Problem Set 2
Problem Set #2
Ec 370 Summer, 2013
Michigan State University M. Naretta
1. Another popular sport on SASN is One-out, Two-base baseball. In this sport there are, obviously, two bases: home and 2nd. The batter hits the ball and runs to 2nd. If he or she (it’s a co-ed sport) gets a hit, then the batter is on second. If it’s an out, then the inning is over and the other team gets to bat. Suppose that it’s a hit. Then the next batter bats with a runner on 2nd base. If that batter makes an out, the inning is over. If that batter gets a hit, the run scores and the game and his or her team wins. The probability of getting a hit is 0.6.
a. Draw the tree.
b. Write an equation for the value of being the team at bat with no one on base.. (Hint: let V be the value of being at bat with no one on base. Then –V is the value of your opponent being at bat with no one on base.)
V+-V
c. Solve the equation in part b. Value = __.72______
d. What is the probability that the team at bat with no one on base will win the game?
Probability = ____.36______ 2. More on One-out, Two-base baseball. The key strategic variable for the team in the field is where to position the rover fielder. The key strategic variable for the batting team is where to hit the ball. The following table gives the strategies and payoffs for the first play. The number in the table is the probability of a hit. The team at bat wants a large probability, the team in the field wants a small one. Experience has taught the rovers to wait at the mound and then move suddenly to the left, right or center field as the ball is hit. Thus, you can think of this as a simultaneous move situation.
Team in the field
right center left pitcher’s field field field mound
Bunt .300 .400 .350 .250
Hit to right .100 .250 .300 .200
Team at bat Hit to left .350 .250 .100 .220
Hit to center .250 .100 .250
Ec 370 Summer, 2013
Michigan State University M. Naretta
1. Another popular sport on SASN is One-out, Two-base baseball. In this sport there are, obviously, two bases: home and 2nd. The batter hits the ball and runs to 2nd. If he or she (it’s a co-ed sport) gets a hit, then the batter is on second. If it’s an out, then the inning is over and the other team gets to bat. Suppose that it’s a hit. Then the next batter bats with a runner on 2nd base. If that batter makes an out, the inning is over. If that batter gets a hit, the run scores and the game and his or her team wins. The probability of getting a hit is 0.6.
a. Draw the tree.
b. Write an equation for the value of being the team at bat with no one on base.. (Hint: let V be the value of being at bat with no one on base. Then –V is the value of your opponent being at bat with no one on base.)
V+-V
c. Solve the equation in part b. Value = __.72______
d. What is the probability that the team at bat with no one on base will win the game?
Probability = ____.36______ 2. More on One-out, Two-base baseball. The key strategic variable for the team in the field is where to position the rover fielder. The key strategic variable for the batting team is where to hit the ball. The following table gives the strategies and payoffs for the first play. The number in the table is the probability of a hit. The team at bat wants a large probability, the team in the field wants a small one. Experience has taught the rovers to wait at the mound and then move suddenly to the left, right or center field as the ball is hit. Thus, you can think of this as a simultaneous move situation.
Team in the field
right center left pitcher’s field field field mound
Bunt .300 .400 .350 .250
Hit to right .100 .250 .300 .200
Team at bat Hit to left .350 .250 .100 .220
Hit to center .250 .100 .250