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

By Wayne Winston | Go to book overview

6
BASEBALL DECISION- MAKING
During the course of a season, managers make many crucial decisions, including the ones listed below.
 • With a man on first and nobody out should we attempt a sacrifice bunt to advance the runner to second base? • With a man on first and one out should we attempt to steal second base? • We are the home team and the score is tied in the top of the ninth inning. The opposing team has a man on third base and none out. Should we play the infield in? This increases the chance of a hit (most people think bringing the infield in makes a .250 hitter a .300 hitter), but bringing the infield in ensures that a ground out will not score the runner from third.

Decision- making in baseball, as in all aspects of life and business, involves making trade-offs. Let's analyze the decision concerning whether to try to bunt with a runner on first and none out. If the bunt succeeds, the runner will advance to second and be one base closer to scoring, but a precious out will have been given up. Is the benefit of the extra base worth giving up the out? We will soon see that in most situations, the benefit obtained from advancing the runner to second base does not justify relinquishing an out.

Possible States during a Baseball Game

The key to developing a framework for baseball decision- making is to realize that during an inning a team is in one of the twenty- four situations (often called states) listed in table 6.1.

Each state is denoted by four numbers. The first number is the number of outs (0, 1, or 2). The second number lets us know if first base is occupied (1 = base occupied, 0 = base not occupied). Similarly, the third and fourth numbers tell us whether second or third base, respectively, are occupied. For example, 1010 means there is one out and a runner on second

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