# Know Your Stats: Weighted Runs Above Average (wRAA)

An article by posted on July 17, 2013

We continue our intro to sabermetrics series with a relatively new statistic, but a very relevant one nonetheless: Weighted Runs Above Average. wRAA is essentially wOBA converted into runs, but understanding wRAA is crucial to understanding Wins Above Replacement (Fangraphs version).

One of the biggest issues with rate statistics like wOBA and On-Base Percentage is it doesn’t put the production into baseball terms. What does a .340 wOBA really mean? wRAA makes it easy by putting it into the “currency” of baseball: runs. Before we get started, here is the wOBA formula with the weights from the 2012 season:

wOBA = (0.691×uBB + 0.722×HBP + 0.884×1B + 1.257×2B + 1.593×3B +
2.058×HR) / (AB + BB – IBB + SF + HBP)

The formula for wRAA is pretty simple. To convert a .350 wOBA to wRAA, you simply subtract the league wOBA (.315 in 2012), and divide that by the wOBA scale for that year, which slightly changes based on the particular weights for that season. Then, to adjust for sample size and playing time, you multiply by plate appearances. Here is the formula:

wRAA = ((wOBA – league wOBA) / wOBA scale) × PA

Now here is the formula for someone from 2012 with 600 plate appearances and a .350 wOBA:

wRAA =  ((.350 – .315) / 1.245) × 600

wRAA = (.035/1.245) x 600

wRAA= 16.87

Just as it sounds, this player would be worth 16.87 runs above average. How good is that exactly? Here is a “rule of thumb” chart for the stat:

Is it perfect? Absolutely not. No statistic is perfect. Is every single created equal? Nope. Some players hit them in the biggest spots. A walk-off single in the ninth inning that drives in two runs is more impactful on a game than a single in the third inning with no one on and your team down by nine runs. However, if you’re trying to break down a player’s production and put it into neutral context, wOBA and it’s variations such as wRAA are the way to go. Don’t think sabermetrics doesn’t consider the in-game situations, however. There are statistics that calculate how important that seventh inning double actually was and how it improved a team’s chances of winning the game. Instead of using broad terms of “clutch” and “not clutch,” some of the statistics can actually break down how clutch that hit was and we’ll cover those later in the series. However, if it’s neutral production that you’re looking at, use wOBA and wRAA. How much of a difference is a .350 wOBA to a .340 in baseball terms? For that, wRAA is the way to go.