Converting wOBA to Runs Above Average

In the previous post, I recommended Weighted On-Base Average ( wOBA) as a measure of overall batting performance.  A limitation of wOBA is that, like OPS, it is a rate stat and does not give a player credit for playing time.  For example, Nationals outfielder Bryce Harper, Reds infielder Jeff Keppinger and Royals utility man Irving Falu all had wOBA's of .352, but had varying numbers of plate appearances:

Harper  597
Keppinger 418
Falu 91

One would guess that Harper contributed the most offensively of the three followed by Keppinger, but wOBA does not tell us that.

We need a counting statistic and the best kind is one that can be expressed in runs.  Once such statistic is Batting Runs which was first presented by Pete Palmer in The Hidden Game of Baseball in 1984.  Tom Tango later re-introduced it in  The Book: Playing the Percentages in Baseball as Weighted Runs Above Average (wRAA).  It is now an important statistic at FanGraphs.   

Getting back to the above example, Harper had 18 Batting Runs in 2012.  This tells us that he contributed an estimated 18 runs above what an average batter would have been expected to contribute in the same number of outs.  Appropriately that was more than Keppinger (12) and Falu (3) accumulated in less playing time.

Percentiles

Table 1 below shows the percentiles for wRAA for players with 250 or more plate appearances (PA) in 2012.  That includes all regulars and part-timers who were considered good enough to see semi-regular playing time.  For example, the 75th percentile for wRAA is 15.  This means that 75 percent of players with 250+ PA had less than 26 wRAA and 25 percent had more than that.  The wRAA column is listed next to the percentiles for RBI to make it a little easier to grasp what's good and bad.  For example, we can see that a 15 wRAA  is equivalent in magnitude to about 73 RBI (although the two numbers measure different things) 

Table 1: Percentiles for Batting Runs

PCTL	wRAA	RBI
100	57	139
90	26	92
75	15	73
50	4	54
25	-5	35
10	-12	26
0	-24	9

 

Calculation

The wRAA metric is based on a player's wOBA and the MLB average wOBA (MLB wOBA) and is calculated as follows:

     wRAA = (wOBA-MLB wOBA)/1.245 x PA.

You may remember from the previous post that 1.245 is the factor which was applied to wOBA to put it on the same scale as On-Base Percentage (this number changes slightly each year).  The MLB average wOBA in 2012 was .315, so Harper had (.352-.315)/1.245 x 597 = 18 wRAA.

More Results

Table 2 below shows the wRAAs for some past and present Tigers.  The final column shows specific percentiles.  For example, Austin Jackson's 28 wRAA  fell at the 91st percentile of all batters with 250 or more PA.  That means he had more more wRAA than 91% of MLB players in 2012.  The percentiles and ordering came out pretty similar to that for wOBA.  There are small differences where players with a lot of playing time moved up and players with less playing time moved down.  The leading Tiger was MVP Miguel Cabrera with 57 wRAA.  He was also the MLB leader.


Table 2: Batting Runs for Tigers, 2012

Player	PA	wOBA	wRAA	PCTL
Cabrera	697	.417	57	100
Fielder	690	.398	46	98
Jackson	617	.371	28	91
Hunter	584	.356	19	83
Dirks	344	.368	15	75
Avila	434	.327	4	53
Infante	588	.310	-2	33
Berry	330	.305	-3	33
Young	608	.305	-5	26
Peralta	585	.301	-7	20
Boesch	503	.288	-11	12
Santiago	259	.253	-13	8
Raburn	229	.256	-18	2