The Pujols signing is interesting in that it’s taking place in an era in which we have vastly more information about likely long-term player value than we had even a few years ago. There are a couple of complicating factors to analyzing the Angels’ decision. First, it’s unclear that Pujols will actually turn 32 next month. If he’s even a year or two older that changes the calculus significantly. Second, we live in an age of better baseball through chemistry, so older data about player aging patterns may not be completely applicable (this isn’t meant to imply anything about Phat Albert’s training regimen in particular).
Anyway, this kind of decision seems to me to illustrate something Taleb calls “the cemetery problem” in The Black Swan — the natural psychological tendency to pay more attention to more visible than less visible data. The idea is that there are lots of great baseball players who have had great seasons in their mid and even late 30s, so it’s reasonable to expect that the Angels will get six or seven outstanding seasons out of Pujols, and that the last three years or so of his contract (when even the most optimistic predictors will admit it’s unlikely he’ll be better than an average first baseman) can be thought of as a signing bonus the team had to pay in order to get all those future great seasons from him.
It’s true that various baseball superstars have had several great seasons between age 32 and 38. (Leaving aside Barry Bonds for obvious reasons 38 seems to be the outer limit). What’s much less obvious is that there are a far larger number of superstars who have had only one or two — or no — great seasons after age 31. We’re far more likely to pay attention the first group of seasons than the second group, because the second group is essentially a cemetery for the failure of former greatness.
Here’s a list from Win Shares that represents the overall percentage value of the greatest 250 or so players in baseball history by age. The players reach their maximum combined value (100%) at 26, and essentially maintain it through age 31, at which they still have 93% of their highest value. Then this happens:
Now starting at age 36 a significant number of the players in the cohort start falling out of the league altogether, which obviously affects the total percentage value in a strong way, but on the other hand there have been lots of truly great players who were completely finished at age 37, and there’s no guarantee that Pujols won’t be one of them.
I think it’s a terrible contract.