Kenneth Kovash and Steven Levitt have a fun (from my perspective!) new “working paper”:http://www.nber.org/papers/w15347 that relies on two giant data sets from major league baseball and the national football league to test whether actors follow minimax strategies in a real world, high stakes situation. The basic conclusion is that pitchers throw more fastballs than they should, and football teams run more often than they should. Here’s the abstract:
bq. Game theory makes strong predictions about how individuals should behave in two player, zero sum games. When players follow a mixed strategy, equilibrium payoffs should be equalized across actions, and choices should be serially uncorrelated. Laboratory experiments have generated large and systematic deviations from the minimax predictions. Data gleaned from real-world settings have been more consistent with minimax, but these latter studies have often been based on small samples with low power to reject. In this paper, we explore minimax play in two high stakes, real world settings that are data rich: choice of pitch type in Major League Baseball and whether to run or pass in the National Football League. We observe more than three million pitches in baseball and 125,000 play choices for football. We find systematic deviations from minimax play in both data sets. Pitchers appear to throw too many fastballs; football teams pass less than they should. In both sports, there is negative serial correlation in play calling. Back of the envelope calculations suggest that correcting these decision making errors could be worth as many as two additional victories a year to a Major League Baseball franchise, and more than a half win per season for a professional football team.
The authors are remarkably thorough in the factors they control for in their analysis, but I was still left with a couple of questions. First, is it possible that pitchers might overuse the fastball because it is less taxing on their arms, especially compared to breaking balls? So yes, the pitch might ultimately be less effective, but might allow them to stay in the game longer (or avoid injury), which would have other benefits to the team. Second, despite what otherwise looks like very systematic data analysis, one of the back of the envelope calculations in the baseball example is based on the fact that “Executives of Major League Baseball teams with whom we spoke estimated that there would be a .150 gap in OPS between a batter who knew for a certain a fastball was coming versus that same batter who mistakenly thought that there was was a 100 percent change the next pitch would not be a fastball, but in fact was surprised and faced a fastball”; this strikes me as fairly arbitrary. Finally, I wonder if the propensity to favor runs over passes in football represents not so much a failure of the minimax strategy, but rather an overarching risk aversion on the part of professional football coaches (similar to the argument made by “David Romer”:http://www.pro-football-reference.com/blog/?p=40 about why football teams continue to punt on 4th down when they probably shouldn’t do that either).
[Hat tip to “The Economist”:http://www.economist.com/businessfinance/displaystory.cfm?story_id=14587290]