Tiger Tales: A Detroit Tigers Blog

I've done this before, but it's time for another wOBA primer.  A few years ago, Tom Tango introduced the Weighted-On-Base-Average (wOBA) statistic in The Book: Playing the Percentages in Baseball.  Not long after that, wOBA was added to the FanGraphs statistics database.  The wOBA measure hasn't become as popular as On Base Plus Slugging (OPS), but it is no longer an obscure statistic used only by hardcore stat guys.

If you spend a lot of time reading about and discussing baseball online (I assume that's most of you here), it's kind of hard to avoid wOBA.  I use it a lot here.  The Bless You Boys and and Motor City Bengals bloggers mention it frequently. You see it on the MotownSports forum and Twitter.  It's all over FanGraphs of course.  It even shows up on mainstream channels like MLB and ESPN on occasion. Despite its growing popularity, I think a lot of people still don't have a great grasp of what wOBA is or how it works, so the annual primer seems worth it.

The wOBA statistic is like an on-base-percentage (OBP), except that it gives appropriate weights to different events.  As you know, the OBP calculation counts every event where a batter reaches base (walk single, double, etc) the same.  In contrast, wOBA gives a hitter more credit for a hit than a walk and more credit for doubles, triples and home runs than singles.  The result is a rate statistic which measures a players total batting contribution.

One of the great things about wOBA is that it is scaled to behave like OBP.  So, we know that .375 or better is very good, .325 is about average for a starter or semi-regular, and below .300 is poor.  The top wOBA for the Tigers last year was Miguel Cabrera at .417.  We know that an OBP of .417 would be outstanding.  A wOBA of .417 is equally outstanding, but it measures Cabrera's overall batting contribution rather than just his ability to get on base.  Ramon Santiago, on the other hand, had a wOBA of .253.  We know that a .253 OBP is horrible and a .253 wOBA is equally horrible.

Why not OPS?   

Why can't we just use OPS?   The problem with OPS is that OBP contributes about 80% more to run scoring than slugging average (SLG).  Since OBP and SLG carry equal weight in the OPS formula, this means that OPS undervalues OBP relative to SLG.  Since wOBA weights events more appropriately, it is a better reflection of a player's total batting contribution.  OPS is a decent measure of a player's overall batting performance and we don't need to abandon it entirely, but wOBA is a better alternative when we want to be more precise.

Percentiles

Table 1 below shows the percentiles for wOBA 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 wOBA is .352.  This means that 75 percent of players with 250+ PA hit below .352 and 25 percent hit better than that.  Since wOBA is listed along side the more familiar OPS and BA, the chart should help some understand it a little better.  For instance, we can see that a .352 wOBA is about equivalent to a .815 OPS or .287 BA.

Table 1: wOBA Percentiles, 2012

PCTL	wOBA	OPS	BA
100	.438	1.041	.346
90	.376	.877	.304
75	.352	.815	.287
50	.325	.743	.261
25	.299	.684	.239
10	.279	.630	.222
0	.243	.530	.176

 

Calculation

In order to calculate wOBA, we need to consider the weight or run value of each event relative to the weight for an out.  We know how much each event is worth by looking at all kinds of situations over thousands of games.  For example, a home run is worth 1.65 runs more than an out on average.  The weights for each event are as follows:

1B 0.71
2B 1.01
3B 1.28
HR 1.65
BB 0.56 (intentional walks excluded)
HBP 0.58

We now have a new formula:

Run Rate = (0.71 x 1B + 1.01 x 2B + 1.28 x 3B + 1.65 x HR + 0.56 x BB + 0.58 x HBP)/(PA-IBB)

The MLB average run rate was .256 per plate appearance for all batters in 2012.  We could stop there, but in order to be on the same scale as OBP we want average wOBA to be about .319, the league average OBP for everyone (not just guys with 250+ PA).  Now, 319 is 24.5% higher than .256, so we multiply all of our weights by 1.245 and arrive at the following formula:

wOBA= (0.88 x 1B + 1.26 x 2B + 1.59 x 3B + 2.06 x HR + 0.69 x BB + 0.72x HBP)/(PA-IBB)

Note that FanGraphs excludes intentional walks from wOBA because they are usually issued in very specific situations and many analysts feel as if they have as much to do with game situation as with player value.

Results

Table 2 below shows the wOBAs for some past and present Tigers.  The final column shows specific percentiles.  For example, Austin Jackson's .371 wOBA fell at the 87th percentile of all batters with 250 or more PA.  That means he hit better than 87% of MLB players in 2012 without regard for position.  Other Tigers with high percentiles were Cabrera (99), Prince Fielder (97) and Andy Dirks (86).  The lowest percentiles were Ramon Santiago (2), Ryan Raburn (2) and Brennan Boesch (17). 

Table 2: wOBA for Tigers, 2012

Player	PA	wOBA	PCTL
Cabrera	697	.417	99
Fielder	690	.398	97
Jackson	617	.371	87
Dirks	344	.368	86
Hunter	584	.356	79
Avila	434	.327	54
Infante	588	.310	36
Berry	330	.305	32
Young	608	.305	32
Peralta	585	.301	27
Boesch	503	.288	17
Raburn	229	.256	2
Santiago	259	.253	2

As the great American League MVP debate raged last summer, one of the reasons some supported Angels outfielder Michael Trout over Tigers third baseman Miguel Cabrera was his speed.  Cabrera backers insisted that speed was far less important than hitting and that Trout's base running contribution should not have been enough to overcome Cabrera's hitting advantage.  They were correct that hitting plays a substantially larger role in winning games than base running but it can make a difference 

Looking at the spread in Batting Runs versus Base Running Runs (BRR) in 2012 shows us how much of an impact hitting had in comparison to base running.  Batting Runs ranged from 114 above average for the Yankees to -109 below average for the Cubs.  On the other hand, Base Running Runs went from 18 for the Angels to -18 for the Nationals.  So, the best and worst hitting teams added/cost six to seven times more runs with their bats than the best and worst base running teams added with their feet.

However, there are some players that create enough runs with their base running where it can not be ignored in calculating a player's involvement in team wins.  According to the FanGraphs base running statistics, Trout added 12 runs or just over one win with his base running, making him the most most valuable base runner in baseball in 2012.  His base running contribution was quite a bit less than either his or Cabrera's or any other big hitter's batting contribution, but it was not insignificant which is why base running is part of Wins Above Replacement (WAR) 

During the 2012 season, FanGraphs decided to separate hitting and base running as components of WAR .  The base running metrics are Weighted Stolen Base Runs (wSB) and Ultimate Base Running (UBR).  I'll use Tigers second baseman Omar Infante to illustrate how wSB is calculated. His combined statistics for the Marlins and Tigers in 2012 were as follows:

PA 554
SB 17
CS   3

By the linear weights theory, Infante gets credit for 0.2 runs for each stolen base and loses 0.4 runs for each caught stealing.  So, that's 17 * 0.2 - 3 * 0.4 = 2.2 runs.  That number then needs to be compared to league average.  Based on MLB totals for plate appearances, stolen bases and caught stealing, the average base runner adds about one run every 1,000 plate appearances.  So, the average player would contribute 554 * (1/1,000) =   0.6 stolen base runs in the same number of plate appearances as Infante.  Finally, subtracting 0.6 from 2.2 yields 1.6 wSB.

There is more to base running than stolen bases though.  For example, a player can use his base running ability to go from first to third on a single or to score on a fly ball.  He can also hurt his team by failing to move up an extra base or being thrown out trying.  Thus, Mitchel Lichtman developed the UBR statistic as a way to account for a runners base running beyond stolen bases and caught stealing.   It is determined using linear weights where each base running event takes on a value according to what bases are occupied, the number of outs and the result of the at bat.  More specifics can be found in the FanGraphs glossary and in Lichtman's primer. 

Infante had a UBR of 1.1 in 2012 meaning that he added one run with his base running other than stolen base and caught stealing over what you would expect from the average runner.  Adding wSB and UBR gives us Base Running Runs.  In Infante's case that's 1.6 wSB + 1.1 UBR = 2.7 BRR.  Since 10 runs run is worth approximately one win, Infante gets about 0.3 wins added to WAR for his base running.

Other Tigers (including newly acquired Torii Hunter)  can be seen in Table 1 below.   The leaders were speedy Quintin Berry (5.9 BRR), Hunter (4.7) and Infante.  The worst base runners were Prince Fielder (-6.6 BRR), Jhonny Peralta (-3.5) and Delmon Young (-3.0).  There are no surprises there.  The most noteworthy result is probably Austin Jackson's -0.7 BRR.  You would think he would take more advantage of his speed which might explain why they recently hired base running coach Jeff Cox.  

Table 1: Base Running Runs for Past and Current Tigers, 2012

Player	wSB	UBR	BRR	Wins
Berry	3.8	2.1	5.9	0.6
Hunter	0.6	4.1	4.7	0.5
Infante	1.6	1.1	2.7	0.3
Boesch	-0.5	1.4	0.9	0.1
Raburn	-0.4	0.4	0.0	0.0
Dirks	-0.6	0.6	0.0	0.0
Santiago	-0.1	-0.2	-0.3	0.0
Jackson	-2.0	1.2	-0.7	-0.1
Avila	-0.1	-2.4	-2.5	-0.2
Cabrera	-0.4	-2.4	-2.8	-0.3
Young	-1.4	-1.6	-3.0	-0.3
Peralta	-1.2	-2.3	-3.5	-0.4
Fielder	-0.7	-5.9	-6.6	-0.7

Data source: FanGraphs.com