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

By Wayne Winston | Go to book overview

20
FOOTBALL STATES AND VALUES

In chapter 8 we discussed how the inning, score margin, outs, and runners on bases were sufficient data when trying to determine whether a baseball team would win a game (assuming two equal teams were playing.) For example, if a team is down by three runs in the top of the seventh inning with two outs and the bases loaded, it has a 15% chance of winning the game. We call the inning, score margin, outs, and runners on bases the state of the baseball game. Once we know the state of the game and have evaluated the chance of winning in each state, we can analyze strategies such as bunting or evaluate (as shown in chapter 8) batters and pitchers based on how they change the team's chance of winning the game.

Football States

If we can define a state for football that is sufficient to determine the chance of winning a game (assuming two equal teams are playing), then we can analyze how plays affect a team's chance of winning. We can then use this information to rate running backs, quarterbacks, and wide receivers. For example, we might find that when running back A carries the ball, on average he adds 0.1 points per carry, while running back B adds 0.3 points per carry. This would indicate that (assuming offensive lines of equal quality) that running back B is better. Comparing running backs based on points added per carry would be a better measure than comparing running backs based on the current metric of yards per carry. We can also use football states to evaluate strategic decisions such as when to go for a two- point conversion after a touchdown (see chapter 24), when to punt on fourth down or go for it, and when to try a field goal on fourth down or go for it, as well as the run- pass mix on first down (see chapter 21).

The state of a football game at any time is specified by the following quantities:

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