in what happens if a field's consensus doesn't understand what a confounding variable is.

Nonetheless, due to this "overperformance" resetting every model's priors about how "off" polls could be, Silver's model was EXTRA careful.

But that's not all...

He didn't use a uniform "uncertainty" procedure.

He used the "poll margin vs election margin" logic FROM EACH STATE to inform his model's range of possible outcomes.

States that had a larger "error" by this 2016 calculation were more likely to have a larger error in 2020, in his model.

In Maine specifically, their model had a sign error!

From my book:

(FiveThirtyEight's analysis) said Hillary was "+6.9 in Maine polls" and "LOST by 3"

A 9.9-point "error" by this metric

THAT'S NOT RIGHT!

Clinton won Maine by 3, which (by his math) is a 3.9-point "error"

Given Biden's "+13" position in Silver's reductionist model, a 9.9-point error being within the range of plausibility is the ONLY way you can conclude a 10% chance of losing.

Copycats

I have come to the highly evidenced conclusion that the only reason my political models ever differ from others is because the other models copy Silver's.

They use the exact same "margin" logic, they use the exact same "well, I have data from like 8 recent elections, that's CERTAINLY a large enough sample size to derive meaning from this invalid polls-as-predictions metric"

When I started, I was either too conceited or lazy to try and copy Silver. I used poll data as a starting point, not a prediction of the result.

That led to some remarkable discoveries.

You can read about them here or here or this interesting article, elsewhere on my Substack, ask me about them, or for a really deep dive, my book.

I'm a math nerd, and a stickler for statistical literacy, so if I told you my tips would make you win your bracket pool, I'd be lying.

The truth is, following these tips will double or triple your chances - depending on how good your competitors are.

Bracket math

If there are 10 people in your pool, you have about a 1/10 chance to win.

If there are 100 people in your pool, you have about a 1/100 chance to win.

And so on.

Yes, that is to say that even math doesn't guarantee you'll win.

But anything you can do to increase your win probability is good.

That all starts with the champion.

Champ Picks

In order to win your bracket pool (assuming your pool is larger than like five people) you will almost certainly need to pick the right champion.

For that reason, you're not competing against everyone in your pool: you're competing against everyone who picks the same champion.

If you are the only person in your pool to pick that champion, your probability of winning your pool is almost exactly equal to that team's probability of winning the championship.

For that reason, we can calculate that the bracket with the best probability of winning a pool is the most unique bracket that has the best chance of truly happening.

In other words: calculated risk. Calculated being a very appropriate term here.

Here's my math for the championship:

A Little Lingo

Small pool = 100 or fewer people

Large pool = 500 or more

Green = good pick (with a few qualifiers)

Red = bad pick (with no qualifiers)

Because you need to pick the right champion to have the best bracket, it's best not to go too crazy here, unless you're in a very large pool. There's nearly a 60% chance that one of Duke, Michigan, or Arizona wins the championship. I will refer to these as “Top 3.”

If you choose one of them as your champion, it's recommended that you choose a few small and/or medium upsets depending on your pool size. Recommendations below.

Upsets Math

Because you want a unique bracket with only calculated risks, my biggest recommendation for anyone not in a very large pool is to not pick too many upsets.

Upsets happen every year. They will happen this year, too. But predicting which ones will happen ahead of time is a mathematically impossible task - literally. Even the most well-informed stats nerd can only get you to a ONE-IN-TWO TRILLION CHANCE at a perfect bracket.

For perspective, it's far more likely that a 16-seed wins the championship.

One of the biggest advantages you can have in your bracket pool is to pick a mostly boring bracket with only a few of the most valuable upsets. Valuable meaning “likely to make your bracket unique without being implausible.” I'll give my recommendations for each region.

“Upset” definition:

I assign “upset points” to various selections to guide which, and how many, upsets you should choose to maximize your chances.

If an upset fits multiple categories below, DO NOT double-count upset points, take only the largest value one time.

Catch all (+x upset points):

• The sum of the seeds in your Final 4 minus 6 (if 6 or less, 0 upset points).

Wise Champion Pick (-1 upset points)

• Duke, Arizona, or Michigan to win the championship. Highly recommended for small pools.

Not an upset (+0 upset points):

• 9 over 8 in the first round.

• A better seed (e.g. 4 over 13) winning.

Small upset (+1 upset point)

• Team with a seed EXACTLY ONE LOWER than their opponent (e.g. 5 over 4) EXCEPT 2 over 1.

• Florida to win the Championship.

Medium upset (+3 upset points)

• Any double-digit seed winning a game in any round (this adds for each victory)

• A team with a seed TWO TO SIX higher than their opponent winning (e.g 6 over 3) OR 2 over 1.

• Any #2 Seed winning the Championship

• Round one only: a team with a seed SEVEN TO NINE higher than their opponent winning (e.g. 12 over 5)

Large Upset (+5 upset points)

• A team with a seed SEVEN TO NINE higher than their opponent winning in any round EXCEPT round one (e.g. 10 over 2)

• A 3 or 4 seed in the Final 4

Huge Upset (+7 upset points)

• A 3 or 4 seed winning the Championship

• A team with a seed TEN OR MORE higher than their opponent winning in any round.

Enormous Upset (+10 upset points)

• Any seed higher than 4 in the Final 4

• Any other champion

Enormous upsets should be reserved for people in enormous pools: 1000 or more.

Small pools (under 100 people): Choose 3-6 upset points

Large pools (over 500 people): Choose 7-14 upset points but no enormous upsets

Enormous pools (over 1000 people): Choose 14-24 upset points, with at least two large or huge first round upsets.

Final 4 Selections

Left Side

On the left side of the bracket, Connecticut, Houston, or Illinois (+3 upset points) are good picks. If you do not choose Duke as your champion, Connecticut over Duke is a good upset choice for large or small pools.

Nebraska or Vanderbilt (+5 upset points) are good choices for large pools.

Louisville or UCLA are good values because almost no one picks them to go far and they have a small chance to do so. But remember: they would likely need multiple upsets BEFORE the Final Four, which makes an “eggs in basket” problem. Enormous pools only.

Right side

Iowa State is a good Final Four choice for large or small pools, as is Purdue (+3 upset points).

Tennessee is a strong 6 seed, and would probably be my favorite pick to make an Elite 8 (large pools) or Final Four (enormous pools) as long as the rest of my bracket was relatively tame.

Round 1

Going quickly because you only have a couple hours to get the brackets in!

Midwest

West

East

South

Good luck!

That doesn't mean people won't try to lie to you.

I'll also remind you, many arguments people make (with statistics or otherwise) have little to do with genuine reasoning. They are simply choosing what they perceive as the “most reasonable” argument to support their desired conclusion.

This meme is especially popular among the right, even cited by the Vice President as proof of gerrymandering “in New England.”

Here's a simple question to test your knowledge on Gerrymandering - and a question I highly recommend you ask anyone before engaging in a discussion on the subject:

Do you think gerrymandering is when a party doesn't receive a number of representatives proportional to their statewide vote percentage?

For example, since Connecticut votes 36% Republican statewide and received 5 Representatives, do you think the fact that they don't have 1 or 2 Representatives from Connecticut is proof of gerrymandering?

Now, this is where it is very important to understand the purpose of this question.

The meme obviously implies that this is the case (despite ignoring some important facts like that Vermont literally has one representative elected statewide).

But when you're “debating” or “arguing” or “discussing” what is true with someone, it is implied that facts and truth are the goal of the conversation. I hate to break it to you, but that's not usually the case.

Do not allow this to remain implied, or their position to remain implied: make them state it explicitly. This is not too much to ask, though they will pretend it is (because it doesn't allow them to engage in performative debate where they can pretend opinion and feelings are substitutes for facts, data, or science).

Anyone who is willing to engage honestly about “gerrymandering” will have no problem defining “gerrymandering” - or more directly - answering a simple yes/no about what gerrymandering is or isn't.

Disingenuous people THRIVE on their arguments not being pinned down, because it gives them escape routes. By pinning them down to a definition immediately, you eliminate their comfort zone.

It happens that debates of fact are systematically biased in favor of those who have facts on their side. My approach is simply a shortcut to the finish line.

This graphic, which I've seen shared by the left and right alike, is a much more subtle piece of misinformation - because it's a nice looking graphic instead of a meme - but it follows the exact same reasoning as the graphic above.

It assumes that “fair” representation is when parties receive a number of representatives Proportional to their statewide percentage.

Districts are winner-take-all. You don't get a tenth of a representative for 10% of the vote. You get 0.

That's exactly how many you get for 40% of the vote.

According to this graphic, that's "unfair.”

There is nothing unfair about “2” in this graphic. The fact that red gets zero reps despite 40% of the population has nothing to do with fairness, everything to do with population distribution and our electoral system. Womp womp.

Districts provide representation to geographical areas, not a state. If lines are not drawn with the explicit purpose of gaining a political advantage, it's not Gerrymandering. 2 is about the fairest map possible.

Does the Northeast Gerrymander?

This section is for people who don't care to debate, and just want to understand facts. I cannot impress upon you enough the importance of NOT skipping here with someone who asserts this to be so. Follow the instructions above.

That being said.

No.

The Northeast has relatively small states that vote more Democratic than average in rural areas, and the large cities (which are even more blue) have to be split to ensure all districts have an equal population.

Massachusetts, for example, receives 9 Representives statewide, and voted about 36% Republican in 2024.

People who don't understand statistics (willfully or otherwise) might be led to believe that ZERO Republican seats can only mean “gerrymandering.”

But fair districts are not drawn to give proportional representation. They are drawn to give geographical representation.

To win any district, a candidate must win the most votes in the district - that percentage of votes is usually at or near 50%.

Here is how Massachusetts districts are drawn:

And here is how those areas voted:

This map shows that even the counties Trump won were not by the margins you see in rural areas of other states. Any accusation of gerrymandering would logically require splitting (unfairly or otherwise) the red areas to prevent them from getting to 50%. Without looking at the population of the counties (an important variable) the accusation of gerrymandering only even looks possible in Districts 1 and 2, and maybe 4 and 9.

District 1: Democrats won with 62.5%

District 2: Democrats won with 68.6%

Those districts can't be shifted in any way where Democrats don't win by 20+.

District 4: Uncontested

District 9: Democrats won with 56.4% - the closest district by far.

The fact is this:

Not only is there no gerrymandering in Massachusetts or other northeastern states…

There's literally no way to draw maps in Massachusetts that would guarantee Republicans even ONE district.

That's correct.

Even if you tried to pack the red areas into a district to get Republicans at least one Representative - a kind of reverse gerrymander - you still wouldn't be able to, because the population of those red areas are too small to qualify as a district!

The best possible reverse-gerrymander for Republicans would MAYBE get them ONE seat. That is, a chance at 1/9 (11.1%) in a state that is about 37% Republican. If you don't understand math, or our electoral system, that might seem “unfair.” And remember, it would require drawing maps with the sole purpose of favoring Republicans as much as possible just to achieve that.

A fun math fact:

When it comes to gerrymandering, the distribution of the population is more important than the overall percentage.

In Massachusetts, Republican votes are scattered.

On the other hand, a state like Missouri (with 8 Representatives) is almost as Republican-leaning statewide as Massachusetts is Democrat-leaning.

However, by nature of Democratic voters being concentrated in major cities - and districts having a set population size - it's impossible to draw maps where Democrats don't get some seats in Missouri.

I'll let you infer which district(s) elected Democrats in 2024.

I also wrote about the anti-democratic practice that is gerrymandering, what's happening in Virginia, and what the paradox of tolerance has to do with this.

If you found this article enlightening or interesting, use your knowledge for good.

Subscribe to get important and insightful updates ahead of midterms (plus some surprises) and scroll my Substack for more analysis.

Likewise, the House of Representatives being artificially capped, though less impactful, also plays a role.

The most aggressive gerrymandering was by Republicans in the 2010 redistricting cycle. The strategy, called REDMAP - which I prefer to call “ratfucking” - disregarded norms and seeked to maximize political gain.

My home district looked like this:

Contrary to popular belief, districts that are “weird shapes” are not inherently unfair or biased.

Moreover, removing myself from the pesky “fairness” mindset - as a strategist - this is exactly what should happen for a party seeking to maximize power. This article isn't to convince you of the ethical problems with gerrymandering. If you'd like to read a short summary of the history and implications, this is a good start.

Unilateral Disarmament

Unilateral disarmament is problematic both strategically and ethically, somewhat akin to the “paradox of tolerance.”

When your opponent exploits loopholes and bends the rules when given the chance, you not doing so in return gives them a disproportionate advantage. For many years, Democrats believed that in order to achieve their eventual goal of abolishing gerrymandering, they needed to maintain a moral consistency of sorts by not gerrymandering. Though not the case across the board, there was a clear lean.

The net result was that the states with the most support for Democrats were mostly “fair” to Republicans, while Republican legislatures largely attempted to maximally disadvantage Democrats.

As Democrats begin to fight back, there's a new map taking shape:

Gerrymandering may be shifting to be a net benefit to Democrats.

This recently passed and approved California map will likely cost Republicans a few seats.

This Virginia map still needs to pass the VA Supreme Court - which is a major hurdle - but would likely net Dems a few more seats.

All-in-all, Democrats have started to fight back…and realized that when they play by the same rules, they may be even better at the game.

Human nature biases us in favor of things that benefit “us” - and against things that don't. We rationalize with excuses (which we call “reasoning”) as to why that system is better….when the real reason is “it benefits me.”

I wrote an article explaining why this happens.

Predictably, Republicans are suddenly concerned with the “disenfranchisement” caused by gerrymandering…how it's “unfair.”

And as Democrats benefit from it, they start to support it, then have no strategic advantage to abolishing it.

In order to abolish gerrymandering, one side will have to sacrifice their own advantage. And the probability one side is willing to abolish it correlates directly with how much benefit the other side has…thus making them unlikely to want to.

Everyone says they want fair maps. Almost no one is willing to accept a process that might disadvantage them next cycle with no one to blame.

If we ever reach that day, the problem is only half-solved. How can we draw maps that are truly fair?

It's Harder Than You Think

For one, let's say some bill was passed to abolish gerrymandering. What does that look like? Bipartisan commissions deciding what a fair map is? A state Supreme Court? That's a larger hurdle than it seems - because of the partisan bias that remains.

Beyond that, some proposals for multi-member districts are theoretically appealing, because it would more closely achieve “representativeness.” Those risk creating a new type of mandering where single-member districts have disproportionate power.

Other proposals that seem fair (like drawing maps according to racial or political boundaries to ensure proportional representativeness) still requires humans to distinguish partisan and/or racial affiliation, and then draw the lines based on this data. Who gets to define what is “fair” creates a new problem.

A truly “representative” map - by my definition - requires all states to agree on a framework, such that no side has an inherent advantage or disadvantage.

Do I think that will happen? No.

But if it did happen - and the states came together and said “we all want to get rid of gerrymandering, we will agree to any system that doesn't guarantee a partisan benefit to either side”

I believe the solution should be to work within the existing system: single-member districts, redrawn every 10 years.

Here's my solution:

Draw Districts At Random

Random does not always equal fair. The point is that it is the fairest approach. It is the only serious answer that can solve the larger problem: it eliminates the systematic bias inherent in the current process.

Here are the constraints I would propose:

• Each district has the same population, plus-or-minus some % tolerance

• Contiguous districts

  Here's what that looks like in practice:

  • Precinct chosen at random by code

  • Continue to continguous precincts at random until the population threshold is reached

Repeat

The only inputs needed to the program are population size by precinct and their respective geography.

Yes, this will often result in “weirdly-shaped” districts, and other aesthetically displeasing things. I'm not sure this is a major issue.

I also understand the resistance to allowing computers to draw maps…this is the most common contention. But I have some news:

Computers already draw the maps. They have for decades.

As of now, the inputs are to maximize partisan advantage. My proposal is to remove all possibility of that.

“But who makes the code?!”

Is also not a substantive rebuttal. Random and contiguous are simple and transparent parameters, not riggable ones.

Why this is fairer than anything else:

• No guaranteed partisan outcome

• Some random maps will favor Democrats. Some will favor Republicans. Across states and cycles, those advantages cancel out.

• Outcomes reflect voters, not partisan bias.

• You can’t rig a randomized procedure.

You can argue about whether a particular outcome is “fair,” but you can’t argue that it was designed to help someone.

No, I don't think this will be adopted.

I created it in response to someone challenging me to create a system such that even if everyone agreed to abolish gerrymandering, it wouldn't still contain strategic partisan loopholes.

I don't think the system of letting partisans draw maps to maximize partisan advantage then relying on partisan and/or biased courts to determine whether said map is technically illegal or not…is a superior option or sustainable.

If you want to propose improvements or argue against this procedure, you're welcome to do so.

I only request that you do better than - who was too cowardly to respond directly to me, and too ignorant to provide any argument of substance.

As with other better-known fallacies like “moving the goalposts,” “appeal to authority,” and the plain old “strawman,” identifying the flawed reasoning is the first step necessary to overcome it.

One of the reasons the “most reasonable excuse” (or “self-strawman”) has not been previously named, I believe, is because it overlaps with several well-known fallacies - but does not neatly fit any individual one. As a result, it escapes classification, even though it represents a distinct and recurring pattern of logical inconsistency and disingenuous argumentation.

First, The Definition

The “most reasonable excuse” or “Self-Strawman Fallacy” is defined as:

Defending an unstated belief by adopting a separate position (the excuse) chosen because the user views it as most effective at defeating an opponent and/or shielding the belief from criticism. Notably, even a successful refutation of the excuse does nothing to overturn or challenge the underlying belief.

Perhaps somewhat impossible to prove - though no less real - some users of this fallacy seem to invoke it on a subconscious level. I'll provide evidence and examples below.

The Rationale/Theory

Whether conscious or unconscious, certain beliefs are deeply held and resistant to change. When these beliefs are threatened, people experience cognitive dissonance - the psychological discomfort that arises from holding conflicting thoughts or from evidence that challenges their core convictions.

While most people simply ignore or rationalize the dissonance in their mind (thus never exposing it to criticism), the increasing prevalence of social media and high visibility, polarizing events has led to more people making statements. Whether those statements reflect their true beliefs or are simply excuses adopted to defend them is central to this fallacy.

The most reasonable excuse fallacy arises as a strategy to manage that dissonance while maintaining the appearance of rationality. I believe this fallacy is most often used when the user knows (again, consciously or subconsciously) the unstated belief is irrational, or perhaps even unethical. I would welcome formal research on this subject.

If my hypothesis is correct, the most common belief that someone who uses this fallacy holds is: “nothing would change my mind.”

Of course, that statement is unscientific (and irrational, by definition) so anyone who wishes to present themselves as a competent, serious person - a prerequisite to engaging in argumentation - could never admit that.

The excuse is selected based on its ease of defense without exposing the true belief, not a particular conviction. There also appears to be Gish Gallop-like element to this tactic, forcing the opponent to combat various positions only indirectly related to the topic - creating a win-win-win for the user:

• If the opponent gives up, or fails to effectively combat the excuse, the user can claim victory

• If the opponent refutes the excuse, but engages in side arguments or the user forces them to become mired in technicalities, the central topic can still be avoided

• Even if the excuse is defeated, the user hasn't lost, because their true position is untouched. More excuses (layers) provide distance between stated contention and true belief

As the excuses are defeated - or ignored until terms are explicitly agreed upon (e.g. “if I defeat this argument will you admit it fails and commit to never using it again?”) - users seem more desperate to escape the argument without meaningful engagement.

For that reason I believe that the layers - the distance between the excuse and the true belief - correlates very highly with the willingness of the user to engage earnestly (or feign earnestness).

While it may seem obvious, it must be mentioned: an individual unwilling to state their position clearly and honestly, and stop using it if disproven, is engaging in performance, not attempting to discover truth. This deception would make it the single largest contributor to ineffective* discourse.

*Ineffective in this context mean failing to resolve conflict in accordance with any scientific validity - a waste of time.

Some people believe that stating an opinion is itself an argument, that this opinion merits as much respect as any scientific fact (framed as your opinion), and take any disagreement as a personal attack.

Before explaining how to combat this without openly asserting bad faith, a few examples to provide some context.

A Few, Short Examples

My first serious contention with this fallacy was one of the most glaring: debates regarding Greta Thunberg.

In her rise to notoriety, Thunberg was a teenager speaking in favor of policies to urgently combat human-driven Climate Change. As a response to her activism, social media and mainstream commentators pointed out:

• “She's just a kid”

• “She's not a scientist”

• “She's not an expert on climate”

Taken at face value, those seem like perfectly rational reasons to reject or even ignore her case. If you don't accept the realities of climate change - or simply dislike her activism - cognitive dissonance demands that the challenge be neutralized.

Remember, since the vast majority of people are not subjecting their beliefs to criticism, any of these rationalizations is accepted by the brain as a resolution to the dissonance.

But as previously discussed, private reasoning leeches into mainstream discourse, and these excuses form the first “line of defense” for users.

How can I say with certainty they are excuses?

Because if an adult, scientist, expert said the same things Thunberg did (defeating all listed excuses) - the users would not accept or consider the same arguments valid. They would introduce some other reason (or excuse) to reject it.

It follows, then, that those “reasons” were not reasons for disbelief - but excuses to dismiss the undesired conclusions.

And that was my first insight into why the fallacy is so prevalent, and how it's used. My first attempt to define this fallacy informally called it the Thunberg/Nye Fallacy.

Why Bill Nye?

As one of the most popular modern commentators on everything science, Bill Nye “The Science Guy” talks about issues that cross over many different fields.

But as anyone who has the unfortunate experience of engaging with anti-science activists, you'll note:

“He doesn't even have a degree in science! He's an engineer! Not a scientist!”

Now, most educated readers understand that engineering requires a lot of science courses - and in any case lack of degree in a specialized discipline does not equal lack of competence in it - and I'd wager in a discussion or debate you'd be tempted to point this out. Most people do.

And that's exactly why anti-science people say it.

I direct you to bullet number two from my win-win-win presentation:

“Engages in side arguments…mired in technicalities.”

The user has successfully deflected from whatever fact or argument was presented by Nye, shifting the debate to his personal credentials.

In both above cases, the “most reasonable excuse” seems reasonable to the user. Their argument takes the form of: I shouldn't be expected to change my scientific beliefs just because a high school student asked me to - or an adult non-scientist made a show about how sex is a spectrum. Why should I?

As with Thunberg, this ad hominem fits neatly into the larger category of “fallacy of relevance.” Once addressed, users move the goalposts.

For that reason, it seems clear that this “most reasonable excuse” fallacy should fit into the same taxonomy. In fact, both arguments above are basically just ad hominems to begin with, followed by moving the goalposts, so it seems like - so far - it shouldn't need a new name.

But the use of excuses does not always use ad hominems, nor does it always fit under the already broad umbrella of “fallacies of relevance,” nor is the excuse always fallacious at all!

Why It Needs A Name

The distinction between this fallacy and others is that what the argument is doesn't always describe how it's being used.

In other words, some use ad hominem sincerely, because they believe it is a valid argument. However, others do it strategically, understanding that the argument is flawed on some level, but do so in an effort to keep layers between their belief.

In the latter case, the fallacy is not the error - it is the instrument. A means to an end. The argument is selected not because it is believed, but because it is perceived as effective. If challenged, even defeated, the user has succeeded at forcing the opponent to expend time and effort to overcome it. Since the argument was not made sincerely, it can be discarded without meaningful concession or dissonance by the user, and the next-most reasonable excuse introduced.

Indeed, much of my experience and research on the subject results in the opponent concluding that the user of various forms of this argumentation is not serious…trolling…or generally just keeps moving the goalposts. All of which may be true.

But because the opponent has engaged in the argument from the beginning (e.g. she's just a kid!) they have implicitly accepted that the person is worth debating. If they later conclude the person is no longer worth debating, even if justified, the user feels as though their (unstated) belief has been successfully defended.

Another person rightly responded that this fallacy also overlaps with the Motte-and-Bailey (itself one of my favorites). But again, I don't think it's quite an accurate characterization:

In the Motte-and-Bailey, the user states a bailey, defends the motte(s), and claims that proves the bailey.

In the "most reasonable excuse" the PURPOSE of the Motte is to PRETEND the Bailey doesn't exist.

The “self strawman” may be any combination of motivated reasoning + moving the goalposts + bad faith argumentation + more…I'm not sure it can be as neatly classified as I'd like, but I do think it merits a new classification, if not further research.

For what it's worth, lots of existing fallacies also overlap with earlier-named ones, but are better explained with the new version. For example:

Gish Gallop is a deliberate pattern of many Red Herrings - but the intent and style give it a separate classification.

Nirvana fallacy is effectively just a false dichotomy, but when used in a specific way, it is better described by the Nirvana fallacy.

The purpose of naming fallacies is to recognize a pattern (and counter it, if necessary).

Other Examples of “Self-Strawman”

A prominent, recent example relates to the COVID vaccine. It is likely the best illustration of this “most reasonable excuse” fallacy in practice, and why I also refer to it as the “Self-Strawman.”

Because the debate relates to a matter of scientific fact that invokes polarizing opinions, people who wish to be perceived as “competent, serious” understand that their opinion is not “reasonable.” So excuses are offered.

When the vaccine first came out, many people who fit the mold of “anti-vaxxer” said things like:

• “I don't want to be first!”

Despite trials being done, this position seemed reasonable enough. Indeed, many people who are not stereotypical anti-vaxxers claimed it. So it follows that after a few weeks or months of proven safety for tens of millions, they'd get it, right?

No. The next-most reasonable excuse is offered.

• “It’s only emergency authorized! Not FDA approved!”

Right. So once it's fully FDA approved you'll get it?

“Nope. Don't trust the data. Seems rushed.”

And so on, until all of these excuses are defeated, and the person finally offers an excuse like:

• “Just to get booster injection jab next year?!”

I'm paraphrasing.

Ultimately, it reaches the point of:

• “It shouldn't be (or have been) mandatory.”

A very common sentiment, though not quite relevant to the safety/efficacy argument, but the user feels it validates their skepticism towards the vaccine(s). Nothing more than a goalpost move.

This is why I call it a Self-Strawman. The regular strawman is when someone creates a weakened version of your position to argue against it. But with the Self-Strawman, they are creating a stronger version of their own position, forcing you to engage with beliefs they don't actually hold!

While “stronger” is relative, remember that for many people, the belief is:

“Nothing will change my mind.”

And even a weak excuse is stronger than that. But because you're spending time and effort to argue against the excuse, and not overturning their unstated belief, once the interaction is over the user feels as though they've successfully defended the belief.

Most people aren't introspective enough to realize that they are not defending their core belief, and those that are won't admit it. So out of the need to defeat dissonance while maintaining the self-image (or public image) of rationality, they invoke whatever excuse seems most reasonable.

Every scientific field with its anti-science counterparts has a list of regurgitated excuses invoked by those who have reached an immovable conclusion, seeking to defend it under the guise of reason.

“It's just a theory.” May be the most common. Feel free to share your favorites in the comments.

P.S. if you think you're immune to this fallacy - probably not. Consider any conversation you've had with a salesman or…dare I guess…a family member whose function you don't want to attend. It's not exclusively applicable to debate, just the most pertinent application.

RIP Alex Pretti

The atrocities in Minneapolis and nationwide at the hands of ICE are unforgivable. I am only writing about this because it is - unfortunately - the most desperate invocation of the “most reasonable excuse” fallacy I've ever seen. Any doubt I may have had about it being a real phenomenon - which was close to zero - is now zero. The mask is metaphorically coming off.

By definition, users want to keep as many layers as possible between their true belief and the excuse. The more layers, and the more reasonable the excuse, the better.

Well…

“But he had a gun.”

That's their best excuse. That's their best excuse? That's their best excuse?

And it appears to be their only excuse.

“No guns at protests!”

Yep. Seriously.

Above all other issues, nothing defines what it means to be MAGA, Conservative, Republican, than the right to own and carry a gun.

Again, you can fall into their trap and argue about the fact that Pretti legally owned the weapon, never had it or even reached for it (side arguments…technicalities) but that's a short one.

And where does the user go from there? There are no more layers. No more excuses.

This is why it's such a troublesome topic, and illustrates the mindset involved.

Rather than make an apparently uncomfortable admission like:

“That ICE agent messed up”

Which is an admission that this case was very bad, but preserves the right to claim there is not a systemic problem…

They can't even do THAT!

By proving that they would rather make an excuse that requires abandoning their most sacred principles than admit a guy they don't like was wrongly killed, they're showing that nothing - literally nothing - that would change their minds.

Who it happened to, not how or why it happened, motivates their reasoning.

It's not hard to deduce, but I fear the unspoken position is “when it happens to someone we don't like, we don't care.”

And that's a very dangerous belief, spoken or not.

How To Combat The Self-Strawman

Preemptively, but not presumptuously.

The easiest rule of thumb to identify a user of this fallacy is that they post “easily disproven nonsense.”

Folks who are more advanced in this arena (the ones at the top of the misinformation pyramid…the influencers who often even have decent credentials) make the nonsense harder to detect and disprove - usually dressed in academic-sounding language, or requiring a level of expertise in the field to refute.

In any case, they want you to engage, and let them dictate both the terms and direction of the discussion.

1. They thrive on keeping distance between their core belief and stated arguments.

2. They discard arguments (with opponents) after they have been defeated, but recycle them when engaging on the same topic with others.

The second argument requires some research and mostly applies to those with a more substantial presence. Unless you're taking part in a more formal debate, it's not worth the effort to research. Though I'll note - it is remarkably effective to keep receipts like this in your back pocket if you find yourself in such a situation.

But in any case, the most effective tool, by far, is to preemptively combat it.

In debates of fact, it is implied that the goal is to discover who is right. Who is right - in rational discourse - is determined by the weight of facts and evidence.

Do not let this goal be implied. Make them state it explicitly, and do not engage with any claims or reasoning until a clear, affirmative response is given.

Here's how you do it:

“If I prove you wrong, will you admit you're wrong?”

This reframes the discussion. It takes them out of their comfort zone, which is tossing excuses for you to spend time and effort to combat, and forces them to answer what should be - for anyone engaging in rational discourse - a very easy answer.

An unqualified “yes” is the only acceptable response. A soft deflection like, “I'd love to see you prove me wrong” is not.

It is striking how effective the question is. It distinguishes rational debate from rhetorical performance. It is not accusatory, nor is it a loaded question. It is the baseline, fundamental question that is left unspoken in debates of fact - and allows disingenuous people to thrive.

So don't let them.

The vast majority of the time - far more than I would have ever expected - the excuse-user gives up the whole game at this one question. They present themselves as a rational, intelligent person originally - confidently making their case - but instantly resort to inflammatory language (intentionally, to try and force you to let them deflect) and any number of odd responses when asked the question.

They are stunned that their usual tactics won't work, and become deeply uncomfortable - and retreat. You've saved yourself lots time and energy, congrats!

“Sorry, I'm not interested in a debate of fact with someone who can't commit to letting facts guide conclusions.”

Or

“The refusal to answer is the answer. I'm establishing whether this is a debate of facts, and you've opted out.”

Do not concede that the excuse is worth engaging with, that the person is worth engaging with, until they can agree to the bare minimum term.

But I'm here to tell you, it's not that simple. And after giving it some thought, I've concluded it's not true at all.

Statistics cannot "lie" any more than long division can. They can only be misunderstood or logically invalid.

The problem starts with the fact that statistics and probability - overlapping but unique fields - are not that complex on their face, especially at the introductory levels. Most individuals who have conquered calculus, differential equations, or astrophysics find it offensive that you would question their comprehension of something so basic as the margin of error formula, for example. Because the calculations seem so simple, users mistake computation and familiarity for understanding.

Indeed, there are a lot of publications by “experts” whose own words prove they do not understand what the margin of error in a given calculation means…and apparently no one bothers to correct them.

Statistics do not lie, but people who do not understand statistics are easily misled.

Lesson 1: What the Data Mean is More Important than What the Data Say

I have read Feynman, Box, Sagan, Asimov, and many other influential scientific educators. I have no doubt, however, that I have read only a miniscule fraction of what exists and stimulates scientific thought.

That being said, I contend that there is no idea more profound, important, and influential in this field - perhaps all of science - than this one. I'm not sure there can be an idea more important, because it strikes at the core of why statistics are used, how they can be misused, and what it means to think critically.

Of course, with my primary topic of research being poll data, this applies directly, and I'll build on it. But make no mistake: this axiom applies to sports data, medical research, population statistics, finance…anywhere statistics are involved.

In introductory stats classes, students are often provided a problem, an equation, and expected to calculate the correct answer. The exercise trains them to follow procedures, plug in numbers, and arrive at a solution. I suppose at the introductory level this is necessary. But this approach rarely teaches them the more important lesson: understanding what the result actually means, and why the formula exists in the first place.

Here's how I think of the problem - and how I propose it be taught:

1. What problem do I want to solve?

2. What data or facts do I need to solve it?

This is perfectly acceptable for an introductory level. It moves beyond selecting a formula and plugging in numbers, and teaches that even if you can't personally solve the problem, you know what information is needed to solve it.

This applies just as well whether the “problem” is finding the area of a rectangle or the efficacy of vaccines.

By understanding the data needed to solve a problem (and perhaps what information seems relevant but isn’t) when a charlatan or purveyor of pseudoscience confidently presents some data, you are not so easily fooled.

In other words, the process emphasizes understanding the meaning of the data over mechanically producing an answer - or even producing an answer at all. Students learn to distinguish between knowing a procedure and understanding a problem.

This is statistical literacy in its purest form.

Richard Feynman, in his lecture on how to test competing theories that both seem to produce valid outputs, lamented that scientists often followed procedures that took the form of:

“Never mind the philosophy…just guess the equations, the problem is only to compute the answers so they agree with experiment.”

Again, finding a formula that works to solve some problem - wonderful, and important. But explaining why it works, and why it might fail - understanding the implicit assumptions - that's a higher level of thinking than “got the right answer who cares bro.”

And identifying in advance such “got the right answer” type thinkers offers the ability for more sophisticated minds to improve on methods by identifying the conditions in which the calculations “got the right answer” and those where they might - or will - eventually fail.

This pattern is evident throughout history. Whether it's something hard to test like the orbit of planets, easy to test like the Monty Hall Problem, or counterintuitive like the mass of an object versus how quickly it falls…

Note how long the world's smartest people believed something that is very incorrect because of how obvious it was.

What seems obvious isn't always obvious, that's why the scientific method exists in the first place; in fact, if you ever have a serious discussion with someone, and you ask them to explain something - and they contend that it's “obvious” - you have likely discovered a gap in their understanding. Stating it's “obvious” is both a deflection and a subtle ad hominem that implies you not fully understanding something reflects on your intelligence, to distract from the fact that they feel like they know it…but can't explain it.

The problem has been explained more in depth recently, and it's called the illusion of knowing.

In short, familiarity produces comfort and fluency, not understanding. Analysts might know all of the terms in the margin of error formula, use it often, and mistake this regular use (or their years of experience in the field) as proof of understanding.

But the reality is, finding the right answer often requires questioning and testing the simplest assumptions - even those that seem obvious - and realizing that reality doesn't particularly care about “years of experience.”

In the case of Ptolemaic Astronomy, they “got the right answer” almost all of the time. As such, it seemed foolish to question the most basic assumptions about whether the Earth was stationary. The world's most brilliant statisticians (including those at MIT) failed to solve a problem a few years ago that many high school students can solve today.

Indeed, one of the most brilliant people in history apparently didn't bother to test the rate with which objects fell because the answer seemed…obvious.

Likewise, Literary Digest’s poll - though unscientific - “accurately predicted” the result of four consecutive elections. As such, it was considered the gold standard…until it wasn't. Getting “the right answer,” not valid processes or even logic is all the field cares about. And not much has changed.

The problem with all of this, I believe, is that otherwise brilliant people believe these are lessons of the past - not the present or future. They believe the solution to the Monty Hall Problem is “obvious” and that if they had been presented the problem in the 1990s - when the credentialed experts were almost universally wrong - they would have obviously been able to solve it and overcome the consensus.

They are born on the shoulders of giants but believe they have climbed there.

Established procedures and accepted assumptions shouldn't be questioned just because you think they might be wrong; they should be questioned because you think they aren't.

Lesson 2: Logic is more important than math

Statistics: what the data says. It is a branch of math

Probability: what the data means. It is a branch of logic

This is not to diminish the importance of statistics. It is to say that without asking what problem needs to be solved, numbers alone cannot guide reasoning. Logic provides the framework for interpreting results, determining what information is relevant, and connecting observations to conclusions. In short, mathematics tells us how to calculate; logic tells us what it means.

Probability itself is a remarkably new field, given the age of relatively more complicated fields like physics and calculus. But probability isn't purely math: probability is the logic of uncertainty.

Uncertainty can be quantified, but as evidenced by the responses to political forecasts that conclude a forecast is “wrong” when someone given “about a 67% chance to win” doesn't eventually win…thinking you understand what something means, and truly understanding it, are quite far apart.

Seemingly simple statistical statements are often very poorly understood.

Indeed, this exact logic holds true at the highest level of political data:

They conclude that a candidate being “ahead” in a poll or poll average - if they don't eventually win - is evidence (or proof) that “polls were wrong/missed/failed.”

When I politely present some simple data - a poll average of 46-43 with 10% undecided, for example - there are a lot of very big assumptions being made if you conclude the person at “46” must eventually win (and win by about 3) or else polls were wrong.

It's simple arithmetic, in fact, to show that undecideds favoring the candidate at “43” can - by itself - cause them to win, even if the poll were perfectly accurate for the population at the time it was taken.

This is a trivial mathematical proof (forgive me for violating my rule on calling things obvious) - but the problem isn't the math. They understand the math.

The problem is the logic.

Because of the 100 years of implicit bias in the field - that undecided behavior can be assumed to follow some rule (splitting evenly or proportionally to decided voters…incompatible and conflicting statistical conventions that literally depend on which country you were born in) the possibility that they could overwhelmingly favor the candidate BEHIND in the data is considered so objectionable that they pretend it can't happen.

Even when presented with irrefutable data that it can and has it's dismissed as a rare exception.

Back to that thing questioning established procedures.

But perhaps most telling about the flaw in reasoning, is that “in the long run” it is implicitly accepted that undecided voters will converge on some split (usually 50-50) - which is the rationale given for pollster grades that assume a 50-50 undecided split. Even if the grades are inaccurate for any given election, “in the long run” the 50-50 assumption will make for accurate grades.

Ahem

Taps microphone

Prove it.

To quote myself:

Of course, the idea that polls are predictions - which is the indisputable (incorrect) consensus within the field - is flawed at its core. But even if I were to grant the grading procedure as worthwhile, it still lacks validity.

Why is a long run 50-50 split for undecided voters accepted as true? Why not 75-25 against the incumbent, and 60-40 against the party of the incumbent when there is no actual incumbent?

Why do we use the same rules for Senate races as House races as midterms as Presidential Elections?

The reasoning, I suspect, is obvious.

The field seems to be so concerned with finding a formula that provides the right answer that they disregard the philosophy behind it.

That's without getting into the discomforting mathematical reality that it would take multiple human lifetimes of data to have a sufficient sample size.

In any case, my work at its fundamental level is simply challenging the field's consensus - the historical assumptions - that undecided behavior can be modeled unconditionally.

Historically, it's as though they're claiming heavy objects fall faster, and I'm climbing a tall building to drop two objects of disparate weight to test it. Instead of anxiously or even passively following what is very easy to test, they demean or understate the value of the findings.

As with “so they fall at the same rate, so what?” - the implications of the understanding that polls aren't predictions are far greater than the headline.

One of them is this:

While polls are not predictions, they are our best tool for informing them. And understanding that polls are not predictions teaches us - as Panagakis also noted - that “rules of analysis are necessary.”

My research shows that a small lead with a poll average close to 50% is far preferable to a larger leads far from it. Indeed, I believe that this is a conclusion that follows directly from an understanding of how polls work: they are an approximate base of support, not a prediction of an outcome. And this understanding is only possible if you allow yourself to escape the trap of polls as predictions that currently forms the field's consensus.

And when published the following in 2012, he concluded that leads of “2 or 3 points” in highly polled states were very strong leads.

He's observing an output with no valid underlying philosophy.

Of course, Panagakis addressed this decades earlier…and there's nothing wrong with not reading everything every person has ever written on the subject.

But the lack of intellectual curiosity in challenging your most fundamental assumptions - that “obviously” how much a candidate is ahead by in a poll average is a meaningful proxy for their win probability - violates the most basic principles of scientific reasoning. The question is not whether the number can be calculated, but whether it answers the question being asked: how likely is this candidate to win this election?

Treating a margin as a probability substitutes familiarity for logic, and convention for understanding. It confuses what the data say with what they are being assumed to mean.

Lesson 3: A Thought Experiment (and Actual Experiment)

I have a database of 10,000 responses to the following question:

Of the following, which is your favorite color?

• Red

• Blue

• Green

The order of the options were randomized in the survey.

Your assignment is to estimate the percentage of respondents who said which color was their favorite.

1. Just guess. Make your best guess.

   *Answers are turned in and reported*

2. As a class, here is the average of what everyone guessed. Based on this information, would you like to update your guess?

   *Answers are turned in*

3. I took a random sample of 600 from my database. It yielded:

   • Blue: 48%

   • Green: 29%

   • Red: 23%

Based on this, would you like to update your guesses?

This step, of course, provides far better information than an individual guess, or wisdom of the crowds. While some students will cling to their original guess like Monty Hall contestants, most understand why this data far supercedes its predecessors. “Why” is a good question here.

Depending on the class, you can even discuss the margin of error.

Now, the first super hard, obvious question:

4. Given that poll data, what does it mean?

Challenging learners to explain what feels obvious is one key difference between teaching and lecturing.

Any answer that takes the form of:

“The 10,000 responses in your database are probably close to those percentages” is fine.

Take a few more polls with the same sample size, to illustrate the variability of these ideal polls.

Blue, at 48%, would probably return some results over 50% and some under 45% given a few random samples.

The lesson “fluctuation is normal and expected” is good here.

Having established that the students understand what the data means - not just what it says - drop the Monty Hall, Literary Digest, Nate Silver-sized piece of variable change on them:

A few days after the earlier survey, I asked the same 10,000 people:

Of the following, which is your favorite color?

• Red

• Blue

5. Estimate the percentage of respondents who said each color was their favorite. Your grade on this assignment requires providing a correct answer. Extra credit for confidence intervals.

Discuss in the comments!

Do you think it's a waste of time? Maybe I can convince you otherwise.

Do you find yourself doing it? This article will teach you how to be better at it - by wasting less time - and maybe give you a sliver of respect for Jake Paul.

You can argue it's not productive to engage with trolls - and you're mostly right - but in my field, understanding how people think, why they think it, and how to effectively combat that level of thinking is very useful. Both for teaching, and for overcoming misinformation.

You may or may not be surprised to learn it, but people at the very top of the fields I work in often employ the exact same tactics as Internet trolls - simply with more followers and (sometimes) better vocabulary.

To use a sports analogy:

I debate internet nobodies for the same reason professional baseball players take batting practice. It's not because soft-tossing a ball to a professional hitter mimics elite competition - but because the form can be refined such that when facing a rare, qualified opponent, performance becomes muscle memory.

Debating Internet Nobodies

I don't use the term “Internet nobodies” demeaningly. It spans a very wide spectrum of literal trolls to educated professionals. Occasionally, though very occasionally, people in this broad category will present something I find useful. The batting practice equivalent of finding a hole in my swing, so to speak. A good hitter can (and arguably, must) respect it and refine their approach.

But more often than not, people who attempt to engage in a debate of fact (but will lose the debate if “winner” and “loser” is judged purely on merit) follow a predictable pattern:

1. Make a claim

2. Refuse to support that claim

   2a. Refuse to admit they're wrong if proven wrong

Of course, the burden of proof in rational debate is on the person who makes the claim.

But in particularly easy cases like above, I'm happy to prove them wrong. Under one condition:

“If I prove you wrong, will you admit you're wrong?”

It's 2026, and this approach is still undefeated.

And still undefeated.

It's the boxing equivalent of putting your opponent in the corner. People who can't win a debate on merit don't like being cornered: their continued performance relies on not being cornered.

The most common techniques in avoidance of defending “2” are:

3. Change the subject (if they don't let you corner them, they can't lose!)

   • Move the goalposts

   • Self-strawman

   • Ad hominem

   • Easily refuted nonsense

You can see Mark try to move the goalposts above, while '“prof” weakly lobs an ad-hominem. There's also

4. Invent a strawman of your position, propose a motte-and-bailey, or outright lie.

My claim on the post below was that an above average male would not defeat an elite female in tennis:

Robolivermd says, but aha! Not “the average medium level male college tennis player” though.

A mouthful of qualifications make it perfectly clear he's changing the subject.

So I bring him back to the original point:

How close are those “average male college tennis player” (his strawman reference point) to “average male?”

He didn't answer. And in an attempt to avoid being held accountable, he simply makes a wild, indefensible claim:

“If they're not a professional, they (are) part of the range of average.”

It would've been easy to dunk on him (another sports reference, whoa!) with a chart like this:

But I've taken enough BP to know what's going on here. I only provided this chart for your entertainment. Hope you love it.

What is happening is that he's offering an argument unrelated to his original claim in an attempt to change the subject - and avoid defending his original claim.

I call it “easily refuted nonsense.”

Robolivermd dangled this easily refuted nonsense in an attempt to again change the subject, to avoid defending his original claim…which also changed the subject. See the pattern?

The more separation an unqualified debate combatant can keep between making a claim and being accountable for it, mentally and tactically, the more comfortable they are engaging.

His claim is so easily refuted that you think you can simply prove them wrong and return to the original point. No. That's the purpose of easily refuted nonsense: (metaphorical) breathing room.

If allowed, he would simply move the goalposts ad infinitum. “No I meant average men IN THE SPORT, not THE POPULATION!” an innocuous misunderstanding! Others accompany such retorts with childish insults like “learn to read” with an optional “moron” (or synonym).

You conclude they're not debating in good faith, they contend they were, and their tactics worked: they never had to concede anything.

Veteran debaters may recognize this “easily refuted nonsense” in the form of:

• “Just a theory”

• Mercury!

• “Abortion is the same as killing babies”

• “Climate has always changed”

• “Mysterious ways”

• Guns don't kill people!

And so on.

While you, veteran debater, most often conclude that people who use these arguments are simply ignorant, and that if only someone could explain it to them clearly, using strong citations and persuasive language, they'd stop making that argument.

I regret to inform you that this is almost never the case.

That is what they want you to think. They often know the point they're making is wrong, and they don't care: that's the point.

It's easily refuted nonsense that keeps distance between their true belief(s), and what you're arguing about.

These arguments commit the fallacy of self-strawman: they misrepresent THEIR OWN beliefs, so their core belief can't be attacked.

The Self-Strawman (and Easily Refuted Nonsense)

Definition:

The act of deliberately presenting a weaker or fabricated version of one’s own belief for debate, so the central topic and user’s actual position (usually irrational and/or unfalsifiable) remains untouched and protected.

It works on three levels:

1. The speaker can “lose” arguments without risking the belief they actually care about,

2. It attempts to force opponents to exert time and energy against something mostly unimportant to either person, keeping distance from the central topic or true belief, and

3. It gives the user an illusion of rationality: that they are subjecting their beliefs to critical debate, and yet they continue to sustain.

Other Tactics

Less academic folks, when cornered, lash out with name-calling and personal attacks. Same subset of argument, same function: deflection. It's an attempt to make you let them change the subject.

Below, a recent example of someone who (believe it or not) portrayed themselves as engaging genuinely, making calm claims and statements of fact. Until cornered…

They use increasingly inflammatory language when cornered (r*tarded is a current favorite, though there are many others) because once you call them on their language you have let them escape the corner of debate.

You might believe you're rightly calling out an important point about respectability or decorum, but that's the thing: they want you to not respect them. In their mind, if you react, you’re the snowflake who “can’t handle it.” And at that point, consciously and subconsciously, that’s why the debate ends. Not because they were wrong, but because you don't like the words they used.

More educated folks rarely sink this low; they stick to more sophisticated insults like “not nearly as smart as you think you are” - but for the same reason. It's an ad hominem designed to try and escape accountability…but won't cost them their job.

Do you see what I mean about batting practice?

I asked a direct question relevant to his claim. He feigned emotional outrage.

I ignored it and asked a direct, relevant question. The corner is uncomfortable! Must escape. Personal attack. Waste of time. Cope.

For bonus points, the claim “you're arguing semantics” is a sophisticated form of easily refuted nonsense! Brilliant gambit, sir!

In fact, his 5 sentences take the form of: Irrelevant. Ad hominem. Easily refuted nonsense. Ad hominem (circumstantial). Ad hominem.

It’s quite impressively done!

You might think it's weird, and it's probably bad that I'm so desensitized to it, but when the trolls resort to a variation of “beta cuck r*tarded soyboy bitch” it hits me the exact same way as Tom's “not nearly as smart as you think you are” string of deflections. They're the same thing! It's adult children screaming about their ego being hurt in an arena where the debate is “what is true?” And/or “who is right?”

Yes, yes, let it all out now. You're a big, smart, alpha boy, aren't you? You sure are.

It's reactive, performative, and consciously or subconsciously only something someone would resort to if they realize they can't win the discussion on any merit. Even if you spend time and effort disproving the easily disproven claim (which they will counter and deflect from) they don't actually hold that belief. It's a misdirect.

That's why the reaction is so emotional, and truly visceral, when you focus your attack discussion on the actual position or claim and don't let them change the topic at will.

“If I prove you wrong, will you admit you're wrong?” Is an inescapable corner.

Quoting their exact, original words to them after they ramble for multiple posts trying to get you to let them out of the corner is quite triggering for some reason.

In any case:

“Is there any collection of fact(s), data, or information that would change your mind?” (and then making them state it) is also undefeated.

Unlike Jake Paul.

Respect For Jake Paul

I don't follow his social media antics much, and I'm sure there are plenty of reasons not to like (or respect) Jake Paul.

But credit where it's due: most of the time when unqualified nobodies talk a big game, they don't stick around to back it up.

They enter the debate “ring” with clearly defined rules, get cornered, then take their gloves off and say something like, “betcha can't beat me at MMA!”

If you keep them on topic:

“Guy, we were just boxing”

They say:

YEAH, SEE, YOU'RE AFRAID TO TAKE ME IN MMA.

And this pattern will continue no matter how many times they are cornered. That's why it's important to give them zero benefit of the doubt:

“Okay, so you're conceding that you lost the boxing match, and now want to change the topic to MMA, is that right?”

They don't like being held accountable. You're being so rude by…establishing accountability.

The other technique - resorting to name-calling - is the equivalent of running out of the ring after getting cornered. The debate - in the ring - had defined rules. They exit the ring shouting obscenities, pretending they never agreed to any such rules.

“I will still fight you! What, you're afraid to chase me over here to this different topic? Bring it beta soyboy!”

They assert that since they challenged you to chase them outside of the ring, even though it's something other than what you originally agreed to, they haven't actually forefited anything.

Same mindset.

In debates of facts - like a combat sport - it doesn't matter what anyone thinks…it matters what you can prove.

When someone steps into the ring - boxing or debate - they're asserting "I think I can beat you"

That's okay. Maybe you can. Only one way to find out.

So, Jake Paul. Respect.

He talked his shit, didn't run away, got his jaw broken…and it was settled.

By Popular Demand

I'm working on my own version of this flow chart, but it's extremely useful.

Use it wisely.

I want to explain this phenomenon from a psychological, statistical, and social perspective. It will get way too deep into topics of misogyny and population statistics, so if you keep reading, you've been warned.

Recently retired Correction - recently recovered from injury, professional tennis player Nick Kyrgios comfortably defeated (6-3, 6-3) the world's top-ranked woman, Aryna Sabalenka. Like past iterations of the event, the rules were slightly modified to favor the female player.

Certain groups of people believe this is proof that females are simply unable to compete with males, and use this to solidify their pre-existing belief in the superiority of men…but totally only in sports. 😅

The fact that people who are most passionate about the topic of male superiority in sports tend to hold negative views of women who exercise power in conventionally male-dominated fields like business and politics is not a coincidence.

Not toxic: males and females competing against each other in sports.

Toxic: using these examples as proof of anything other than what they are: elite male athletes are generally better than ULTRA elite female athletes.

I'll share some statistics on this later. First, the psychology.

The Psychology of Toxicity

It's no secret that a lot of men value stereotypically masculine things: physical strength, athletic superiority, financial status, and even intellectual or technical mastery (thanks, Renaissance).

There is nothing fundamentally wrong with any of this. Competition challenges us to get better, gives many of us purpose, and I would argue that people finding things they value is generally healthy. Sure, coding these things as “masculine” is problematic, but that's a separate topic.

But there's a fine line between valuing something and identifying with it.

Chances are, you've witnessed a female beat a male at something athletics-related, and can attest to the reactions. In most cases, it's light-hearted and most people (men included) take it well. But to borrow a misused saying that's more appropriate here: “not all men.”

Being good at sports is very man. If a girl is better than you, what of your precious status? This is where things go wrong - and where toxic masculinity comes into play.

The fact that some men would disproportionately concern themselves with the athletic superiority of other men can only make sense through the lens of toxic masculinity.

Most of the men who comment on the fact that, in a given sport, the worst professional male is better than the best professional female are not motivated by an interest in any physiological or scientific mindset.

They are doing so because of their own insecurity, and they psychologically identify as "one of the males" to borrow status from elite male performers to maintain an illusion of superiority to females.

This phenomenon is not new or even particularly controversial.

Humans constantly compare themselves with others for the sake of status or identity.

The Physiology of Masculinity

If you've studied biomechanics, physiology, and other related concepts, you understand that it is...not at all surprising that elite men would outperform elite women in many sports. A few factors in performance in most sports:

1. Higher Absolute and Relative Muscle Mass

   • Higher Max and Submax Strength and Power

2. Higher Testosterone Exposure

   • Muscle Hypertrophy

   • Bone Density

   • Tendon Stiffness

   • Motor Unit Recruitment

   • More

3. Greater Hemoglobin Mass & Oxygen-Carrying Capacity

4. Skeletal and Anthropometric Differences (mechanical advantage)

   • Longer limbs

   • Narrower pelvis

5. Essential Bodily Functions

   • Men typically reach peak athletic performance with body fat percentage in the single digits. Women can seldom remain healthy below the teens. Smaller frames + greater non-contractile mass generally reduces athletic performance.

All of these well-known facts (of which there are more) is my way of illustrating that I'm not some ideologue who believes that if only females had more opportunities, they could compete with elite men.

By nature of dealing with a nonrandom selection of “elite athletes,” we are by definition dealing with both genetic and physiological outliers. In order to quantify performance on the same scale, we can define the “elite” male as x standard deviations above average and the elite female as x+y standard deviations above average.

In general, most male versus female athletic performance can be summarized as something like this:

Given objective standards (like Special Ops Forces) we should expect to see far more men than women above a certain physical threshold.

But notice: there are many men who qualify as “elite” who would not outperform very elite females.

And the above is a generalized chart. Other areas show greater disparity:

And other areas less disparity:

We see a similar pattern in high levels of Olympic and Professional Sports.

It's not really a coincidence that these charts closely mirror sex differences in height.

You'll note that the majority of the NBA is not even represented on this chart, with a median height of about 6’7. Stats nerds will note median height for males (about 5’10) is less thick than that of females, which means greater variance.

With greater variance, that right tail (very tall people, on this chart) is exponentially different. The number of males who are, say, 6’6 is roughly 99.9-percentile for males (about 1/1000) compared to one in several million for females. As a result, the number of males to be selected from this category is in the tens of thousands. The number of females is in the dozens.

Competitive sports nonrandomly select outliers.

And with all that being said:

The gap between professional female and professional male is still FAR SMALLER than the gap between average male and professional female. I summarize this simple fact as:

Caitlin Clark is closer to Steph Curry than you are to Caitlin Clark

(H/T Brian Scalabrine)

This statement triggers all the right people because it punctures the fragile psychological shortcuts they take. Bringing “you” into the discussion - which can be taken many different ways but can be generally interpreted as “the average” is what causes the puncture.

Many men derive vicarious comfort from their identity as “man” - which is quickly conflated with “good at sports” …which then mutates into “better than women at sports” … and this discomfort is evident in the (ironic) emotional recoil.

If I had a nickel for every time an insecure man said BUT US WOMEN'S SOCCER VERSUS HIGH SCHOOL BOYS I'd be in Forbes. The fact that the match was a scrimmage is not considered relevant - because the result confirms the pre-existing belief. The fact that the teenage boys were a select team, many of whom are currently professional or Division 1 Athletes - details.

Ask the men who cite that select U15 boys team if they could outperform the US Women's Soccer Players…or the U15 boys…and the borrowed status bubble is popped.

The need for facts is secondary for the need to support the feeling. This story is regularly, wrongly cited as they lost to “pre-teen boys,” and that they lost to “a high school team” on social media, which is a strong indicator that the feeling informs the facts and not the other way around.

The fact that (retired) US Women recently lost to (retired) Wrexham players was also recently cited to support the claim about… teenage athletes being better than elite women. A well-informed group, to be sure.

The move is emotional, not scientific. Mediocre men invoke elite male athletes (even teenage ones) as if they’re on the same team in any meaningful sense, using group identity as a crutch to convert someone else’s excellence into their own imagined superiority. For some, it’s less about proving male superiority than asserting female excellence can never be enough.

“They might be better than me, but not my (imagined) team” is a textbook cope.

And that discomfort is precisely why the conversation keeps getting rerouted to elite men, away from themselves, because borrowed status feels safer.

The Statistical and Social Whatever

The gap in ability is far from equal across sports, and this is without yet getting into the highly relevant fact that girls were practically forbidden from participating in sports until very recently, and the mediocre compensation for elite females disincentivizes athletes (therefore coaches, therefore trainers, therefore…domino effect) from pursuing or investing in it.

When the male league-minimum is higher than the top-paid female, there is a clear incentive structure. Even in more equitable sports like golf, the median PGA pay is roughly 700% larger than the median LPGA salary.

Note, I'm not making any moral or even economic claim here about what pay “should” be: it's a simple incentive structure, with some social scaffolding. Which leads me to…

The Math

Wherever there is a larger pool of participants (which is true of male sports), we should expect the number of those selected for being elite to be greater, and those who are elite (but not selected) to be greater!

Reducing the discussion/debate - or far more often, diatribe - to “athletic superiority” illustrates a reductionist flaw commonly present in unscientific arguments.

Ignoring the performance differences for the moment, assume two equally talented populations: one with a population of 1,000,000 compared to another with a population of 100,000. Here's what that distribution looks like:

Elite athletics don't deal in percentiles, they deal in absolute maximums: the best of the best. You can probably field every team's starting lineup (if not a whole league) just in that tiny area between maximums given the population sizes. Bench players from one population would be better than stars from the other.

And remember: this only due to population size - BEFORE controlling for performance differences!

The consequence is that if we segregate the two leagues of different population sizes (we can use US Basketball versus France Basketball, as a timely and non-sex related example) we will get an occasional outlier - Victor Wembanyama may soon have a case as one of the best players of all time - while the next best players are the likes of Tony Parker, Boris Diaw, Evan Fournier, and many other very talented players…who were never the best players on their NBA team. Not far down the list, you get players who would not even make an NBA roster.

This is not a statement on the country's relative athletic prowess, it should be understood as an inevitable result from the fact that the US has more people, basketball is far more popular here, and we invest far more money into developing our (basketball) athletes - with a much larger financial incentive to be elite.

Some may be able to draw the analogy between intra-country comparisons and intra-sex comparisons. While there is indisputably a physiological factor in the latter, it doesn't exist across borders. And yet, US natives indisputably comprise almost all of the all-time top-100 basketball players (shoutout to Hakeem, Dirk, Nash, and Jokic) - but none of this has anything to do with a country’s physiological superiority! It's population statistics.

Indeed, if you go down a tier or two in France, you would get professional teams that would struggle against top US high school teams.

Even still, the number of elite basketball players from outside the US has accelerated drastically in recent years - and it's not a coincidence. That acceleration coincides very closely globalization of basketball infrastructure: expanded youth academies, international scouting, analytics-driven talent identification, and - critically - the rise of the NBA as a credible, lucrative incentive for non-U.S. athletes.

As barriers to entry fell and the expected payoff rose, the effective global participant pool expanded. What started as a trickle with a few foreign players making solid NBA contributions, quickly rose into a flood of competitive participants. The result was not a gradual shift, but a nonlinear jump in right-tail outcomes: Petrovic and Kukoc became Ginóbili and Gasols which evolved into Nowitzki, Jokic, Giannis, Doncic, Embiid, Wembanyama, and so on. This is exactly what selection theory predicts when a large, previously under-sampled population becomes more integrated into a high-incentive system.

It's not a difficult hypothetical to conclude that if the international infrastructure hadn't grown, and basketball were not as popular globally, those elite players would not be in the NBA today, and their predecessors wouldn't have been either…largely because their predecessors weren't. The current performance does not exist independently of the past, just because the players are different.

The Infrastructure

In case you still mistake me for an America-supremacist because I'm talking about American sports, I'll be honest:

We suck at sports like Rugby and Cricket. Despite our enormous population, the huge crossover in skill sets between American Football and Baseball, why doesn't America also dominate them? Wouldn't it make sense for players who fail to make it professionally in their preferred sport to just convert?

Well, that infrastructure simply doesn't exist, because we (generally speaking) don't play them. Other countries, even those with tiny populations, even those with holy shit less than a million people, dominate because it's their favorite sport. It sounds boring, but it's (in large part) a math problem: their best athletes are training in this sport from a young age, so they invest in it, and have a larger population of elite athletes to select from in that sport. America doesn't.

Given the size of a country like New Zealand or Fiji, and even a much larger one like South Africa, their dominance in Rugby can't be explained solely by population statistics or even financial ones, though. And certainly not physiology. There must also be a social factor driving competition: a social concentration of athletic talent. A similar phenomenon happens with professional baseball.

This means comparing male to female athletic prowess is not as straightforward of a problem as people think.

There is, no question, a physiological difference between men and women. But stating “better because physiology” is proven to be insufficient when the same physiology systematically produces inferior outcomes due solely to environmental and social pressures.

The gap between elite U.S. basketball players and elite players from low-participation countries is often larger than the gap attributed to sex differences alone. Outcomes at the extreme right tail are driven by who enters the funnel, how competitive it is, and how much pressure exists to reach the maximum.

Physiology sets limits and bounds, it does not determine results.

The Funnel

The “sports funnel” starts from a young age, where kids of all skill levels participate. By their teens, there is a strong selection effect against below-average performers. Put simply, the more people forced through the funnel, and the more capital pumped into it (capital referring to either literal money, labor of coaches and others, or social status) the farther you can force the maxima to the right.

This is not speculative, it is a direct implication of selection theory. Larger, more competitive, better-resourced funnels do not merely produce more elite athletes - they produce better ones, because the surviving set is drawn from a deeper and more intensely filtered pool.

To illustrate how the funnel works, here is a clip of back-to-back plays from the New York Knickerbockers game in 1950. These are elite male basketball players.

To be fair, this isn't a fully representative sample of the game - there were some nice plays. The kind of plays you might call “nice” in a modern High School JV game, anyways. You can watch a condensed version of the game here, if you want to cringe.

No serious observer would compare the performance from that game - two teams that finished in the middle of the league standings - and conclude that today's WNBA players wouldn't overwhelmingly dominate this level of competition. Physiology and all.

Before the very modern NBA era, being large and mobile was more than sufficient to land an NBA job. Now, guys who are even larger and more mobile are also elite shooters and ball handlers…and even that doesn't guarantee you're good enough to play. Al Horford is a better 3-point shooter than Larry Bird was - a fact determined by both three-point percentage and volume - and Bird was indisputably one of the best shooters of his era, Horford isn't close. Selection pressures have aggressively raised the bar for playing in the NBA.

As such, we can easily see that League-wide improvements in performance is measured in years and decades, not generations. This trend is seen across all sports.

The elite male athletes from the 80s and 90s were motivated by the elite male athletes of the 60s and 70s. Though earlier generations were largely less skilled, the funnel filled, and pressure drove progress. That pressure increased as sports rose in popularity and compensation.

And to bring this all together, the above clip is from 1950, while the WNBA wasn't founded until 1996. That raises an obvious question: who was motivating female athletes to be elite before that point? How many existed in the funnel, and what pressures were forcing them to improve?

For most of the 20th century, the answer is: very few, and almost none. While millions of girls were probably interested in basketball and other sports if only because they watched the boys play, there was no professional league for them to dream about, no stable developmental pipeline, limited youth participation, minimal coaching infrastructure, and little social or financial incentive to pursue elite performance. The right tail simply wasn’t being populated.

The Head Start

The modern Olympics were established in 1896, but women weren't allowed to compete in the marathon until 1984. Katherine Switzer was violently assaulted by the Director of the Boston Marathon for the unthinkable act of Woman Participating - but finished the race with her friends protecting her. This is not ancient history; she still runs!

And yet this structural, misogynistic disadvantage is ignored when discussing performance disparities because it makes people uncomfortable. Observers who lack historical context or statistical literacy assume that athletes exist in a vacuum, as if people are born independently of the systems, incentives, and barriers surrounding them. The result is a persistent misattribution: outcomes are treated as innate, rather than the product of decades-long social, institutional, and developmental funnels.

This phenomenon is not unique to sports or even the general public: it is a form of hindsight bias seen in science as well. From the next article on your reading list:

Fortunately, there are lots of good scientists who put their personal biases aside to perform valuable research.

This study illustrates empirically the concept I've discussed in this article, with record time progression over the decades in males and females. They nicely summarize “policies that explicitly forbade females” as “social factors.”

Men in the 70’s compared their scores in the 70’s to women's and called the enormous gap laughable. By the 80’s, it narrowed substantially. Into the 90’s, the 12% performance gap, though small, remained as proof of male physiological superiority. What they must not understand (or more likely, ignore due to cognitive dissonance) is that women in that same decade would have outperformed men from just a few decades earlier. Physiology alone cannot explain that - and this is for a sport where physical ability dominates rather than a mix of technical skills.

While that performance gap has sustained among the very elite, it's important to be very clear: no above-average male in 2026 who decides to train can simply outperform elite females because Male. Not in marathon running or any well-developed sport. That was not the case in 1970. What changed, and will continue to change more rapidly as women are allowed to participate in sports and they grow in popularity, is the right tail pressure.

What we are seeing in the 2020s is plausibly only the first or second true wave of fully professionalized female basketball: athletes who grew up knowing a league existed, who trained year-round, who faced dense competition from childhood, and who were pushed by real incentives to reach the extreme right tail.

Physiology explains performance ceilings, clearly illustrated in the chart above, but it does not and cannot explain how quickly those ceilings are approached, how many people get near them, or why performance accelerates when systems mature. Claiming otherwise isn’t biological or scientific - it requires both historical and statistical ignorance.

Elite male athletes did not emerge in a vacuum. The right tail of the NBA pulls the right tail of college sports which pulls the right tail of high school sports. Each level raises the incentive and selection pressure on the one below it, progressively densifying the extreme right tail.

Stating that there are some high school males who can or do outperform some professional females isn't proof that the entire sex enjoys physiological superiority, though many men desire that conclusion. There is a distribution overlap influenced by asymmetric selection. The selection pressures make the right tail more dense for males, raising the bar for what qualifies as “elite male,” in the first place.

They were produced by decades of early access, dense competition, cultural reinforcement, professional pathways, and sustained capital investment. To attribute the resulting gap entirely to biology is to ignore the very mechanisms that created elite male sports.

Because of this century-plus head start, plus the real physiological factors that exist - which are not independent - I don't expect a female athlete to supplant a male at the highest level of any sport, though some overlap would not be shocking. I do expect, however, that with continued development and investment, the right tail of female sports and will grow and widen significantly. Just as elite male athletes have separated themselves from their past generations (and the population averages) elite females will too.

I made this chart for angry male commenters who disliked the conclusions I made from literal data, and I'm adding it here so I don't lose it:

Minutes are reflected by a decimal, which in hindsight, would've been much easier to reflect as minutes & seconds, but the point holds.

“Top 1%” is approximate derived from Army Physical Fitness test and a few other sources - mile and 5k times among self-selected competitors who train - then corrected to determine an approximate number of people who don't jog or run (90%) correcting upward for people who are generally somewhat active but don't run then a little more for people who used to run, then setting lower bounds above a brisk walking pace.

https://www.elon.edu/assets/docs/rotc/APFT%20standards.pdf

https://www.mdpi.com/1660-4601/20/19/6872

In short, every thrown pitch in baseball results in a “strike,” “ball,” or ball hit in play. Some places that allow wagers on sports (sportsbooks) have an option to bet on what the “first pitch” will result in.

The lawsuit claims (with lots of evidence) that bettors conspired with at least two pitchers to throw a first pitch “ball” when they entered the game. While this single pitch cannot reasonably be asserted to have changed the outcome of any game, it's clearly a major ethical violation and the sports equivalent of insider trading.

“Sports betting” to a professional is little more than quantifying uncertainty, risk, and attempting to optimize returns. While it is “gambling” in every sense of the word - many people conflate chance-based play with the analytics that underlie informed betting decisions.

HOWEVER

Most participants who gamble do so in part or entirely for entertainment value: maybe they think they have an edge, maybe they're just betting on their favorite team. In any case, fairness is expected (and now, strictly regulated) all-around, from the oddsmakers to the participants.

Wherever there is gambling, there will be unethical actors trying to exploit those markets for profit. The fact that these players were caught illustrates that the system works. As someone who is always looking for exploitable loopholes (whether to exploit them or prevent them from being exploited) I am inclined to point out some of the issues that remain, and how to resolve them.

Who Needs Gambling?

Let me get this out of the way early: no, making gambling illegal would not eliminate this problem. While the volume of wagers may decrease, underground markets would still exist.

And counterproductively, it would make the prospect of collusion (up to outright match-fixing) much worse. Legalized gambling comes with increased data collection and regulations. That data collection flags unexpected events or player performance for additional scrutiny.

Individual rare events (by the nature of probability) happen every game. But when those rare events happen in favor of a given outcome…or over an extended number of games/matches…that's when investigations are done.

Match-fixing

The most obvious (and impactful) way to “fix” a game is to control who wins and loses. Very few players in team sports have the ability to individually determine that, but because many games have a point spread (the amount by which a team will win, not just whether they win) individual players can influence it. By slowing the pace of play, turning the ball over, or intentionally performing poorly, players can “shave” points from their team total.

Further, the game's “over/under” is commonly bet - the total number of combined points - and this is actually easier for certain players to control by simply slowing the pace of the game - not necessarily even performing poorly. As such, subtle action or inaction is harder to detect.

Scandals are not uncommon, though they're less common in the modern era. The most notable recent conspiracy was actually by a referee, whose ability to call fouls can obviously influence who wins and the total points scored.

What's New, Then?

While betting scandals have existed for a long time - the amount of effort needed to successfully (and covertly) pull it off was immense, until very recently.

Remember: data is closely tracked from every game, so a sequence of unlikely, uncommon, or otherwise suspicious events favoring a specific outcome gets flagged.

For most of sports betting history, bettable events were the point spread and over/under: both of which require substantial influence from a player or players (or referee) to “fix.”

With the legalization and growth of sports betting apps - and the hypercompetitive markets to attract players and blatant attempts get them addicted (allegedly) - they will let players bet on almost anything.

That “almost anything” includes the speed or outcome of individual pitches in baseball, whether the “next play” in football will be a run or a pass, and similar granular events that individual players (or coaches) can control - with zero outcome on the game - where players and bettors can covertly collude.

“Covert” LOL

Emmanuel Clase, one of the best pitchers in baseball thanks to his combination of elite velocity and command, is one pitcher implicated in this scandal.

The bet that he would throw a “first pitch ball” is the data point in question. And he almost always did, with the majority of them being absolutely terrible pitches.

Once, twice, even ten of these events spread out over a season…while perhaps suspicious…would probably not have triggered an investigation.

But these gamblers (and players) are not exactly well-reasoned.

Note: data analytics doesn't only apply to the player. It also applies to the bettor!

A bettor who makes money from being the world's best “Clase first pitch ball” bettor - but bets very little on anything else, and few/no other player’s “first pitch” outcome - huge red flag. Especially if this trend is over weeks or months, and he almost always wins.

Greed, Stupidity

Any bettor who hits a large percentage of bets over an extended period of time, or bets large amounts only on oddly specific events, will get flagged.

Anyone who operates in the gray area of covert, “only illegal if I get caught” mindset should understand: a plan is only as good as your ability not to get caught.

If the system observing you is more sophisticated than the system you’re using to conceal behavior, exposure is inevitable.

This is NOT advice on how to get away with it, it is a warning about why weak guardrails make exploits predictable - and why exploits will occur whenever incentives and oversight are misaligned.

The fact that this occurred at the Major League level where players make 7 and 8 figures annually (for alleged returns in the thousands) illustrates both greed and stupidity. But make no mistake: there is potential for larger returns, and ways to avoid being detected. This is without getting into mid and low-tier college programs where thousands of dollars may constitute a windfall.

In sports betting - and investing more broadly - returns do not need to be spectacular to be transformative. A modest but sustained positive return on investment compounds over time. Wealth in markets (betting or otherwise) is built not by winning every wager or scoring massive one-off payouts, but by consistently winning more than you lose, in the long run…and doing it legally, or not getting caught.

A large informational edge becomes obvious if it is exploited too cleanly. A modest win rate over a long period of time is indistinguishable from a mildly sharp (or lucky) gambler.

For that reason, to evade detection, betting on games and players where you have inside information - that is, events where you are ~100% to win - must be “laundered” by random events with no inside information, with bets of similar amounts. Sometimes you'll win them and sometimes you'll lose. But in the long run, by virtue of winning the inside info bets, you'll make money.

Further, even on the player/coach with whom you have inside info, you must make bets on that same subject without it, such that your win rate is not ~100% or even extremely close to it. Sometimes, you will lose money in a given game. The greedy mind will not accept this, but a rational actor must.

In the long run, if you have a substantial edge, preserving it should be far superior to making huge chunks of money in a short period and risking detection.

This is sometimes called avoiding “heat.”

Because of this, the code between colluder and colludee must be flexible: not one variable like “if first pitch → throw ball”

Behavior that varies across multiple dimensions is harder to distinguish from background noise, especially when no single factor reliably predicts the outcome.

There are other wagers for football, like “next play run/pass” that can easily be hidden between conspirators.

Given the amount of money to be made, and the fact that stupid people have been exposed for this, makes it extremely unlikely in my mind that more sophisticated systems are not actively employed right now.

My Recommendation

Ban wagers on individual events where individual players can determine the outcome without any obvious deviation in performance.

They have recently agreed to cap the betting limits for specific bets, but the restriction is simply too narrow. Limiting stake size limits exposure, not vulnerability.

Many single-event wagers can be resolved through perfectly ordinary actions. The speed of a pitch in baseball can be manipulated by throwing an offspeed pitch - no red flags. Whether the next play in football is a run or a pass - also a trivial proposition. These events are all indistinguishable from legitimate strategy, but all can be known with inside information and a mildly complex system.

Sportsbooks make billions in profits, and these types of “more, constant action” events are another mode of profit that serves to increase the addiction of players. There is a medium to be found here.

In short, this is a high-impact, low-cost regulatory fix. Removing wagers that hinge on trivial, individually controlled actions would materially improve market integrity while imposing minimal economic downside - making it one of the most efficient reforms available.

The goalposts will be moved again

You probably do, because outliers like this (which end up looking quite bad) are most memorable. I believe the story of Selzer unfortunately overlaps with the impact of my work: a pollster who was said to consistently have produced the most accurate polls (for decades!) can be tossed aside for - apparently - one “inaccurate” poll. This reality perfectly encompasses the unscientific, statistical ignorance demanded by the field’s leaders.

Analysts love to use terms like “outside the margin of error” despite their published (mathematical) admission that they don't know what it means in relation to poll data.

Two notes from my book:

1. Berkeley Haas researchers:

   

2. Nate Silver's published and apparently peer-reviewed analysis:

and corresponding somewhat technical note:

As readers of my work may understand: this all relates back to the foundational belief that polls are intended to predict election results. They aren't.

And criticizing a poll for being an outlier is nothing new, either.

did the same thing when he criticized a pollster in Wisconsin for having the audacity to release poll numbers with Biden at 57.

Because pollsters know they will be judged by this flawed “polls as predictions” standard, they have no incentive to release data that says anything that sharply disagrees with what other pollsters say.

See a problem with that?

Watch this short clip from my chat on the .

Eat Poo

“Eat poo” might not be the most eloquent way of putting it, but it is a creative way to say that in statistics, there are certain mathematical guarantees, and there's nothing you or anyone can do about it.

It is a guarantee that, given the 95% confidence interval that all scientific polls are reported with, about 5% (1/20) will fall outside the margin of error. Sure, this gets into ideal polls (which political polls aren't) but it hammers home the point of the ideal poll as a benchmark: we know that 1/20 ideal polls will fall outside the margin of error, eat poo. It is mathematically impossible for a non-ideal poll to perform better over a meaningful sample size without herding (nudging their numbers closer to the average under the guise of weighting).

Because of this, it is the more reputable pollsters who are more likely to publish outlier results! Integrity and transparency have become things that the status quo PUNISHES. Pollsters concerned with their individual reputation have no incentive NOT to herd, because publishing outliers damages it. And yes, still needs to shut the f**k up about it - it's literally his fault. (This is a pretty good and Thanksgiving-timely article, read it next maybe.)

Pollsters who publish these polls that turn out to be outliers - in a proper scientific field where weighting techniques were transparent and data not shelved/herded for fear of hurting your reputation - are providing very important data. Only with more scientifically-sound standards (which I have proposed) can these conflicts of interest be resolved. Occasional outliers are not proof (or even evidence) of poor methodology, they are a statistical guarantee. This nuance should not be nuance, it should be common knowledge of people in the field.

Comparing highly transparent, scientific pollsters to unscientific ones like Literary Digest (as Morris did in his book, cited below) serves no purpose except to mislead the public he believes he is informing.

I understand it's not intuitive to accept the fact that a poll that is truly “outside the margin of error” is not necessarily worse than one that precisely measures whatever population parameter. But I do think it can be understood - if these people would stop misinforming the public ffs.

Outside The Margin of Error

For one, and I can't believe I have to explain this, but I swear to you people who literally have degrees in the subject have argued with me about it:

The “margin of error” (given by the statistical formula) and “margin” (referring to the difference between the top two candidates in a poll) are not the same topic.

No, a candidate “up by 10” in a poll with a margin of error of +/- 4% does not have a lead outside the margin of error with respect to the election result.

For one, it's why I use the term “spread” - to avoid such confusion.

Anyone who has ever had to explain to someone that a scientific theory is not the same as someone who says “I have a theory about that” may be able to relate.

If the margin of error in a poll is +/- 4%, and a poll says:

Candidate A: 45%

Candidate B: 35%

Undecided: 20%

Then the margin of error applies to all of those values. In poll data, that means:

Given a simultaneous census, that population would almost certainly (95% confidence) be within the margin of error for all of those options: A, B, and Undecided.

It does not mean, contrary to what analysts seem to believe (and what they teach), that “If polls are accurate then Candidate A should win by 10 plus-or-minus some amount.”

Absolutely not. Not even close.

That calculation requires multiple steps, the largest of which is projecting undecideds, which is not information that came from the poll. As undecideds shrink to 0 at the election, they may break:

• Evenly

• Toward the candidate polling “ahead”

• Toward the candidate polling in “second”

• Toward other candidates, if they exist

• Toward the incumbent

• Toward the challenger

• Toward whichever major candidate shares their demographic profile

• Or in some asymmetric, unpredictable way

If any analyst claims to know the exact probability each of those events occurs, you can guess what I'd tell them to eat.

Given a margin of error of +/- 4%, analysts today, no exaggeration, would claim that Candidate A’s lead is “outside the margin of error.” Yet simple arithmetic would allow you to understand that if 15% of the 20% undecided break for Candidate B, they could win even if the poll was perfectly accurate.

But the reality is even dumber than that:

When grading polls for accuracy, most US analysts just assume undecideds break evenly.

Most non-US analysts just assume they break proportionally to the decided.

Don't think too long about the fact that these assumptions are incompatible but are allowed to co-exist without conflict because f**k science, stay with me on the fact that both of these assumptions are analyst assumptions, not poll assumptions.

You can't say a poll is outside the margin of error because it didn't accurately measure something it didn't try to measure. I mean, you can, but you're just making shit up at that point - and proving you're bad at statistics (fortunate for me). On a similar note, your IQ is 99 because that's what the thermometer said.

To use more appropriate and direct language:

How you think undecideds voted and how they actually voted are not interchangeable.

Your assumptions may be wonderfully reasonable, bless your heart, but they are not part of the measured sampling error. They are model risk, not poll error.

False Precision

When someone tells you who the “most accurate pollsters” were, they are using their country's convention to inform that calculation. Not science, not math, just a traditional assumption.

One day, in textbooks around the world, this will be published in the same chapter as the lesson on Literary Digest.

Remember, that “average error” calculation comes from the assumption that undecideds split evenly, and that no one changed their mind in the last three weeks of the election.

Is that true?

Are you sure? How sure are you?

No one changed their mind in the last week of the election? Not even 1%? We know that's not true - and so do they. Doesn't stop them.

Undecideds split evenly? Exactly 50-50? Absolutely impossible it was 60-40? 40-60? Of course, they could never go something crazy like 66% to one candidate. Probably for sure.

It's remarkably easy to illustrate why this analysis fails: it produces a single number - no margin of error, no confidence interval - where it is mathematically impossible for one not to exist.

This is the exact definition of “false precision” - and for people who work in a field that is literally founded on being honest about uncertainty…you can see why my work (I think) is quite important.

It's ironic, if you think about it: all of the value created by the field of inferential statistics - from which poll data derives all meaning - is quantifying uncertainty! They believe poll error exists…but uncertain model assumptions, undecided behavior, turnout patterns and late shifts simply evaporate by declaration. They claim all of those factors are just “poll error,” too.

Can pollsters be graded? For sure. The question “on what metrics?” can be discussed in a different place.

But can we at least say which pollsters are “more accurate”?

Well, you tell me.

For the 67th time (+/- 57) on my Substack, I'm presenting my “textbook” problem.

But I'm going to ask a bonus question that only very smart people can answer.

I don't want to know which poll was more accurate, because we can all agree (readers of my work, in spite of the worldwide expert consensus) that asking “which poll was more accurate?” Is a stupid question, and concluding that it was Poll 1 is not the right answer.

But there is a real question that needs answered here.

What is the probability that Poll 1 was more accurate?

Provide your answer, guess, thoughts, and/or process in the comments.

Thanks as always.

Check out my full chat on the Talkin' Politics and Religion Podcast on YouTube

Or the podcast/audio version:

Spotify

Apple

But like a good scientist, I'll do a little test. In this article, I'm going to do my best: limited snark and commentary, just facts and data - and an analogy or two.

Help me ruin the results of this experiment by sharing the hell out of this post, tagging your favorite analyst, and posting the link on your social medias, and tagging me.

Why “Spread” Exists In The First Place

The question “who is ahead and by how much?” is a good question to answer, if you can. And it's how poll data is almost always reported: something like “Candidate A is up by 6.”

After which people are then left to their own biases and assumptions to figure out if “up by 6” is a lot, a little, or irrelevant.

50-44 is up by 6.

37-31 is also up by 6.

Are those the same? Similar? Even remotely comparable?

Saying “up by 6” is not right. It’s not even wrong.

There is only one answer to whether “up by” any number is a lot, a little, or irrelevant:

It depends.

For that reason, I have concluded:

Spread is always misleading, sometimes misinformative, and never useful

The more complete answer, which is why I suspect you would read an article like this, is that the utility of “spread” depends on many variables. The three main variables are:

1. How many candidates are there?

   a. How much declared support does each have?

   b. If there are more than two options, what are the respective ideological overlaps with the main options?

2. How many undecided voters are there?

3. How much time is left for things to change between the poll and election?

and other analysts taught us to use the "spread" as a proxy for win probability: "up by" bigger number equals better chance to win. Famously, Silver published this in 2012 regarding Obama's chances:

In fairness, this idea feels logical. Being up by more should be better.

But much like the idea that the Earth is stationary (I don't feel like it's moving, do you?) what feels logical isn't always true. And the scientific consequences of using an invalid assumption because it “feels logical” without subjecting it to serious inquiry can cause a cascade of misattributed errors.

A flawed premise doesn’t stay small; it becomes the starting point of an entire analytical system, and every calculation built on top of it inherits and amplifies that original mistake.

The Spread-Win Probability Model

Without boring you with the process of my research and my book, I'll summarize by saying that the fact that I publish in this field is entirely thanks to my background in science and building predictive models for sports and human performance, and that I was bold (or arrogant, or lazy) enough to try and build a forecast before studying existing forecasting approaches.

Instead of copying other models and trying to innovate within that framework, I approached the “forecast” problem as if it were novel - starting from scratch. Not because I thought I could do better - simply because I liked the challenge. I very quickly noticed some discrepancies between my work and others.

My forecast uses poll data, other forecasts use poll data. Why, then, do we often come to very different win probabilities even in races that are highly polled - such that polls comprise almost all (or all) of the inputs to the model?

The first, most notable discrepancy between my forecast and FiveThirtyEight was this forecast for Maine in 2020:

Our inputs were almost identical - aside from that “undecided” allocation -

Nonetheless, despite Biden's “13-point lead” in Maine, according to FiveThirtyEight, Biden had a 10% chance of losing.

(Remember, just two elections prior, he claimed a 3-point lead yielded a win probability near 90%…ad hoc math is common in pseudoscience)

My forecast used a nearly identical poll average to yield a “Biden loses Maine” probability of…less than 1%.

You may or may not appreciate the significance of that difference, but consider a hypothetical wager: Setting “fair odds” at 10/1 versus 100/1 are different universes.

It is, roughly, the difference between correctly guessing a coin flip 3 times in a row…versus 7 times in a row.

As confident as I may sound about my conclusions today - please understand, it is only because of extensive research and attempts to disprove my own work that I have developed such confidence. The downstream impacts of my research - such as improved forecasting - is small compared to the underlying statistical methods: how to analyze poll data, and how to teach inferential statistics.

Nonetheless, at the very early stage of my research outlined by Maine 2020, my default assumption was that I was the one missing something.

Eager to figure out what was missing, instead of assuming I was right or wrong. I simply…researched it. My working theory - which informed my forecasts - was as follows:

• Because polls can only tell you approximately how many undecideds there are (not who they'll eventually support) poll numbers represent an approximate base of support for each candidate, not a prediction or projection. This logic comes directly from the Margin of Error formula itself, which tells us that inferring anything more from the data than “this is approximately the state of the population right now” is inappropriate.

Therefore

• Candidates should very rarely underperform the percentage given by their poll averages: undecideds can only add to their total in the election result. More undecideds should make it more rare.

Therefore

• Candidates whose poll average is at or near 50% should almost always win. Regardless of other variables - the number of candidates, undecided voters, or any other variable - 50% (in an election) guarantees victory. While 50-45 (+5) in polls should be much stronger - all else equal - than 50-48 (+2)…

• Smaller leads closer to 50 should yield a higher win probability than larger leads farther from it.

These are all easily testable concepts, and I had no issue subjecting them to testing.

That last, bolded point is, perhaps, the sharpest distinction between my hypothesis and the field's consensus - and the one most easily tested. A couple more testable concepts that can be drawn from this theory:

• Not all six-point leads yield a higher win probability than all three-point leads.

• You can't even logically conclude that the candidate with the lead in a poll average is favored - because future preference of those polled as undecided, and to an extent, polled third-party voters - can only be modeled as a conditional probability, not an unconditional one.

None of the above can make sense - or be true - under the Silver-Spread model that:

• Similar spreads should produce similar win probabilities.

If it needs to be said, the competing theories are irreconcilable.

Because this is a phenomenon capable of being studied, I'm not particularly interested in hearing people's opinions about it. It doesn't matter how experienced you are, or what your degrees are - we can test it.

Indeed, my “debate” with resulted in him simply making claims without any data to support it:

Yes, the margin of error applies about equally to both cases…and the margin of error applies to the numbers for each candidate, not the spread. The margin of error also applies to the number of undecideds.

A small overestimate of the candidate “ahead” in the former example results in them still having 50% support. They win; there is no quibbling about probability here. The same overestimate in the second example gives the “leading” candidate only 46% support - they might not win.

In the former example, a small underestimate of the leading candidate’s support would place them at 52%; again, they win, there is nothing to debate. An “underestimate” of the same size for the latter example puts them at 48%; again, they might not win.

If being theoretically true is not enough for your taste, my work proved it’s wrong historically too. And it's not even close. It's so not even close, that I'd wager even after reading about how not close it is, you still underestimate the magnitude of difference.

I find this kind of research fun, because science and statistics allow us to measure and quantify things we cannot intuitively understand. It's a testable claim, so I tested it - apparently a novel approach to some. Feeling as though something is “intuitively” true, therefore doesn't need testing or data to support it, is a violation of the most basic scientific principles.

And that's what continues to astonish me about this field: how confidently many make claims like the above without ever examining supporting data. “Spread” is accepted as settled science. That disconnect between tradition and science is one reason my tone is sometimes interpreted as abrasive: an expert’s confidence is not a substitute for a newcomer’s evidence. I may be the “newbie,” but seniority does not determine the truth (this is the Planck Principle, in nicer terms).

I would strongly encourage any other interested researcher to replicate my findings, because reproducibility is a major principle in science - and more people researching what I have researched will lead to more people reaching the same conclusions…and better informing students and the public. And it is very likely that others researching the topic from a different background will lead to findings I have not yet even considered.

For my research, I used RealClearPolitics data going back to 2004 for highly polled, statewide races. Not because their poll averages are a gold standard - simply because they have a long track record, and their methodology (as of 2022, anyways) is transparent. Others can use whatever method you'd like.

Below, I plotted all of the data points - leader’s poll number, and “spread” lead. All of the races shown below had a spread of 4 or less.

Gray = loss

Black = win

What do you notice?

The numbers can be squeezed even more, to a spread of 3:

Note - my book contains this data through recent elections, here, I'm including through 2020 because that's where my research began.

Note how drastically the win-loss percentage shifts at 48 and 49%. My theory would assert that it's not a coincidence - it's an inevitable mathematical consequence of polls being generally accurate, and serving as a base of support.

Followers of the “spread” hypothesis must believe this relationship is strictly coincidence, and unexplainable.

We can't both be right. This are irreconcilable and mutually exclusive findings.

And this is where the standoff currently stands between my published work, which predicts that this phenomenon should exist, and the field's consensus, which cannot explain it (and doesn't even know it exists!).

But the value of science and statistics is not only informing predictions. It is not only in presenting data. It rests in explaining why patterns occur, and revealing where and why conventional reasoning quietly breaks down.

My attempt to quantify, understand, and ultimately teach these concepts have gone from a narrow application of political polls…to a broad and honestly remarkable process of changing how inferential statistics can be understood in the first place. A few examples:

Ideal Polls: polls whose only source of error is the margin of error itself

Plan Polls: polls that ask about a future preference (i.e. one can logically be undecided and/or change their mind)

Present Polls: about a current or past state (i.e. cannot logically be undecided and future mind changing is irrelevant to the question)

Simultaneous Census: The “true value” that polls attempt to measure.

The mathematical reasoning as to WHY Spread fails to be a useful metric can be expressed a few different ways.

One that appeals to people both logically and mathematically is the concept of dimensionality.

The Dimensionality Problem

In science, dimensionality refers to the number of data points needed to specify a point in space.

In the SIMPLEST cases, elections have two options: I'll call them A or B.

However, pre-Election data has THREE options (A, B, Undecided)

Since poll results must always sum to 100%, the number of data points needed to specify a point in “poll” space - in the simplest, two-option races - is two.

If you know A and B, you can infer undecided. If you know B and undecided, you can infer A…and so on.

Since you need two data points (representing two degrees of freedom) the data can be plotted, completely, with zero loss of information, in a two-dimensional space.

Here, a poll of:

Candidate A: 46

Candidate B: 44

Undecided: 10

Is shown by that little black dot

All possible poll outcomes occupies exactly one point on this plot. Every possibility is covered.

The same cannot be said for the one-dimensional representation given by "up by 2"

"Up by 2" can mean...very many different things IN POLLS.

If you are restricted to one-dimension (a line segment from 0 to 100) then 51-49...50-48... 42-40.... 20-18.... Are all plotted on top of each other.

This is known as dimensionality reduction.

All dimensionality reduction loses some information. This is not inherently a flawed process - our brains are generally not well-equipped to intuitively reason in spaces beyond three or four dimensions, and even when we can work with higher-dimensional data mathematically, simplifying that data can have practical value. The key is understanding which information is lost, and whether that lost information is relevant to the conclusions we draw.

Most people are familiar with map projections like Mercator. In school, though they may not teach it in such a technical way, we are taught that the map is distorted. Squeezing three dimensional data (a spheroid) into a two-dimensional surface (a map) causes PREDICTABLE DISTORTION.

Greenland isn't this big - not close. It's not that the Mercator projection is useless, however: the projection preserves ANGLES for navigation, at the expense of SIZE.

The distortions are a trade-off. More importantly, they are known/knowable, and quantifiable.

People who understand how the Mercator projection works would not use it to make claims about size. For example, someone who looks at this map and says “Greenland is bigger than Australia” would be wrong. Yes, if you measure the two with a ruler, Greenland certainly appears bigger on the map - but they're ignoring the information lost in the projection.

Similarly, analysts who use “spread” across elections with varying numbers of undecideds, and varying numbers of people who say they support third-parties, are illustrating that they do not understand the tool they're using and the information lost in the projection.

In the map analogy, it's like comparing the sizes of different countries using the Mercator projection, because Brazil versus Libya are “basically correct”…Venezuela versus Mauritania is “basically correct”…and as for Canada versus Russia..well how bad could it be? (And that's as far as the internal critique goes).

Even in the simplest case, reducing (A%, B%, Undecided %) to a single “spread” number throws away crucial information about undecided voters, yet the resulting one-dimensional number is frequently treated as if it fully captures the underlying state of the race.

A direct point to prove this for those who don't like analogies…consider two polls taken in different elections:

34-30, with 36% undecided.

51-47, with 2% undecided.

Both can be simplified to “up by 4”

Indeed, in analysis done by organizations like AAPOR and British Polling Council, elections with results literally this disparate are put in the same category. But it's an easily-noticable error:

Do the candidates with the lead have equal win probabilities? Why or why not?

Is the probability of a 4 point “error” (as currently defined: poll spread minus election spread) equally likely in both scenarios? Why or why not?

Because we logically understand that undecideds represent a source of uncertainty, most people would draw the theoretically correct answer (which is empirically verifiable): the win probability and range of likely outcomes is much wider with more undecideds.

But the existing methods are definitionally incapable of explaining that simple fact.

Methods that are incapable of explaining empirically verifiable behavior cannot claim to measure reality.

Yet analysts use spread as a “gold standard” metric.

My research - which starts by testing “extremes” like 36% undecided vs. 2% - has shown that even seemingly small differences (like 5% vs 10% undecided) are remarkably different - defying intuition- because our minds default to a linear space and the relationship appears to be exponential. Getting ahead of myself.

With Spread, there is no comparable utility to Mercator other than the fact that one number (up by 2) is easier than two numbers (46-44).

And with Spread, because of how polls are improperly analyzed and judged as if they are predictions:

This one-dimensional, incomplete, distorted piece of data is used to yield a projection of what the election result "should be.”

Up by two in the poll? Well, if they win by two the poll was accurate. If they win by 6? Poll was off. If they lose? Poll was off. The existing analysis is literally that simple.

What's happening is that, implicitly, undecideds are "projected" evenly to the two candidates.

46-44 -> 51-49

42-40 -> 51-49

And so on

The piece of data lost in this one-dimensional spread analysis is the (approximate) number of undecided voters

Given a poll of 46-44 with 10% undecided, it is not hard to see how even a VERY ACCURATE poll (by the appropriate simultaneous census standard) could yield a result rather far from "Candidate A up by 2"

Undecideds splitting unevenly - even just 60-40 - creates major projection problems.

As illustrated above, a 60-40 split of just 10% undecided yields a two point discrepancy between the poll spread and election spread, even if the poll were perfectly accurate. This discrepancy is misattributed as “poll error” by analysts using the one-dimensional spread metric.

Many people believe “two points” of error - in this 60-40 example - is not enough to concern themselves with. This kind of goalpost shifting may be appropriate for a social media forum of laymen, but it is not acceptable for scientific discourse.

The debate is not surrounding the significance of two points of error. The point is that given this very modest example, this method has provably assigned two more points of error to the poll than the poll had. If we can agree that the method used is imprecise, I would accept that as a starting point for true scientific progress. But, as of writing, it has not. This is proven by the fact that analysts like , , and … literally every other I've ever read…believe Spread alone is a viable metric for declaring which pollsters were most accurate in any given election.

My classic, “textbook” example:

Given a population at the time the poll was taken of “45-45-10” the polls each had an identical, small, absolute error.

Yet, that's not at all what the existing methods would calculate. A small error in the “wrong direction” is punished. A small error in the “right direction” is lauded as “more accurate.” It's hindsight bias and hot-hand fallacy masquerading as science.

It’s a mental motte-and-bailey, to protect the existing “spread” metric for no reason other than status quo bias. They analyze my example as “not that big of a deal” … and use that “close enough” mindset (the motte) - which has no place in a reputable statistical field - to ignore the imprecision inherent in their analysis, and assert spread as a gold standard (the Bailey).

If two points isn't important, then why are polls with two points of “error” considered pretty accurate…but four points of error said to have “missed”? It's irreconcilable.

Using “Spread” to compare poll data to election data is like using “Mercator” projection to compare the physical size of countries. Sometimes, this metric will correctly identify which poll had more error - and which country is larger. Sometimes it will fail. But there is always a distortion created when you use either method due to the dimensionality problem.

Inability - or refusal - to acknowledge a model’s distortions is not a defense of the tool; it's an admission you don't understand the tool you're using.

There is no other explanation for using Spread as a meaningful metric - and it's currently used as a gold standard.

If you want to help me fix it, you can contact me.

Support my ability to fix the unscientific conventions of the field by liking and sharing this video, as well as the podcast itself.

Perhaps relevant to folks like , , , , , and others you are encouraged to tag in the comments.

Get the full version here on YouTube

Or the podcast/audio version:

Spotify

Apple

Junk math, invalid science, misleading the public - never solving problems.

Polls are not predictions.

The field will move forward with or without you. Do let's focus on fixing it quickly and informing the public so we can solve harder problems.

In short, not much has changed from the forecast a week ago. Mamdani remains a strong favorite, though the probability he wins by 20 is slightly lower than last week’s forecast.

NYC Mayoral Forecast

Important to note that the numbers on the chart are medians listed for clarity…not projections.

Go ahead and skip to the NJ Forecast if you don’t care about math stuff.

With three candidates receiving a large number of votes (and the third-place candidate being somewhat closer ideologically to the second-place candidate) there’s a very big strategic voting problem forecasters have to account for. Basically, it’s far more likely that someone who is polled as a Sliwa supporter - if they change their mind - votes for Cuomo.

Good forecasts can account for this, mine does, but a lot of analysts simply ignore this problem as non-existent. Because they think polls and forecasts are the same thing.

Basic science calls this a “confounding variable.”

Slightly less basic science refers to this as a dimensionality problem. If you want to read more about the problems with projecting a 3-D world onto a 2-D map…or a 2-D election result onto a 1-D representation of it (which is the field’s worldwide practice!) you can read a bit more in depth here.

The short version - a big part of which inspired me to make forecasts and get involved in the first place:

There are two methods for calculating poll accuracy; they are mathematically contradictory, used interchangeably by analysts, but both assume that accurate polls will predict the election result, and that third-parties are irrelevant. Given the NYC Mayoral poll averages, here is what each method would say for the below election results:

Two-dimensional.

But below, the one-dimensional line-segment that analysts force this two-dimensional data onto.

The problem here is that “undecided” and “third-party” are forced into the same bin - due to the loss of dimensionality - when we know they’re not the same. This is not good science and I plan to fix it. End of rant for now.

NJ Governor Forecast

A little easier in terms of forecasting - though a lower win probability - Sherrill has consistently polled in the upper 40s. I wrote a whole ass book based in part on the significance of this discovery - and the underlying statistical and scientific reasons no one else in the field knows or cares about it.

49% in polls is very strong, but it is not as strong as 50%. Those numbers feel close but the relationship is not linear in terms of win probability - it's exponential. Sherrill is a big favorite - stronger than the surrounding commentary seems to think. But there's no such thing as certainty.

California Prop 50

There’s no such thing as certainty…but this one slowly approaches it.

The only reason I can’t be more certain (i.e. a narrower range of outcomes) is the relative lack of polling and precedent. But this one is almost certain to pass.