In this paper, we consider the National Football League`s rules for overtime. We use Markov chain models to represent sudden death, modified sudden death 15-minute overtime, the newly changed modified sudden death 10-minute overtime, and our theoretical alternative modified sudden death. Through our model analysis, we find the average length of overtime and the probability of the team possessing the ball first during overtime winning the game. Our analysis shows that the modified sudden death rule change increased the average overtime from 7 minutes 1 second to 7 minutes 37 seconds and that the probability of the team possessing the ball first winning decreased from 59.9% to 55.4%. Furthermore, we predict the 10-minute overtime change will result in the team possessing the ball first winning 54.1% of the time and the probability of a game ending in a tie increasing to 11.2% from under 2% in the current 15-minute overtime. Finally, we propose a system where both teams are required to possess the ball at least once before the game ends and conclude this system would increase the average overtime length to 7 minutes 57 seconds and the probability of the team possessing the ball first winning would be 54.7%.
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