Statistics and Baseball

Today we talked about the Mud Hens - Sky Chiefs game we watched last night. Here are some things we discussed.

• The Mud Hens lost primarily due to their weak hitting. We compared the Mud Hens and Sky Chiefs from two perspectives: their outcomes of plate appearances, such as SO, BB, H, and non-SO Outs, and the distribution of on-base hits, such as BB or HBP, singles, doubles, triples and home runs. It seemed that the Mud Hens had a lot of strikeouts, no walks, and few hits.
• The most significant plays were the clutch hits for the Sky Chiefs in the top of the 2nd inning.
• Was there luck in the game? There were several base hits that barely missed the infielders. There was a lucky bloop single by a hitter who was fooled by the pitch.

We talked more about estimating a player's ability on the basis of his performance.

• A 95% confidence interval is helpful in learning about a batter's hitting probability on the basis of his batting average.
• The length of the interval depends on the sample size n and the confidence level.
• Confidence intervals are helpful in comparing batter abilities. If the intervals for the abilities of two hitters overlap, then we can't say that one batter is "better" than the other.

We concluded by watching parts of the Disney version of Angels In the Outfield. Maybe Angels are controlling the chance variation that we see in baseball (or maybe not).