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## Dealing with probabilities in real life

Posted by Victor Wang at 1:04am

I had an interesting dilemma a few days ago. The sports analytics club that I run on my college campus was having its first meeting of the quarter. However, that night wind chills were projected to be between -25 to -30 degrees. The weather next week was projected to be a little bit warmer. Obviously a club wants to maximize the number of participants that attend. If nothing else was being considered, I probably would have canceled and rescheduled for next week. However, I had other variables to consider including a speaker coming in the next week and the need to gather information from club members for bringing in a potential speaker.

Ideally, I would be able to know the probability of each person coming to the meeting in the cold weather versus coming to a rescheduled meeting. I would also be able to know the probability of getting the first meeting rescheduled in time before our first speaker was scheduled. However, I did not have these probabilities and had about one hour to make a decision.

Why am I bringing up this situation? It reminded me that when we're dealing with decision making in the real world, we don't have nice textbook-style probabilities in front of us. This brings to mind what Nassim Taleb calls the ludic fallacy. The ludic fallacy is defined simply as the use of games and textbook examples to model real-life situations incorrectly.

Relating this to my situation, we can see that there were no probabilities given to me. In fact, even if I'd had the time, it would have been rather difficult to acquire the exact probabilities I needed. And who knows how long that would have taken. Real-world decision making often involves a number of complex variables that are difficult to model. This is not to say that I disagree with attempting to use analytics in decision making. If a company has the resources to model its situation, by all means I think it should ago ahead and do so.

Another example of the difficulties of using probability in real life is given by Taleb, which we will apply to baseball. You often hear the expression that a player is essentially a "lottery ticket." What is meant by this is that he has a very low chance of succeeding, but if he does succeed, his impact will be very large. However, with lottery tickets we know the exact probabilities. We can calculate our expected value of buying the ticket. While progress is being made, we can't calculate exact probabilities of how a player could perform. If a player truly were a lottery ticket, we would be able to calculate these probabilities and we could figure out that player's value for every team.

In fantasy, we face a similar situation. We aren't given basic probabilities for any players. A few systems give percentiles, including THT's projection system which will soon include these, but these have yet to be empirically tested. And even if we could project a range of outcomes, this doesn't account for the number of additional things that can occur in real life. For example, we don't know the odds of a player having a freak injury. We also don't know if a player is suddenly going through personal struggles. There are many more examples of such events that could occur.

In conclusion, I think it's very important to remember that we'll never have probabilities in the clear-cut way a casino has them. There will always be some degree of subjective belief we'll need to incorporate, at least for the near future. So keep in mind that while our projection systems and statistical analysis continue to improve and become more accurate, there will always be an element we can't model.

Victor Wang's work on OPS has been featured in SABR's By the Numbers magazine, and was the 2007 recipient of SABR's Jack Kavanagh Memorial Youth Baseball Research Award. He can be reached via email here.

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