Explaining Terms: wRC+

Explaining Terms is a many part series in which I explain certain Sabermetric terms in order to make them more accessible.

wRC+ stands for Weighted Runs Created plus. It is a statistic that attempts to give a reader a one-shot glance at a player’s hitting ability by boiling down all contribution at the plate into one concise number. 100 is average, and higher is better.

wRC+ is weighted, which means that each outcome (single, double, triple etc.) is weighted by how much it helps a team score runs, on average.

wRC+ is context independent. It is not meant to encapsulate a player’s situational value. Instead, the statistic gives each player the average run production value for each outcome, so the player is not unduly rewarded or punished for the performance of his teammates.

wRC+ is park adjusted. Every ballpark is different, and wRC+ uses Fangraphs’ component park factors to essentially attempt to annul the undue effects of a ballpark on a player’s visible statistics. In doing so, wRC+ becomes directly comparable between teams.

wRC+ is league adjusted. The offensive environment varies year to year, so you can see how Babe Ruth performed in his time against how Barry Bonds performed in his, and you do not need to do the mental math to see which season was better in the context of each player’s peers. wRC+ does it for you.

wRC+ is housed at Fangraphs, and you can find it on every player page.

For the math inclined, wRC+ is calculated thusly:

1. Find each player’s wOBA, Weighted On Base Average. At this point, you can either divide every term by the component park factors, or divide the answer by the total park factor. The component park factor will correct for everything the park changes, whereas the total park factor would only correct for the park as a whole. The former is more valuable to predict future results with a different team, and the latter more useful in determining how useful a player was to the team at hand. Both approaches have their benefits. The equation for 2012 was:

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

uBB is unintentional walks.

2. Convert wOBA to wRAA.

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

League wOBA is the league average wOBA for that season. wOBA scale is a constant applied to wOBA in order to convert it to “runs”, a recognizable unit. Here you can find the wOBA scale for each season, along with the league average wOBA.

3. Convert wRAA to wRC+.

wRC+ = ((wRAA / PA) / lg RPA + 1) x 100

Lg RPA is the league average production of runs per plate appearance. It’s also available here.

I hope you find this useful. Feel free to ask questions in the comments!

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4 Responses to Explaining Terms: wRC+

  1. DPassovoy says:

    This was helpful. Thanks

  2. Eggy says:

    How can I extract an actual runs per game number for a player from wRC+?

    • Anirudh Kilambi says:

      Well, a good rule of thumb for runs above average per 600 PAs is (player wRC+ – 100)*0.66. So that means you’re about 6.6 runs above average for every 10 points of wRC+, in this run environment. Per game would depend on the number of PAs per game and whatnot, but that’s easily extricable.

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