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Adding Defensive Adjustments to ERA+

Pitching in front of sub-par defenses for a substantial amount of time can have an extremely detrimental effect on a pitchers league-adjusted, park-adjusted statistics. Yet we still continue to cite these metrics with confidence more and more often. What happens when we try to account for these factors that exist outside of the pitcher's control? Which players benefit the most?

Zack Greinke is more bomb than a triceratops and chicken nuggets.
Zack Greinke is more bomb than a triceratops and chicken nuggets.
Jeff Gross

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


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.