Re-WERCing Things

Linear Weights guru Tom Tango likes to use wOBA against for pitchers as well as hitters.  However, he told me yesterday that Base Runs is preferable to trying to convert wOBA to runs as I did in my last post.  So, I'm going to do some leader boards according to Base Runs today.  It turns out they aren't radically different from the linear weights leaders presented my previous post, although linear weights seemed to inflate the value of star pitchers (runs saved above average) a little bit

The Base Runs measure was created by David Smythe in the early 1990s.  It is based on the idea that we can estimate team runs scored if we know the number of base runners, total bases, home runs and the typical score rate (the score rate is the percentage of base runners that score on average.  Base Runs also works well for individual pitchers.  The complete formula can be found here.

Justin Verlander has 39 Base Runs Against in 151 innings so far this year.  This means that he should have allowed an estimated 39 runs based on the number of base runners, total bases and home runs he has allowed.  He has allowed 39 actual runs, so runs are scoring against him at the exact rate you would expect.

Verlander has allowed 33 Base Runs Above Average (RAA) which means that he has saved the Tigers an estimated 33 runs compared to the average pitcher in the same number of innings.  Table 1 shows that he is tied for first in the American League with Angels ace Jered Weaver.


Table 1 - AL Base Runs Allowed Above Average Leaders as of July 10

Player	Team	IP	Base Runs Against	RAA
Jered Weaver	LAA	140.1	33	33
Justin Verlander	DET	151.0	39	33
Josh Beckett	BOS	111.0	27	25
James Shields	TBR	142.2	44	24
Dan Haren	LAA	134.1	40	24
CC Sabathia*	NYY	145.2	47	22
Felix Hernandez	SEA	144.0	49	19
Michael Pineda	SEA	113.0	35	18
Philip Humber	CHW	107.1	34	17
Alexi Ogando	TEX	104.2	33	16

Table 2 shows that Verlander has allowed 2.32 Base Runs per nine innings.  About 93% of runs are earned, so multiply this result by .93. to put it on the same scale as ERA. The final result is a weighted component ERA.  Although, I am no longer using linear weights here, I'll keep calling it WERC because others have said the like the name. It's really not a novel idea though.  U.S. Patriot of Walk Like a Saber has been using Base Runs to evaluate pitchers for a while but prefers to not convert to the ERA scale.

Getting back to the example, Verlander has a 2.16 WERC.  Since his Base Runs Allowed is the same as his actual runs allowed, this is almost the same as his real ERA.  He is third in the league behind Weaver (1.98) and Josh Beckett of the Red Sox (2.06). 


Table 2: AL WERC Leaders as of July 10

Player	Team	IP	Base Runs/9 IP	WERC
Jered Weaver	LAA	140.1	2.13	1.98
Josh Beckett	BOS	111.0	2.21	2.06
Justin Verlander	DET	151.0	2.32	2.16
Dan Haren	LAA	134.1	2.68	2.49
James Shields	TBR	142.2	2.77	2.58
Michael Pineda	SEA	113.0	2.83	2.63
Philip Humber	CHW	107.1	2.87	2.67
Alexi Ogando	TEX	104.2	2.89	2.68
CC Sabathia*	NYY	145.2	2.92	2.72
Felix Hernandez	SEA	144.0	3.09	2.87

The raw data used to create the statistics in this post was extracted from Baseball-Reference.

Doing Some WERC During the Break

The limitations of ERA are well known in the blogosphere.  Two of the biggest issues are:

(1) ERA gives pitchers full credit/blame for results of batted balls in play despite the fact that they share that responsibility with fielders.  For example, a pitcher with a strong defense behind him will tend to give up fewer hits (and thus fewer runs) than if he had a poor defense behind him.

(2) ERA gives pitchers full responsibility for sequencing or timing of events, that is, it assumes that they can control when they give up hits and walks. For example, if a pitcher pitches extraordinarily well with runners in scoring position in a given year, he will have a lower ERA than if he had a typical year in those situations.

In reality, pitchers have limited control over both the number of batted balls that drop for hits and sequencing of events.  Thus, Defense Independent Pitching Statistics (DIPS) such as FIP, xFIP, tERA and SIERA have been developed to remove some of the noise of ERA.  DIPS are based on things that pitchers do control for the most part - walks, hit batsmen, strikeouts, home runs and types of batted balls (ground balls , fly balls, line drives, pop flies). 

Because they are based on things that pitchers essentially control, the DIPS metrics are said to be better measures of true talent than ERA.  As a result, they are also better than ERA at predicting future performance. However, they only measure a portion of a pitcher's talent and should be used as complements to ERA rather than as replacements.

More and more fans are becoming comfortable with DIPS theory, but it is still a really difficult concept to get across to the mainstream.  If you ever try to explain FIP or any other DIPS statistic to the uninitiated, you will probably find that they are skeptical of a pitching statistic which ignores hits.  They are not likely to buy into it even if they realize the limitations of ERA. 

So, rather than asking fans to take the big leap from ERA to FIP, why not meet them half way?   Instead of removing hit prevention and sequencing in one step, it might be better to remove one factor at a time.  Bill James did that with his Component ERA (ERC).  Applying the runs created methodology to pitchers, he determined what a pitcher's ERA should have been based on walks, hit batsmen,  strikeouts, homers AND hits allowed.  The runs created model is not used so much now and linear weights are better, so I wanted to find a similar statistic based on linear weights.

J.T. Jordan at Hardball Times got us part of the way there.  He used the Baseball -Reference data on batting against pitchers to calculate wOBA against (or wOBAA).  wOBAA for pitchers is calculated the same as wOBA for hitters.  The MLB leaders for 2011 are shown in Table 1 below.

Table 1: AL wOBAA Leaders in 2011

Player	Team	IP	wOBAA
Jered Weaver	LAA	140.1	.238
Justin Verlander	DET	151.0	.242
Josh Beckett	BOS	111.0	.251
Dan Haren	LAA	134.1	.258
Michael Pineda	SEA	113.0	.268
James Shields	TBR	142.2	.268
Alexi Ogando	TEX	104.2	.270
Philip Humber	CHW	107.1	.272
CC Sabathia*	NYY	145.2	.276
Jason Vargas*	SEA	121.1	.283

One good feature of wOBA is that it can easily be translated into runs above average (wRAA or RAA).  To calculate RAA, subtract league average wOBAA from a player's wOBAA, divide by 1.19 (that number changes from year to year but is usually between 1.15 and 1.25) and multiply by plate appearances.  The 2011 leaders are listed in Table 2.  Tigers ace Justin Verlander tops the list with 37 RAA meaning that he has saved the Tigers an estimated 37 runs compared to an average pitcher.   Jered Weaver of the Angels is a close second with 36 RAA. 



Table 2: AL RAA Leaders in 2011

Player	Team	IP	RAA
Justin Verlander	DET	151.0	37
Jered Weaver	LAA	140.1	36
Dan Haren	LAA	134.1	27
Josh Beckett	BOS	111.0	24
James Shields	TBR	142.2	23
CC Sabathia*	NYY	145.2	21
Michael Pineda	SEA	113.0	19
Alexi Ogando	TEX	104.2	17
Philip Humber	CHW	107.1	17
Felix Hernandez	SEA	144.0	16

So, we are almost there.  All we need to do is turn RAA into an ERA.  Here are the steps:

(1) Calculate MLB average runs scored per nine innings (4.2 in 2011)

(2) Subtract a pitcher' runs above average per nine innings pitched from the league average:
4.2- 9 x RAA/IP

(3) About 93% of runs are earned, so multiply the result in step (2) by .93.  The final result is a linear weights component ERA.  I'll call it WERC.

Table 3 shows that Weaver leads the league with a 1.87 WERC in 2011.  


Table 3: AL WERC Leaders in 2011

Player	Team	IP	WERC
Jered Weaver	LAA	140.1	1.87
Justin Verlander	DET	151.0	2.01
Josh Beckett	BOS	111.0	2.23
Dan Haren	LAA	134.1	2.39
Michael Pineda	SEA	113.0	2.68
Alexi Ogando	TEX	104.2	2.73
James Shields	TBR	142.2	2.75
Philip Humber	CHW	107.1	2.79
CC Sabathia*	NYY	145.2	2.88
Jason Vargas*	SEA	121.1	3.12

 WERC is useful because it gives us an intermediate step between ERA and FIP.  For example, Rangers right hander Alexi Ogando has a fairly large discrepancy between his ERA (2.92) and FIP (3.51).  His WERC is 2.73 which is closer to his ERA.  This suggests that a large amount of the difference between Ogando's FIP and ERA is due to batted balls in play rather than sequencing.  We could have figured this out by examining other numbers such as BABIP and LOB%, but it's more convenient to compare three stats on the ERA scale. 

Another example is Athletics fire baller Gio Gonzalez.  Gonzalez's ERA (2.47) was lower than his FIP (3.57).  However, his WERC was 3.62 which hints that the discrepancy was more due to sequencing than hits allowed.

I will apply these statistics to Tigers pitchers in a later post.