# Mathletics: How Gamblers, Managers, and Sports Enthusiasts Use Mathematics in Baseball, Basketball, and Football

By Wayne Winston | Go to book overview

26
WHY IS THE NFL'S OVERTIME SYSTEM
FATALLY FLAWED?

When an NFL game goes into overtime a coin toss takes place and the team that wins the coin toss has the choice of kicking off or receiving. Since the overtime is sudden death, the team winning the coin toss invariably chooses to receive so they have the first chance to score and win the game. During the 1994–2006 seasons the team that received the kickoff in overtime won 60% of the games. It seems unfair that in NFL overtime the team winning the coin flip should have such a huge edge. In attempt to lessen the impact of the coin flip result on the game's outcome, the NFL recently proposed moving the kickoff from the 30- to the 35- yard line. This would give the team receiving the kickoff slightly worse field position and theoretically would decrease the chance that the team receiving the kickoff would score on the first possession. This should give the team kicking off a better chance to win the game. As we will see, a simple mathematical analysis (our model is a simplified version of Jones's model)1 indicates that it will be difficult to give each team an equal chance to win in sudden death if the overtime begins with a kickoff.

A Simple Mathematical Model
of Sudden Death Overtime

Let p be the probability that an average NFL team scores on a possession. Assuming that each team has a probability p of scoring on each possession, what is the probability that the team receiving the kickoff will win the game? During the regular NFL season, overtime games last only one quarter. If no team scores during the first overtime session, the game is a tie. This happens

1 M. A. Jones, “Win, Lose, or Draw: A Markov Chain Analysis of Overtime in the
National Football League,” College Mathematics Journal 35 (November 2004): 330–36.

-175-

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