Sabermetric Spring Training: wRC and wRC+

After looking at what is the basis for much of our sabermetric offensive value in wOBA, I wanted to take a look at the next stat which attempts to build off of Bill James stat RC (runs created) and combine it with wOBA.  Runs Created was originally instituted by James to display how many runs a player was responsible for instead of trying to value R, RBI, SB, etc, which can often be misleading.  Not every run scored is fully the value of the base runner and not every RBI is earned by the hitter.

Tom Tango took this and instead of using the raw numbers, used wOBA, which is a more accurate valuation of a player and used this to calculate wRC+.  The equation for wRC+ is:

(((wOBA – lgwOBA) / wOBAScale) + (lgR/PA)) * PA

According to FanGraphs the wOBAScale is usually around 1.15, but changes year to year and is calculated based on wOBA weighting.

This stat is very informative, but much like OPS and wOBA it can be difficult to gauge what the number always means when comparing to other players.  To account for this Tango created wRC++, which much like OPS+ scales to 100 to gauge value compared to league average.  To calculate wRC++ is a bit more involved, but according to this  you calculate like this:

a = league runs per PA
b = wRAA/PA
c = a/b + 1
d = 100*c
d = wRC++

*wRAA is another Tango stat and is similar to wRC+, but tells you the number of runs created above average and not total.

Once you calculate wRC++ you can use it much like OPS+ and it scales much the same way.  Here are some values for 2011 to display what each stat looks like.

Player            wRC+       wRC++
Jose Bautista            139       181
Jacoby Ellsbury          132       150
Jason Bay                 57       100
Carl Crawford             55        83
Alex Rios                 41        59

This should give you an idea of how the stat works, but to be more specific Ellsbury was worth 77 more runs to the Red Sox than Carl Crawford or 32 more runs than the average player.  Looking at wRC++ Ellsbury was 50 percent better than league average.  As you can see a wRC+ of about 57 was average in 2011.

Categories: Boston Red Sox Sabermetric Spring Training

After taking an interest in sabermetrics and statistical analysis Troy began trying to use it to an advantage in fantasy baseball. He started the website and also spent time at and After a few years the interest in the Red Sox drew him to start a Red Sox-oriented site (Yawkey Way Academy) with fellow writer Lee Perrault. A short time later he joined Fire Brand. Writer from: December 14, 2009 – July 24, 2010, March 3, 2011 – May 10, 2012.

2 Responses to “Sabermetric Spring Training: wRC and wRC+” Subscribe

  1. tonez March 1, 2012 at 4:49 PM #

    I was ok until the last paragraph with the ellsbury example. You tell us that Ellsbury was worth 77 more runs than CC, using the difference in their wRC+ to get that number. If the average wRC+ in 2011 was 57, and ellsbury had a wRC+ of 132, how do you get that ellsbury was only worth 32 more runs than the average player? Is the average player not considered to hold roughly the league average? I hope this question doesn't make you face palm, I'm just trying to figure this all out.

    • TroyPatterson March 2, 2012 at 10:52 AM #

      Wow. You are correct tonez, the only facepalming is at my own mistake. Ellsbury was 75 runs over the average.