No sport generates as many statistics as baseball. Reporters, managers, and fans argue and discuss strategies on the basis of these statistics. An article in Chance (“A Statistician Reads the Sports Page,” Hal S. Stern, Vol. 1, winter 1997) offers baseball lovers another opportunity to analyze numbers associated with the game. Table 1 lists the probabilities of scoring at least one run in situations that are defined by the number of outs and the bases occupied.
1. The hunt is successful. The runner (or runners) advances one base, and the hatter is out.
2. The hatter is out hut fails to advance the runner.
3. The hatter hunts into a double play.
4. The hatter is safe (hit or error), and the runner advances. Suppose that you are an American league manager. The game is tied in the middle innings of a game, and there is a runner on first base with no one out. Given the following probabilities of the four outcomes of a hunt for the hatter at the plate, should you signal the hatter to sacrifice hunt?
P(Outcome 1) = .75
P(Outcome 2) = .10
P(Outcome 3) = .10
P(Outcome 4) = .05
Assume for simplicity that after the hit or error in outcome 4, there will he men on first and second base and no one out.