Monday, May 26, 2014

What is wOBA?

I'm seeing a lot of talk about "wOBA" on twitter this morning, so it's time for my annual wOBA primer.
Several 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 this year is Victor Martinez at .417.  We know that an OBP of .417 would be outstanding.  A wOBA of .417 is equally outstanding, but it measures Martinez's overall batting contribution rather than just his ability to get on base.  Andrew Romine, on the other hand, has a wOBA of .239.  We know that a .239 OBP is horrible and a .239 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.

wOBA versus OPS

Table 1 below shows where Tigers rank among American League hitters with at least 130 plate appearances in 2014.  You can see that Martinez leads the league in both wOBA and OPS and that most players rank similarly on the two measures.  The biggest discrepancy on the Tigers is catcher Alex Avila who ranks 33rd on wOBA and 40th on OPS.  The reason for the less favorable rank on OPS is because OPS does not give Avila enough credit for his best offensive skill - getting on base.  The lesson to be learned here is that OPS usually works pretty well, but that wOBA gives you a more accurate assessment of some players.

Table 1: Tigers Ranks in wOBA and OPS
Player
wOBA
wOBA Rank
OPS
OPS Rank
Martinez
.417
1
1.004
1
Cabrera
.387
8
.902
9
Kinsler
.366
20
.837
21
Avila
.348
33
.772
40
Hunter
.333
44
.761
44
Davis
.330
48
.746
50
Jackson
.328
52
.753
48
Median
.326
56
.732
56
Castellanos
.279
101
.635
97
Data source: FanGraphs.com

If you don't like math, you can stop here hopefully with a better understanding of wOBA.  If you want to see the details, read on.

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 1.64 runs more than an out on average.  The weights for each event are as follows:

1B 0.69
2B 0.99
3B 1.26
HR 1.64
BB 0.54 (intentional walks excluded)
HBP 0.56

We now have a new formula:

Run Rate = (0.69 x 1B + 0.99 x 2B + 1.26 x 3B + 1.64 x HR + 0.54 x BB + 0.56 x HBP)/(PA-IBB)

The MLB average run rate is .244 per plate appearance relative to the run value of an out for all batters in 2014.  We could stop there, but in order to be on the same scale as OBP we want average wOBA to be about .317, the league average OBP for everyone (not just guys with 130+ PA).  Now, 317 is 29.9% higher than .244, so we multiply all of our weights by 1.299 and arrive at the following formula:

wOBA= (0.90 x 1B + 1.29 x 2B + 1.64 x 3B + 2.13 x HR + 0.70 x BB + 0.73x 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.

Saturday, May 24, 2014

Miguel Cabrera Adding Runs With Situational Hitting

Many fans grumble that statistics such as OPS and Batting Runs do not account for situational hitting.  For example, if Tigers slugger Miguel Cabrera singles with a runners on second and third to drive home two runs, he gets the same credit as he would for a single with the bases empty.  Some will argue that this is not fair because he contributes more to his team in the former scenario than the latter.  In this post, I will re-introduce an under used statistic which accounts for a hitter's performance in different circumstances. 

Traditional fans like to address situational hitting with the familiar Runs Batted In statistic, but that is a team dependent measure.  A player has more or less opportunity to drive in runs depending on who is batting in front of him.  Thus, a player gets acknowledged for driving home runs, but does not get penalized for failing to drive home runs.  So, the RBI count is not an adequate measure of situational hitting.

Other fans point to batting average with runners in scoring position, but that is based on a limited number of plate appearances.  It also doesn't consider the number of outs, the specific base runners (e.g. bases loaded versus second base only) or the type of hit (single, double, triple or home run).  Moreover, it ignores a player's performance when no runners are in scoring position.  

What we want is a statistic which gives a player credit for everything he does including situational hitting.  Batting Runs Above Average by the 24 Base/Out States (RE24) - found at FanGraphs - does just that.  The RE24 statistic is also sometimes referred to as "Value Added".  This metric will give a player credit for his singles, doubles, and all other events, and gives him extra credit for hits occurring with runners on base.  It even gives him points for a scenario which most other metrics ignore - moving a runner over with a ground out.  On the other hand, it subtracts extra points for hitting into double plays.

In past posts, I discussed just plain Batting Runs or Weighted Runs Above Average (wRAA or RAA) which is an estimate of how many runs a player contributed to his team beyond what an average hitter would have contributed in his place.  The RE24 metric is similar to RAA except that it uses base/out states in the calculation.  An example of a base/out state is "runners at first and third and one out".  There are 24 possible base/out states and RE24 takes all of them into consideration. 

In the calculation of RAA, a double with the bases loaded and two outs counts the same (0.770 runs) as a double with the bases empty and no outs.  Conversely, RE24 counts the bases loaded double more than the bases empty double (2.544 versus 0.632) because it does more to increase the expected runs scored in the inning.

The RE24 metric for one at bat gives us the difference between run expectancy at the beginning and end of a play.  For example, suppose Cabrera bats with a runner on first and one out. In that situation, we would expect 0.556 runs to score by the end of the inning.  Assume that Cabrera then doubles, putting runners on second and third with one out. In that situation, we would expect 1.447 runs to score by the end of the inning. Therefore, Cabrera's double is worth 0.891 runs.

Summing RE24 over all of a batter’s plate appearances yields his season total RE24. For
example, Cabrera has a RE24 of 16.8 this year.  So, by that measure, he contributed about 17 runs above what an average batter would have been expected to contribute given the same opportunities. This is higher than his 11.2 RAA, which means that Cabrera has been especially good in situations with high run expectancy and has added more to his team’s runs total than RAA indicates.  We can estimate that he has contributed an extra 6 runs with his situational hitting.

Since situational hitting is largely (although not completely) random, RE24 is less predictive than RAA and should not generally be used as a measure of ability.  It is, however, a good alternative to RAA for looking at past performance.

Table 1 below shows that Cabrera is second in the American League in RE24 behind Athletics outfielder Brandon Moss (20.8).  Using RAA, Cabrera would rank only 8th in the league.  Another player who looks quite different using RE24 versus RAA is David Murphy of the Indians (15.8 versus 4.8 or a difference of 11 runs).

Table 1: AL RE24 Leaders
Name
Team
RE24
RAA
RE24-RAA
Brandon Moss
Athletics
20.8
14.9
5.9
Miguel Cabrera
Tigers
16.8
11.2
5.6
Michael Brantley
Indians
16.7
11.5
5.2
Mike Trout
Angels
16.1
11.1
5.0
David Murphy
Indians
15.8
4.8
11.0
Jose Bautista
Blue Jays
15.4
19.3
-3.9
Josh Donaldson
Athletics
14.8
10.3
4.5
Shin-Soo Choo
Rangers
14.6
13.4
1.2
Alexei Ramirez
White Sox
13.7
9.7
4.0
Nelson Cruz
Orioles
13.6
13.1
0.5
Jose Abreu
White Sox
12.2
10.1
2.1
Melky Cabrera
Blue Jays
11.8
10.8
1.0
Adam Dunn
White Sox
11.6
9.7
1.9
Kurt Suzuki
Twins
10.5
4.2
6.3
Chris Davis
Orioles
10.3
8.2
2.1
Robinson Cano
Mariners
9.7
4.5
5.2
Brett Gardner
Yankees
9.7
5.7
4.0
Dayan Viciedo
White Sox
9.5
5.0
4.5
David Ortiz
Red Sox
9.2
9.2
0.0
Yangervis Solarte
Yankees
8.7
9.0
-0.3
Data source: FanGraphs.com

Table 2 shows that designated hitter Victor Martinez (8.7) and second baseman Ian Kinsler (6.5) rank second and third among the Tigers in RE24.  Martinez leads the Tigers with 13.4 RAA, but has not performed as well in high leverage at bats as average at bats, so has a differential of -4.7.  Catcher Alex Avila (-4.1 differential) is another Tiger who has not done as well in high leverage opportunities.   

Table 2: Tigers RE24 Leaders
Name
RE24
RAA
RE24-RAA
Miguel Cabrera
16.8
11.2
5.6
Victor Martinez
8.7
13.4
-4.7
Ian Kinsler
6.5
8.1
-1.6
Torii Hunter
4.6
3.8
0.8
Rajai Davis
3.0
0.7
2.3
Austin Jackson
1.1
1.8
-0.8
Alex Avila
-0.7
3.4
-4.1
Nick Castellanos
-4.8
-4.7
-0.1
Andrew Romine
-9.2
-6.8
-2.4



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