Empirical evidence shows...

that every odd numbered blog post of mine is about football. I read an intuitive proof to the fact that coaches are too conservative when making 4th down decisions. It goes as follows, consider how you feel when the opposing team trots out their punter when they have 4th and 2 at the 50 yard line. Most fans (including me) are relieved. Because I am rooting for the opposing team to do a certain action, and because in the end a football game is zero-sum, that action is bad for the opposing team. At first I bought this as a valid argument.

However, if fans are risk averse in probabilities of winning, then it could be that both sets of fans are rooting for the same action. Romer suggests that one explanation to the 4th down question is that coaches, fans, etc. are risk averse in probabilities of winning. They prefer a sure 50% chance of winning to a 50% chance of having a 70% chance of winning and a 50% chance of having a 30% chance of winning. The conscious part of the brain initially registers this idea as ridiculous, the team either wins or not, so that's all I should care about.

Consider the following thought experiment, ignoring how it would destroy sports. You think your team has a 49% chance of winning the game, and are given the option that the coin flip determines the result of the game. Then you are choosing between having a sure 49% chance of winning after the coin flip, and having a sure 100% chance with 50% probability and having a 0% chance with 50% probability after the coin flip. Now my conscious mind would probably prevail in this situation and take the coin flip, but my unconscious mind would be screaming bloody murder. And to be honest, if someone else was making the decision, I would probably be relieved if they chose the 49% sure thing. I would also have more regret if choosing the coin toss option over the 49% chance option.

It seems a bit strange for football fans to get utility out of the probability of their team winning rather than just the end result of winning or losing. But if the Eagles are winning by 30 points at the beginning of the 4th quarter, my happiness does not increase very much throughout the 4th quarter and after the game when they win. This does not seem as strange. The probabilities of winning are acting as value proxies for the ultimate desired outcome of winning the game. Just as the bell becomes a value proxy for Pavlov's dogs, the probability of winning becomes a value proxy for a fan base.

There are easy evolutionary reasons for both risk aversion and value proxies. I do not see an evolutionary reason for risk aversion in value proxies themselves, but given that evolution works in a series of kludges, it is plausible that we developed value proxies and risk aversion independently, and that having them both is better than having just one, even if it means we sometimes make sub-optimal decisions when being risk averse in our value proxies. In addition to being able to understand run-on sentences, maybe the conscious mind of humans is the closest thing evolution has come to eliminating risk aversion in value proxies.