### Stat of the Week: wRC+ (Weighted Runs Created plus)

Last week, we took a look at Weighted On-Base Average, wOBA, which represents a player’s total offensive value in the form of a percentage. This week, we will attempt to both index a player’s total offensive value to the league average and adjust it for ballpark factors with Weighted Runs Created plus, or wRC+.

wRC+ was created in response to OPS+, which measures On-Base plus Slugging Percentage, OPS, against league average and adjusts it for ballpark factors. Measuring OPS against league average essentially adjusts for the run-scoring environment in a given year. In 1925, the league average OPS was .765, while the league average OPS in 1967 was .664. Let’s take two hitters, hitter A and hitter B. Hitter A played in 1925, while hitter B played in 1967. Both hitter A and hitter B each had a .765 OPS. However, hitter B did it in a season where the average OPS was .664 as opposed to .765. Hitter A was a league average player, while hitter B was approximately 30% better than league average, according to OPS+, where,

OPS+ = 100 * [(OBP/lgOBP) + (SLG/lgSLG) - 1].

As you can see, adjusting for the run-scoring environment of a given year is important in evaluating a player’s true offensive value. OPS+ also adjusts OPS for ballpark factors - hitter C benefitted from playing in the Ballpark at Arlington, while hitter D was hurt from playing in PETCO park. You can also see that adjusting for ballpark factors is important in evaluating’s a player’s true offensive value.

However, since OPS is aflawed statistic, sabermetricians decided to create a more accurate statistic to evaluate offensive value adjusted for run-scoring environment and ballpark factors. As we saw last week, wOBA is much better at evaluating a player’s offensive value than OPS; thus, we will use wOBA to create a league adjusted and ballpark adjusted statistic that encompasses a player’s offensive value.

Weighted Runs Created, wRC, measures a player’s total offensive value by runs. It uses wOBA to calculate the total runs created as a result of a player’s offense.

wRC = [((wOBA - lgwOBA)/wOBAScale) + (lgR/PA)] * PA.

It essentially takes a player’s wOBA, subtracts the league average wOBA, and then divides the difference by wOBAScale - a multiplier that converts wOBA to runs per plate appearance; it then adds the league average runs per plate appearance, and multiplies the resulting sum by the number of plate appearances the player had.* We now have a player’s wRC.

In order to get wRC+, you simply divide a player’s wRC by the league average wRC, and multiply it by 100. A wRC+ of 100 is average. A wRC+ greater than 100 is above average, and every point above 100 is a percentage point above league average. For example, a 130 wRC+ means a player created 30% more runs than the league average. Likewise, a wRC+ less than 100 is below average, and every point below 100 is a percentage point below league average. For example, a 70 wRC+ means a player created 30% fewer runs than the league average. wRC+ translates wOBA into a run-based measure of a player’s offensive value, while adjusting for both the player’s run-scoring environment and for ballpark factors.

With wRC+, you can now compare Babe Ruth and Albert Pujols, even though they played in different run-environments and different ballparks.

* In other words, wRC converts the player’s excess wOBA into runs per plate appearance above league average, adds league average runs per plate appearance, and multiplies by plate appearances to get the total runs created.