Adding Defensive Adjustments to ERA+

All of us know by this point that it benefits us to use as many stats as we can when evaluating pitching performance. We can not simply stop at ERA, FIP, ERA+, ERA- or even WAR and then call it a day. We instead have to consider the whole spectrum of data that is available to us.

This isn't to say, however, that we've all stopped using these metrics on their own as quick and instant evaluators. It seems almost impossible not to lean heavily on one singular statistic in a post-Twitter world, where every argument is scaled-down into a rudimentary, bite-sized 140-character format. Because when consumed just one bit at a time this form of abbreviated evaluation can appear very misleading.

Generally it seems that a plurality of people prefer to use ERA+ as their quick go-to stat for pitchers (though I'm just guessing here), and I'm certainly just as guilty as any of us for doing so on occasion. Some of us have moved on to FIP and it's league adjusted, park-adjusted brethren, but today I want to focus on one of the major pitfalls we can fall into when we lean too heavily on ERA+.

This same topic was addressed over at High Heat Stats this weekend, perhaps indirectly, when Adam Darowski re-evaluated the career of the under-appreciated Rick Reuschel. In listing off the reasons why Reuschel might have been undervalued by the general baseball fan throughout the course of the right-hander's career, Adam reveals this very enlightening, very telling bit of information:

He played in front of some horrendous defenses. Phil Niekro must sympathize with him. If you think about how bad his defenses were and how many unearned runs they must have led to, you realize that the actual number of unearned runs Reuschel allowed was probably unbelievably low. He helped this by not walking many players and not allowing many home runs. Those are easy ways to be beaten and Reuschel didn’t let his opponents do it.

Reuschel's career ERA+ is a modest 114 (88 ERA-) and not quite worthy of a Hall of Famer. And it's a good bet that writers and fans alike remember this about Reuschel. But the long time Cub fares surprisingly well when it comes to WAR estimates. Why is this?

One of the great many features of WAR is that, in addition to other factors, Baseball-Reference adjusts for quality of defense. In fact, if we turn to xRA_def_pitcher, the component of WAR that attempts to quantify the number of runs for which a pitcher's defense was responsible, we find that inferior glove-handling was more damaging to just five pitchers other than Reuschel since 1900:

WORST Career Defenses, since 1900

#	Name	Debut	IP	xRA_def
1	Phil Niekro	1964	5404.0	-109.3
2	Tom Candiotti	1983	2725.0	-77.5
3	Larry Dierker	1964	2333.3	-77.0
4	Ned Garver	1948	2477.3	-70.4
5	Wilbur Wood	1961	2684.3	-69.6
6	Rick Reuschel	1972	3548.3	-69.5
7	Turk Farrell	1956	1705.0	-67.8
8	Pedro Ramos	1955	2355.3	-66.2
9	Kenny Rogers	1989	3302.7	-61.9
10	Kevin Gross	1983	2487.7	-60.4

How has this affected Rick Rueschel's ERA+, then? How badly is ERA+ misrepresenting the run-preventing abilities of Adam's underdog?

Well, in order to determine this, we would need to adjust the formula to include Reuschel's expected Runs Allowed if he had a league-average defense, rather than his actual Runs Allowed.

Oh man, here comes xRA9+

Because we can not presume to know how many of these theoretical runs would have been earned or not, we must first drop ERA+ in favor of RA9+. Conveniently, Reuschel's RA9+ is the same as his ERA+ at 114.

So the next step is to add in his negative xRA to his RA totals from each season.

[ [ lgRA / lgIP * 9 ] / [ (RA + xRA_def) / IP *9 ] ] *park factor = xRA9_plus

This would give Reuschel a career xRA9+ of 120, significantly higher than his ERA+ of 114. Enough to change your opinion on his Hall of Fame worthiness? Perhaps not, but it is important enough to when conducting serious inquires into the merit of Reuschel's career.

For individual seasons the difference in his ERA+ and xRA9+ (denoted as 'X-E' below) prove to be quite different at times:

Rick Reuschel season by season xRA9+

Year	IP	ERA+	RA9+	xRA9p+	X-E
1972	129.0	127	131	138	11
1973	237.0	130	122	132	2
1974	240.7	89	90	108	19
1975	234.0	101	96	109	8
1976	260.0	110	107	114	4
1977	252.0	155	161	177	22
1978	242.7	115	122	125	10
1979	239.0	114	119	129	15
1980	257.0	114	111	121	7
1981	85.7	110	101	118	8
1981	70.7	136	132	123	-13
1983	20.7	97	110	115	18
1984	92.3	74	79	80	6
1985	194.0	160	153	164	4
1986	215.7	97	97	93	-4
1987	177.0	150	143	126	-24
1987	50.0	92	87	86	-6
1988	245.0	106	115	112	6
1989	208.3	114	117	108	-6
1990	87.0	93	98	103	10
1991	10.7	80	89	86	6

But I can hear the younger generation of Beyond the Box Score's readership already, "Hey, what about me, I'm young and 19 years old and I party all the time and use questionable slang terms to describe my chicken nuggets, what do I care about Rick Reuschel?

Well, for contemporary leaders, xRA_def generates some interesting leaderboards with some names you'd likely expect:

WORST Career Defenses, since 2000

#	Name	Debut	IP	xRA_def	xRA_def /200 IP
1	Zack Greinke	2004	1492.0	-47.6	-6.4
2	Ricky Nolasco	2006	1113.3	-29.9	-5.4
3	Mark Buehrle	2000	2679.0	-27.1	-2.0
4	Brian Bannister	2006	667.3	-26.0	-7.8
5	Carlos Zambrano	2001	1959.0	-25.2	-2.6
6	Chien-Ming Wang	2005	765.3	-24.4	-6.4
7	Anibal Sanchez	2006	869.0	-24.2	-5.6
8	John Danks	2007	971.3	-24.1	-5.0
9	Josh Johnson	2005	916.7	-22.1	-4.8
10	Dontrelle Willis	2003	1221.7	-21.3	-3.5
11	Luke Hochevar	2007	771.0	-20.8	-5.4
12	Brian Lawrence	2001	963.0	-20.5	-4.3
13	Jose Contreras	2003	1168.0	-20.3	-3.5
14	D.J. Carrasco	2003	493.7	-20.2	-8.2
15	Kyle Davies	2005	768.0	-19.4	-5.0
16	Gavin Floyd	2004	1127.0	-18.8	-3.3
17	Nick Blackburn	2007	818.7	-18.0	-4.4
18	Paul Maholm	2005	1332.7	-17.8	-2.7
19	Jae Weong Seo	2002	606.3	-17.4	-5.7
20	Chris Volstad	2008	695.3	-17.1	-4.9

Greinke at the top of this list should surprise no one, as he's been one of the more famous E-F abusers in recent seasons, with a good chunk of that discrepancy owed to some terrible defensive support (namely a one Yuniesky Betancourt).

For his career, Greinke breaks down like this:

Name	ERA+	RA9+	xRA9+
Zack Greinke	114	115	123

A difference of almost 10 'points' between his expected Runs Allowed and his actual Earned Runs Allowed is an important omission. It certainly goes a long way in beginning to explain the chasm of talent between Greinke and Chad Billingsley:

Name	ERA+	RA9+	xRA9+
Chad Billingsley	110	110	112

Poll

I think that we sometimes assume that variations in the quality of a pitcher's defense behind him will 'cancel out' over the course of a long career like Reuschel's or even Greinke's, but that is obviously not always the case. It's comparable to expecting a pitcher's park factors to neutralize over the course of a career, which is obviously not even remotely true. We have to remember that these factors don't always stabilize. Park factors are accounted for in intermediate-level stats like ERA+ and ERA-, but defense is not. It is certainly something we ought to keep in mind when applying those metrics so definitively.

I understand that we're not all comfortable using modern defensive metrics, especially in smaller one-season samples. (I even wrote about the issue myself, just last week.) But insofar as considering a pitcher's career value, a performance evaluator like xRA9+ might be something a to consider adopting, at least in these extreme cases, especially since we're using it in the rWAR formula already (in a manner of speaking).

So, what do you think?

. . .

NOTE: I am aware of the fact that xRA_def_pitcher as it's listed at Baseball-Reference may already be park-adjusted and is actually in effect being park-adjusted again in my formula. It's not going to make a significant difference in these numbers in this article, but for future reference it would be something to consider.

Thanks to Baseball-Reference and the Lahman database.

James Gentile writes about baseball at Beyond the Box Score and The Hardball Times. You can follow him on twitter @JDGentile.