Attached (sim.mpl) is a simple game simulation with data from last years World Series champion Red Sox. Bump up infolevel to see what's going on during a game (as shown below).

In the "Maple Baseball" post I wanted to see if the number of runs our team was scoring was appropriate. Obviously, the rule of thumb, 3-hits = 1 run is poor at best. What I really want to find out is if there is a way to improve our scoring chances. The standard baseball batting-order uses the following heuristic:

• lead off with someone with a high on-base percentage (and who can maybe steal a base)
• next 2 are good contact hitters
• batter 4 is your "clean-up" hitter; someone with power
• etc.

Early this season, after the Maplesoft team came out on the wrong side of a 13-6 loss, we were frustrated by the team's inability to score more runs. The previous year we averaged 14 runs a game. This started me wondering, just how many runs can our team expect with a given lineup?

Suppose you assume that it takes three hits in an inning to start scoring runs. Now, let's assume you have five .500 hitters coming up to bat. What is the probability that you'll get 3 hits among those five batters, thus scoring one run?