Know Your Stats: Weighted Runs Above Average (wRAA)

We continue our widely-beloved “Know Your Stats” series with a “gateway stat:” Weighted Runs Above Average. wRAA is essentially wOBA converted into runs, but understanding wRAA is crucial to understanding Wins Above Replacement and Weighted Runs Created Plus, which we’ll be talking about this afternoon.

One of the biggest issues with rate statistics like wOBA and On-Base Percentage is that they don’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 this year

wOBA = (0.688×uBB + 0.719×HBP + 0.878×1B + 1.245×2B + 1.576×3B + 2.030×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 (.313 in 2015), 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 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 last with 600 plate appearances and a .350 wOBA:

wRAA =  ((.350 – .313) / 1.251) × 600

wRAA = (.037/1.251) x 600

wRAA= 17.7 runs above average

Just as it sounds, this player would be worth 17.7 runs above average at the plate. How good is that exactly? Here is a “rule of thumb” chart for the stat, courtesy of Fangraphs:

Of course, it’s important to remember that like wOBA and any traditional rate stat, wRAA is context-neutral. Also, wRAA is critical for understanding Wins Above Replacement, since it is the offensive component. You won’t see it used much in articles because it doesn’t have all that much practical use on its own, but as you’ll see, knowing it makes it easier to wrap your head around a few more widely-used stats. That’s why it’s in some ways a “gateway stat.”