| Abstract: |
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. |