Daters, scammers, and Zeckhauser

Maxim Five: low probability events

When a low probability event occurs (say an underdog wins a sports championship), we tend to come up with reasons why we might have expected it. This phenomenon is often referred to as hindsight bias, a tendency to perceive past events as having been more predictable than they actually were. But if we consider that many events occur in a year, we should expect at least some to be low-probability events. For example, there are many championships in a given year, so we should not be surprised that every year there is a championship outcome in some sport (say tennis, golf, football, etc.) that no one expected.Dan Levy, Maxims for Thinking

Something is always happening because with enough parts, something happens. The odds that one low-probability event, a 100:1 long shot wins an event, occurs is low. But the odds that any low probability event occurs is fair. Tonight many people will go to many bars. To bet that Your Friend will meet their spouse is ridiculous. To bet that Anyone’s Friend will meet their spouse is a no-brainer.

The bar points out the mechanism we use everyday: a filter. Not everyone at the bar will be there to meet a spouse and those that are there for that will very likely leave without doing so, but being at-the-bar is the filtering mechanism. It’s the same mechanism the Nigerian Prince uses.

It’s well noted that scamming emails contain misspellings, outlandish claims, and hard-to-swallow facts as a filter. A scammer, like a dater, only wants to draw from an eligible pool. And the scammer and the dater both have the same reason: resources. A scam email has minimal costs. A visit to the bar has minimal costs. These filters have to exist because the follow up is expensive.

Something is always happening, but we often don’t want ‘something’. We want ‘this thing’. One tool is to increase the probability (p) it occurs. Go to the coffee bar. Send the email with mistakes. Another tool is to increase the number (N). Will Michigan ever lose again as a thirty-point favorite? Maybe. Will a division one football team lose as a thirty point favorite? Probably. Will any football team lose as a thirty point favorite? Definitely.

Low probability events will always occur and the mechanism of a large Number or rising probability influence how often. Maxim 5 is “the world is much more uncertain than you think.” Levy, writing about Richard Zeckhauser notes, “so the next time you find yourself thinking that some event will happen for sure or that some other event has no chance of happening, pause to remind yourself of this maxim.”


Thanks to Eric Bradlow on the Wharton Moneyball podcast for articulating the idea “large N small p”.

Favorites or the field?


The top five S&P companies account for 22% of the index’s earnings and a similar percent of the market cap.

“To me that is an interesting market question right now. If you were a betting man would you take the other 495? Would you take the field or would you take the Lakers with LeBron, a healthy Anthony Davis, James Harden and Kevin Durant on the team too?” – Carl Kawaja, Invest Like the Best, July 2021

One way to improve decision making is to understand the mechanics of a system. The physics system for example is relatively stable and that’s why, with great work, engineers can land the Perseverance rover in a Martian area twice as wide and one-third as long as Manhattan. Other systems, like social systems, follow the rules of network effects like the friendship paradox.

Sometimes analogies help to understand the type of system. One sporting analogy is to take the favorites or the field. When Kawaja’s episode was released, the Chiefs and Bucs had a cumulative 33% chance to win the NFL big game. Sports vary though. In January 2020, three NFL favorites had cumulative odds of about 30%. Meanwhile the top three NCAAF football favorites had odds of about 75%. Three tennis players at the French Open get a bettor to better than ninety-five percent. Want to bet the PGA Master favorites? The top seven golfers only get you better than a coin flip.

Odds in January 2020

One reason to take the field is that more can go wrong than go right. Something is always happening and it’s more likely to be a “negative tail” event than a positive one. During the 2020-21 NFL season we guessed that Tom Brady would not hit the over on passing yards (he did) by guessing that injury, Covid, and new teammates had a much larger downside area. Kawaja recognizes this too, noting “guys get injured”.

It’s not that the field or the favorite is better, but which is cheaper relative to the expected returns. During the Big Game for instance, things happening (safety, two-point conversation, etc.) are priced higher because people like to bet more on something happening. Successful betting and investing isn’t about finding the best, but finding the best odds. Yes, the Chiefs and Apple are great teams but is there value in the high prices?


Physics systems or social systems are wonderfully illuminated in Nassim Taleb’s book Antifragile.