Baseball Hacks

Measure Batting with Linear Weights

Calculate one of the most accurate and intuitive measurements of offensive performance ever developed: linear weights.

The runs created formula in “Measure Batting with Runs Created” [Hack #45] measures the absolute performance of players. But what if we want to compare a player’s contributions to an “average player?” The linear weights formula helps us do this.

The linear weights formula, also called batter runs (BR), is designed to reflect the offensive contributions of each batter accurately. The formula is weighted so that a league average player does not add or subtract value from his team; the BR for a league average player will be zero. The idea is to compare how much better or worse than average a player is.

The linear weights system assigns an average value to each baseball event. The BR formula sums the total value of a player’s contributions, weighted by the value of each action. The idea is to measure the value of everything a batter does (hit a single, hit a home run, walk, steal a base, strike out, etc.), and rate hitters based on the number of times they performed each action.

Let’s take a simple example. Suppose a batter is at the plate with no outs and no men on base. At this point, his team can expect to score .54 runs in that inning if an average player were batting (just take my word for it right now; I’ll explain why later). Now, suppose this batter hits a home run. His team gains one run immediately and his team will be back ...