Technical Note—How to Win by Losing

Can it ever be advantageous for a football team intentionally to lose or tie a game that it could otherwise win? This paper cites real-life examples from the 1971 NFL season when such situations apparently arose. These stem from the league rule admitting a second-place team (“wild card”) to the playoffs in each conference. Even without such a rule, however, similar paradoxes could occur. These are based on the assumption (generally conceded to be true) that team-over-team advantages in individual games are not necessarily transitive. The examples assume that tie games are omitted in figuring final standings, and ties in the standings are settled by playoffs. Using Markov-chain methods, a set of decision rules is derived to tell a team whether or not to play for a win. A convenient graphical form of presentation of these rules is given.