In Case, we presented the probabilities of scoring at least one run and asked you to determine whether the manager should signal for the batter to sacrifice bunt. The decision was made on the basis of comparing the probability of scoring at least one run when the manager signaled for the bunt and when he signaled the batter to swing away. Another factor that should be incorporated into the decision is the number of runs the manager expects his team to score. In the same article referred to in Case, the author also computed the expected number of runs scored for each situation. Table 1 lists the expected number of runs in situations that are defined by the number of outs and the bases occupied.

Assume that the manager wishes to score as many runs as possible. Using the same probabilities of the four outcomes of a bunt listed in Case, determine whether the manager should signal the batter to sacrificebunt.

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Bases Occupied Bases empty 49 27 10 First base 0 Out 1 Out 2 Outs .85 52 23 Second base 1.06 69 34 Third base 1.21 82 38 First base and second base 1.461.00 48 First base and third base 65 1.10 .51 Second base and third base 1.941.50 62 Bases loaded 2.3 1.62 82