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The Value of a Closer

At The Book Blog, MGL fleshes out an opinion which goes against the Sabermetric consensus that closers are overpaid:

A replacement level short reliever allows around .5 runs per game more than an average pitcher.

An elite closer allows around 1 run better than an average pitcher, or 1.5 runs per game less than a replacement reliever.

A typical elite closer pitches around 70 innings with an average Leverage Index (LI) of 2.0. That means that he pitches 140 “effective” innings.

For 140 innings at 1.5 per 9 innings less than a replacement reliever, that is 23.33 runs better than a replacement reliever, or 2.33 WAR.

In other words, an elite closer is worth around 2.33 WAR per season.

What is that worth in the FA market? Almost 12 million dollars. So, Brian Wilson, Heath Bell, et al. are actually underpaid.

Does that mean that a team cannot acquire a very good reliever who can function as a closer for less than market value, based on his expected (projected) WAR? No, it does not. In fact, it is much easier for a savvy team to acquire and/or use a cheap but good reliever as a closer than it is for a team to do so with any other position.

Still, closers are NOT overpaid as a class, especially the elite ones. In fact, you can make the argument that they are underpaid. Some are of course. But, so are players at any other position.

I take issue with the conclusion for its use of replacement level. Replacement level is great for position players because they are usually replaced by an actual replacement-level player. This isn’t the case for closers. The Cincinnati Reds didn’t replace Ryan Madson with Sam LeCure; they called on Sean Marshall, a lefty who has been nothing short of elite since moving to the bullpen in 2009.

The pecking order for high-leverage relievers is deeper than that of position players or even starting pitchers. It’s a math problem, simply. The bullpen consists of, generally, seven pitchers whose sole job is to get through one inning of work with the least amount of damage. Based on skill, experience, and reputation, those one inning stints will come in a variety of situations, so you have a closer, a set-up man (eighth inning), a LOOGY, a long reliever (two-plus innings in blowouts), and a few middle relievers.

At second base, the Phillies went from Chase Utley to Freddy Galvis, who is your typical replacement level player. Conversely, if Jonathan Papelbon goes down, they simply go to Chad Qualls or Antonio Bastardo, two arms that are decidedly not replacement-level. Those high-leverage innings aren’t given to Michael Schwimer or Joe Savery. The replacement level for closers should be significantly higher than for relievers in general, which is why MGL’s comparison is not accurate.

As an example, let’s say you’re on Yelp, looking for roof repair. You read reviews for a bunch of different candidates, noticing very little correlation between price and competency. The lesser-known roofing companies (LK) have won as many Roofing Company of the Year awards as the big-name companies (BNC). You also notice the lower-quality roofing companies (LQ) who don’t do nearly as good of a job, but some of them charge as much or more than the lesser-known, higher-quality roofing companies. MGL is saying the equivalent of, “BNC aren’t too pricy — they’re cheaper than LQ and do a much better job! LQ only do shingles!” When, in reality, relative to their actual competition (no smart consumer will hire LQ), LK is the much better value: they do the same job at a cheaper price.

When the home team is ahead by one run going into the top of the eighth inning, they are sending their set-up man into a situation with a leverage index of 2.2. When they do the same with their closer in the ninth, the LI is 2.9. Even considering that both titles are fabricated and entirely meaningless in the grand scheme of things, the average salaries of the two positions are not proportional — the closer makes significantly more than the set-up man. By that notion alone, closers are vastly overpaid.

I went through last year’s most frequent eighth- and ninth-inning relievers and noted their 2011 salaries as well. These were the results:

Team Set-Up Salary Closer Salary Difference
NYY Robertson $0.46 M Rivera $15.00 M $14.54 M
NYM Isringhausen Rodriguez $12.17 M $12.17 M
BOS Bard $0.51 M Papelbon $12.00 M $11.50 M
CIN Masset $1.55 M Cordero $12.13 M $10.58 M
MIN Perkins $0.70 M Capps $7.15 M $6.45 M
SDP Adams $2.54 M Bell $7.50 M $4.97 M
SFG J. Lopez $2.38 M Wilson $6.50 M $4.13 M
PHI Bastardo $0.42 M Madson $4.50 M $4.08 M
ARI Hernandez $0.42 M Putz $4.00 M $3.58 M
COL Betancourt $3.78 M Street $7.30 M $3.53 M
BAL Johnson $0.98 M Gregg $4.20 M $3.23 M
TOR Janssen $1.10 M Francisco $4.00 M $2.91 M
FLA Mujica $0.80 M Nunez $3.65 M $2.85 M
KCR Crow $1.40 M Soria $4.00 M $2.60 M
TBR Peralta $0.93 M Farnsworth $3.25 M $2.33 M
CLE Pestano $0.41 M Perez $2.23 M $1.81 M
CHC Wood $1.50 M Marmol $3.20 M $1.70 M
DET Benoit $5.50 M Valverde $7.00 M $1.50 M
PIT Veras Hanrahan $1.40 M $1.40 M
SEA Wright $0.90 M League $2.25 M $1.35 M
STL Motte $0.44 M Salas $0.41 M -$0.02 M
HOU W. Lopez $0.44 M Melancon $0.42 M -$0.02 M
WSN Clippard $0.44 M Storen $0.42 M -$0.03 M
ATL Venters $0.53 M Kimbrel $0.42 M -$0.11 M
MIL Loe $1.25 M Axford $0.44 M -$0.81 M
LAD Guerrier $1.50 M Guerra -$1.50 M
CHW Thornton $3.00 M Santos $0.44 M -$2.57 M
TEX Oliver $3.25 M Feliz $0.46 M -$2.79 M
OAK Balfour $3.75 M Bailey $0.47 M -$3.29 M
LAA Downs $5.00 M Walden $0.41 M -$4.59 M
AVG $1.64 M $4.39 M

(Blank spaces in the “salary” columns indicate that the player was on a Minor League contract. Cot’s Contracts did not list a salary figure, but it was likely around $415,000.)

Note that while some teams used a more expensive set-up man, the highest set-up salary belonged to Joaquin Benoit at $5.5 million. Five closer salaries exceeded that (four more than doubled it, in fact) and an additional six were between $4-5.5 million.

For the average closer’s salary to have been proportional to the average set-up man’s salary, with regard to their typical leverage index (2.2 to 2.9), it should have been $2.16 million as opposed to $4.39 million. So, based on last year’s data, the average closer was paid roughly twice what he was worth on average relative to set-up men — their next-of-kin.