Photo: Kirby Lee, USA Today Sports

Gambling on the NFL is big business, especially after a 2018 Supreme Court decision striking down a federal ban on sports betting. Recent estimates suggest that as many as 46.6 million people will place a bet on the NFL this year, representing nearly one out of every five Americans of legal gambling age. As a result, there's been an explosion in sports betting content, most of which promises to make you a more profitable bettor. Given that backdrop, it can be hard to know who to trust.

Fortunately, you can trust me when I promise that I'm not going to make you a more profitable sports bettor. And neither will any of those other columns. It's essentially impossible for any written column to do so, for a number of reasons I detailed here. (I'm not saying it's impossible to be profitable betting on the NFL, just that it's impossible to get there thanks to a weekly picks column.)

This column's animating philosophy is not to make betting more profitable but to make betting more entertaining. And maybe along the way, we can make it a bit less unprofitable in the process, discussing how to find bets where the house's edge is smaller, how to manage your bankroll, and how to dramatically increase your return on investment in any family or office pick pools (because Dave in HR and Sarah in accounting are much softer marks than Caesar's and MGM).

If that sounds interesting to you, feel free to join me as we discuss the weekly Odds and Ends.

"Unders" Update

I figure we'll just make it a weekly feature to track the performance of "under" bets through the season. Last week the unders went 6-8, which leaves them 37-33 since we noticed how well they were performing five weeks ago.

Sam Bankman-Fried Apparently Doesn't Read Odds and Ends

For those who haven't been following the saga of Sam Bankman-Fried (or "SBF"), CEO of a company called FTX that was one of the largest cryptocurrency marketplaces, he's been having a very bad couple of weeks. On November 8, it came out that FTX had been taking customer deposits and, rather than holding them, loaning them out to a cryptocurrency hedge fund to make leveraged bets with them. Those bets did poorly, FTX lost most of the money, and when customers went to withdraw their deposits the company couldn't oblige, resulting in a bank run that drove the company to bankruptcy.

SBF lost 94% of his net worth in a single day, falling from over $10 billion to "just" $900 million, the largest single-day drop in history. His net worth would continue its freefall as more and more financial malfeasance came to light until he was left with functionally nothing.

Over the last few weeks, I've been inundated by concerned readers who were terrified that they'd be the next SBF, so I wanted to write a few words explaining just how unlikely it would be that you, an enlightened reader of Odds and Ends, would make the same mistakes SBF made.

Let's Talk About Kelly Criteria

Back in Week 8, I talked about the importance of bet sizing and walked through the math to determine what percentage of your bankroll you should bet to maximize your return. The formula I used determines the "Kelly criteria" or "Kelly bet", which is the mathematically optimal bet size to maximize wealth growth (provided you know the true odds underlying the bet). That bet was often surprisingly small even for extraordinarily favorable bets. (If Vegas paid you a 10% vigorish for every bet you made, you should still not bet more than 1/12th of your bankroll at a time.)

In December of 2020, SBF posted a Twitter thread that demonstrated he knew the math behind Kelly bet sizing. He mentioned a hypothetical game that paid out 10% of the time but returned 10,000 times your initial stake when it hit. This is an exceptionally good bet-- the expected value of it is 1,000 times your initial bet. But even with a bet this ludicrously favorable, Kelly criteria suggest a conservative bet of just 10% of your total bankroll. (Technically, 9.991%.)

And after clearly posting the correct answer to the problem, SBF indicated that he just... disagreed with math, I guess, and he'd be willing to bet 5x Kelly on this hypothetical bet. He framed this in terms of having a higher risk tolerance and wanting to maximize earnings so he could donate to charities and improve the world. But again, the Kelly criteria is the value that maximizes long-term growth. If you're routinely betting 5x Kelly, the odds of it resulting in more wealth than purely Kelly bets over a long timeline is astronomically low; the most likely outcome is bankruptcy.

In theory, if you just handwave away the math and say "let's assume I'll be extraordinarily lucky", betting higher than Kelly can maximize long-term wealth growth. If you assume that your outcomes will fall within the 90th percentile (meaning if 100 people made 100 similar bets, you'd win more than about 90 of them just through pure luck), then the bet size that maximizes expected wealth is 1.8x Kelly.

How lucky would you have to be for 5x Kelly to maximize wealth growth? I'm not sure. This blog post attempts to answer the question but the resulting point was so rare that he broke his computer attempting to find it; even in the 99.99th percentile for luck optimal bet sizing was still just around 3.2x Kelly.

Now, this is bet sizing in a theoretical world where we know a bet's true payout and odds. In the real world, bets are never like that; our model might say that the Giants are 55% likely to cover the spread, but our model is probably off and maybe the true value is 48% or 63%. As a result, real-world bets are typically done at "fractional Kelly" (half or even a quarter of the calculated Kelly bet size).

Betting several times Kelly isn't just an insane amount of risk; it's dramatically reducing the amount of money you're expected to make. SBF knew the math, but he thought the laws of math simply... didn't apply to him, I guess. Which is why I'm confident that if any of my readers ever find themselves operating out of a drug-fueled compound in the Bahamas while making bets with tens of billions of dollars, they would never make such a rookie mistake as betting so far beyond the optimal amount. The reason for betting such a tiny fraction of your total bankroll on any one bet (no matter how juicy) isn't anything as lame as risk aversion. It's because those small bets are the best way to maximize your long-term growth and not go bankrupt in the process.

Lines I'm Seeing