Statistics and Baseball

Today, we used spaghetti to illustrate fitting lines to (x, y) plots. Since spaghetti is Italian, we fit a line to (HR, SLG) data for Mike Piazza (great player of Italian descent) for the years that he played with the Mets.

• We want a fitted line to be close to the points in some sense.
• We define a residual to be the difference between the observed y value and the y value one would predict from the line.
• We measure the goodness of a fit by the sum of squared residuals.
• The best line, the least-squares line, is the one that makes the sum of squared residuals as small as possible.

In the computer lab, we explored team batting data from the 2005 season. We focus on using different statistics like AVG, SLG, OBP, and OPS to predict a team's runs scored per game.

• Fathom has a neat way of showing graphically the squared residuals. By playing with a movable line, we tried to make the sum of squared residuals small.
• In this trial-and-error approach, we get a pretty good line, but the least-squares line is the best one from the viewpoint of smallest sum of squared residuals.
• We can compare different predictors by looking at the "sum of squares". Generally, we see that OPS is the best predictor, followed by SLG and OBP, and then by AVG.

This work has implications on how we evaluate hitters. Next week, we'll look at the two greatest hitters from Japan who are currently in the MLB.