Optimal Convert Strategies in Football

Abstract

A frequently occurring situation in college and professional football is that of a team catching up through two touchdowns after trailing by 14 points, with the game outcome being determined by the extra-point plays. For leagues allowing two-point converts, an optimal point-after strategy exists under quite reasonable assumptions, and depends upon the relative utility to the team of a win, tie, or loss and the probability of success with a (one-point) kick as opposed to a (two-point) run/pass. We illustrate with reference to the January 1984 Orange Bowl game, where the favored team followed a possibly suboptimal strategy, losing the game and the national championship.

Key Words:

• optimal strategy
• decision theory
• utility theory
• football