It's Fourth Down and What Does the Bellman Equation Say? A Dynamic Programming Analysis of Football Strategy

Romer, David H.

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It's Fourth Down and What Does the Bellman Equation Say? A Dynamic Programming Analysis of Football Strategy

NBER Working Paper No. w9024

35 Pages Posted: 21 Jun 2002 Last revised: 29 Aug 2022

See all articles by David H. Romer

David H. Romer

University of California, Berkeley - Department of Economics; National Bureau of Economic Research (NBER)

Date Written: June 2002

Abstract

This paper uses play-by-play accounts of virtually all regular season National Football League games for 1998-2000 to analyze teams' choices on fourth down between trying for a first down and kicking. Dynamic programming is used to estimate the values of possessing the ball at different points on the field. These estimates are combined with data on the results of kicks and conventional plays to estimate the average payoffs to kicking and going for it under different circumstances. Examination of teams' actual decisions shows systematic, overwhelmingly statistically significant, and quantitatively large departures from the decisions the dynamic-programming analysis implies are preferable.

Suggested Citation: Suggested Citation

Romer, David H., It's Fourth Down and What Does the Bellman Equation Say? A Dynamic Programming Analysis of Football Strategy (June 2002). NBER Working Paper No. w9024, Available at SSRN: https://ssrn.com/abstract=316803