Professional Football In Exercise 40 of the first. section of this chapter, the method used by the NFL to determine the winner in an overtime game from 1974 to 2010 was analyzed. In this system, a coin was tossed and the winning team got to decide whether to kickoff or to receive the ball. The first team to score won. Based on data from the 2008 season, the following transition matrix was determined. The first row tells the probability of being in any given situation after one possession, assuming team A started with the ball. Source: Mathematics in Sports.
(a) Find F and FR.
(b) Find the probability that, if team A gets the ball first, team A wins.
(c) Find the probability that, if team B gets the ball first, team B wins.
(d) What is the expected number of possessions to determine a winner in overtime?
(e) Determine the strategy that each team should take. What does this imply about the winner of the coin loss (the one who gets to decide who gets the ball first)?
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