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”.