Odds and Ends: Week 16

How "the law of small numbers" makes bettors look better.

Adam Harstad's Odds and Ends: Week 16 Adam Harstad Published 12/18/2025

© Corey Perrine/Florida Times-Union / USA TODAY NETWORK via Imagn Images odds

A good sports betting column should be backed by a profitable gambler with a proven track record. It should offer picks generated by a sophisticated and conceptually sound model. Most importantly, it should treat the subject with the seriousness it warrants.

This is not that column.

Instead, this will be an offbeat look at the sports betting industry-- why Vegas keeps winning, why gambling advice is almost certainly not worth the money, and the structural reasons why even if a bettor were profitable, anything they wrote would be unlikely to make their readers net profitable, too.

While we're at it, we'll discuss ways to minimize Vegas' edge and make recreational betting more fun, explain how to gain an advantage in your office pick pools, preview games through an offbeat lens (with picks guaranteed to be no worse than chance), and touch on various other Odds and Ends along the way.

Why Don't Touts Pick Every Game?

One of this column's main theses is that anyone selling you gambling advice (at least as far as game picks are concerned) is scamming you. Beating Vegas is hard, and while there are people out there who can do it, they don't talk about it because Vegas will shut down their edge. The only people for whom talking about betting is more valuable than betting are people without an edge. Making picks is risky, but selling picks is risk-free.

Selling picks isn't easy, though; lots of people would love a slice of that action, so you need some way to differentiate yourself and hook an audience. Sometimes they'll resort to genuine scams, but most often they'll just rely on aggressive marketing (the term "tout", after all, means to promote or to peddle).

It'd be fairly trivial to apply my "model" to each game and make up some nonsensical justification for each pick, so why don't I pick every game every week? Because I'm satirizing touts, and most touts don't pick every game every week. 

Why don't most touts pick every game every week? I think there are two primary reasons for this, and both go back to marketing, to manufacturing the illusion of an edge.

Reason #1: Good Models Pick and Choose

If someone wanted to beat Vegas, they would build a projection model, find places where their model differed from Vegas' line, and then bet on their model. The bettor's advantage (one of the very few advantages available to them, in fact) is that they get to pick and choose which games to bet on. Their model doesn't have to outperform Vegas in every game; they merely need to know which games it outperforms Vegas in.

In fact, most long-term profitable sports bettors will agree with Vegas more often than they disagree. They will be uninterested in most of the lines Vegas is offering because their model tells them those lines are largely correct.

If a tout wants to look like a long-term profitable sports bettor, it helps to create the illusion that you have a model that likes some games more than others. But this is just an illusion. The biggest giveaway? The regularity of the picks. Someone with a genuinely profitable model might have some weeks where they don't love any lines and other weeks where they love lots of lines. But touts typically have exactly one "lock of the week" every week. If you're making picks, "I'm going to sit this week out because I don't see an edge" is a very profitable decision. If you're selling picks, though... well, that's not exactly going to fly.

Reason #2: The Law of Small Numbers

The Law of Large Numbers is the mathematical law stating that if you run a trial enough times, the distribution of outcomes will eventually converge on the true underlying distribution.The Law of Small Numbers, therefore, is the idea that if you run a trial few enough times, you're much more likely to get outcomes that radically diverge from the true underlying distribution.

Let's say I'm a 50% bettor (which, incidentally, is true; I have no edge whatsoever). Because of the vigorish, if I make all my bets at the standard -110 odds, I need to get at least 52.4% of my picks correct to remain in the black. What are my chances of hitting that mark?

There are 272 games in an NFL regular season; if I pick every game, there's a 21.53% chance I at least break even on the season. (As an aside: Is this higher than you'd think? If so, this is why Vegas keeps making money; there's a very reasonable chance for hot streaks to persist long enough to convince any bettor that they're a genuine reflection of skill and not a fleeting mirage.)

What if I pick three games a week, instead? That's 54 total games for the season; now my odds of finishing in the black jump to 34.17%. I've gone from about 1-in-5 to about 1-in-3.

But that's with just one iron in the fire. Let's say I also add a "lock of the week". With just 18 picks, there's a 40.73% chance I turn a profit for the season.

Reason #3: The Forking Paths Problem

And what if I combine the two approaches? If I have a three-pick slate and a one-pick slate every week, there's a 61.99% chance that one or the other is profitable on the season. If the three-pick slate is profitable and the "lock of the week" is not, I can say "the lock didn't work because of small samples, but my larger body of picks shows my model works". If the lock turns a profit and the larger slate doesn't, I can say "we struggled in the games the model was lukewarm on, but the evidence in the games it likes the best speaks for itself".

This process where you look at the outcomes and then decide after the fact what is meaningful is called the "garden of forking paths problem" and is a big reason why most scientific research from the last 30 years is failing to replicate; researchers gathered the data and then looked at it to see what kind of statistically significant results they could tease out of it.

Once you're aware of these kinds of sleights of hand, you start to notice them more. How about shows or columns that have multiple experts making picks every week? Some of those experts will wind up with a good record (law of small numbers) and casual bettors will start to tail their picks specifically (forking paths problem).

Now, the downside of the law of small numbers is that just as you're more likely to finish with an extraordinarily good record, you're also more likely to finish with an extraordinarily bad one. If you're a 50% bettor, your odds of finishing with a 33% success rate or lower over a full slate of 272 picks are approximately 1-in-100,000,000. Your odds of finishing there over 54 picks, by contrast, are 1-in-100.

But there's a lot less consequence for being extra wrong. When you're trying to sell your picks, it doesn't really matter whether your record is 33% or 45%, no one will be buying either way. And anyway, you can just forking-path away your bad samples and generate new ones, each with their own opportunities to compile implausibly good records.

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