Sabermetrics 101: wRC and wRC+

Introduction

Last week, we took a look at Weighted On-Base Average, wOBA, which represents a hitter's total offensive value. This week, we will attempt to both index a hitter's total offensive value to the league average and adjust it for park effects 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 park effects. 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 who played in 1925, and hitter B who played in 1967. Both hitter A and 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 we 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 park effects -- hitter C benefited from playing in Rangers Ballpark, while hitter D was hurt from playing in PETCO Park. The park adjustment is administered by adjusting each of the player's offensive outcomes by his home park factor and then recalculating the player's OBP and SLG. Adjusting for park effects is also an important step in the process of evaluating a player's true offensive value.

Constructing wRC and wRC+

However, since wOBA is a better measure of a player's offensive value than OPS, sabermetricians decided to create a league and park adjusted statistic based on wOBA: Weighted Runs Created. wRC, measures a player's total offensive value by runs. It uses wOBA to calculate the total runs created by a hitter.

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 that the player had.* The park adjustment is once again calculated by adjusting each of the player's offensive outcomes by his home park and then recalculating his wOBA. We now have a player's wRC.

In order to get wRC+, we simply divide a player's wRC by the league average wRC and multiply it by 100.

wRC+ = 100 * (wRC/lgwRC)

A wRC+ of 100 is average. A wRC+ greater than 100 is above average, and every point above 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 is a percentage point below league average. For example a 70 wRC+ means a player created 30% fewer runs than the league average. wRC+ indexes a player's offensive value against league average, while adjusting for park effects.

Conclusion

With wRC+, we can now compare Ernie Banks and Ryne Sandberg, even though they played in different eras.

Footnotes

* In other words, the formula first determines how good or bad a player is relative to the league, condenses that into a per plate appearance number, adds the league average runs per plate appearance to get the player's runs per plate appearance, and then multiplies by the number of plate appearances to get total runs created.