EVALUATING HITTERS BY LINEAR WEIGHTS
In chapter 2 we saw how knowledge of a hitter's AB, BB+HBP, singles, 2B, 3B, and HR allows us to compare hitters via the Runs Created metric. As we will see in this chapter, the Linear Weights approach can also be used to compare hitters. In business and science we often try to predict a given variable (called Y or the dependent variable) from a set of independent variables (x1, x2, … x). Usually we try to find weights B1, B2, … Bn and a constant that make the quantity
Constant + B1x1 + B2x2 + …Bnxn
a good predictor for the dependent variable.
Statisticians call the search for the weights and constant that best predict Y running a multiple linear regression. Sabermetricians (people who apply math to baseball) call the weights Linear Weights.
For our team batting data for the years 2000–2006
Y = dependent variable = runs scored in a season.
For independent variables we will use BB + HBP, singles, 2B, 3B, HR, SB [Stolen Bases]), and CS (Caught Stealing). Thus our prediction equation will look like this.
Let's see if we can use basic arithmetic to come up with a crude estimate of the value of a HR. For the years 2000–2006, an average MLB team has 38 batters come to the plate and scores 4.8 runs in a game so roughly 1 out of 8