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Binomial Simulation

The Binomial Probability Distribution

Page 1

Baseball Simulation

The goal of this activity is to use the computer program Excel to simulate a baseball player’s

distribution of hits.

During the 2007 season, Matt Holliday’s hitting average was .340. As the third hitter in the

lineup, Holliday typically has four at bats in a game. Assume that each time Holliday bats, his

chance of getting a hit is .340 and that each at bat is an independent event. Simulate an entire

162 game season to determine the distribution of the number of hits Holliday gets each game.

1. In cells A1 to E1, enter the column titles 1, 2, 3, 4, and Total.

2. Enter Holliday’s batting average in cell F1.

3. To simulate whether Holliday gets a hit or not in his first at bat in game 1, enter the following

formula in cell A2.

=IF(RAND()<$F$1,1,0)

4. Highlight cell A2 and select Copy (in the Edit menu). Then highlight cells B2, C2, and D2

and select paste (in the Edit menu) to copy and paste the formula to simulate the rest of his at

bats in game 1.

5. To count the number of hit Holliday had in game 1, enter the following formula in cell E2;

=COUNTIF(A2:D2,1)

6. Highlight cells A2 – E2 and copy and paste the cells in rows 3 through 163 to simulate the

remaining 161 games of the season.

7. To create a probability distribution, first enter the table headers “x” in cell G1 and “P(x)” in

cell H1.

8. In the “x” column (cells G2 – G6) enter the possible number of hits Holliday can hit in a

game: 0, 1, 2, 3, and 4

9. To determine the probability of getting zero hits per game in the season, enter the following

formula in cell H2.

=COUNTIF($E$2:$E$163,G2)/162

10. Copy cell H2 and paste it in cells H3 – H6.

11. Save the file as Holliday.

Robert A. Powers

University of Northern Colorado

Binomial Simulation