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.

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13 comments

  1. Common Sense

    April 27, 2012 07:27 AM

    The replacement level is fine as a baaseline. The next guy in line if the close goes down is also above replacement level, just by not as much.

    Its like temperature. Does 0 degrees mean there is a lack of degrees? No, it means according to an arbitrary baseline, that level of temperature is zero.

    Is 100 degrees twice as hot as 50? Again, no, it is just twice as much on a ratio scale. WAR works the same way, it is meant as a ratio scale to a baseline, and it is different for every player. While most teams have multiple above replacement pitchers in their pen, you would not know that without first establishing your baseline.

  2. Keith

    April 27, 2012 07:56 AM

    Great article. Very good rebuttal and good points. Definately like the idea that the replacement level should be higher for closers.

  3. Tyler

    April 27, 2012 08:04 AM

    I think the next step in your counterargument here is to compare ‘elite closer’ WAR against ‘elite set up man’ WAR. I’d wager that, in the end, both probably deserve close to the same paycheck and also that the elite closer is not nearly as common as MGL seems to imply. Most teams don’t have an elite closer, and most elite closers seem to only be elite for a part of their career.

    By MGL’s standard here, paying Papelbon $12 million is paying him at value. For 2012, that will almost definitely be true. But proper player value would account for length of contract–expecting Papelbon to sustain the same level of quality through 2015 is the part of his contract people don’t like. I’d guess that elite closer-level performance may very well be one of the most difficult to predict.

  4. Bxe1234

    April 27, 2012 08:07 AM

    Replacement level for the bullpen is so odd to me in general. The guy replacing anyone in the pen is, in nearly every case, (unless you’re replacing Brad Lidge with Jose Contreras instead of Ryan Madson for some reason), probably the next best in a line of 7 big leaguers (and the AAAA or prospect types that come behind that). Same is true in the rotation, to a lesser extent. I wonder if the replacement level calculations in the bullpen are bound to be in dispute more than any other position, making quantification of the pen more difficult than any other group of players.

  5. hk

    April 27, 2012 08:45 AM

    Bxe,

    The same is not true of the rotation. When a Cliff Lee gets hurt, he is replaced by a Kyle Kendrick. The drop-off from most teams’ average starting P to their 6th starter is > the drop-off from most teams’ closer to their next best reliever.

  6. John

    April 27, 2012 09:25 AM

    Wow, those poor 8th inning guys are vastly underpaid. Using the same numbers from your table, if closers average $4.39 mil. for their 2.9 TLI, then the set-up guys should be getting $3.33 mil for their 2.2TLI.

    Sarcasm aside, is Kendrick really Lee’s replacement? Using the bullpen hierarchy approach, isn’t Hamels Lee’s replacement, then Worley is Hamels’ replacement. Blanton is Worley’s replacement, and finally, Kendrick is Blanton’s replacement. Each one’s a little worse then the guy he’s replacing, but it’s not as drastic as Kendrick for Lee.

    If Pap blows out his elbow, and all the other dominoes fall in line (Qualls to the 9th, etc), we wouldn’t say that Herndon is replacing Pap, even though the end result is that he’ll probably end up pitching more, and in more high leverage situations than he would if everyone remained in their “designated inning” or “defined role.”

  7. hk

    April 27, 2012 09:37 AM

    John,

    No, you can’t use the bullpen hierarchy approach because that one is leverage driven. The 8th inning guy becomes the closer, the 7th inning guy becomes the 8th inning guy and so on. If Papelbon gets injured, you may replace him on the roster with Schwimer or Savery, but when Schwimer or Savery pitch, it should be in a much lower leverage situation than the ones in which Papelbon was pitching. On the other hand, when Kyle Kendrick replaces Cliff Lee, he pitches the same innings (the 1st inning until he is replaced) that Lee would have pitched.

  8. nik

    April 27, 2012 09:49 AM

    hk, but each guy in the bullpen is now pitching in a higher leverage situation, as the mop-up guy now might get into some closer games because there is a new mop-up guy coming in from AAA. The cumulative effect is such that John’s point is exactly correct. So I agree with John and disagree with the premise of this article.

  9. John

    April 27, 2012 09:54 AM

    HK,

    Good point, but I’m not thinking of just a single game. Over the long haul, either way (starter down vs. closer down) you end up with someone pitching more innings, and higher leverage ones at that, than is ideal.

    I’m also assuming that when off days allow for the 5th starter to be skipped, the Phillies might be more inclined to skip Kendrick and keep everyone else on regular rest. In that way, he’s not replacing Lee, because there’s no way (short of injury) that Lee would get skipped just because there was an off day.

  10. Bxe1234

    April 27, 2012 10:21 AM

    So when I said “to a lesser extent”, I may have been right, but had nothing to back it up. That’s like hitting .330 with few XBH and making a mess of base running mistakes. Call me Juan.

  11. Billion Memes

    April 27, 2012 12:41 PM

    I tend to think that MGL’s premise is a pretty good explanation of how the closer’s market functions in reality. That doesn’t mean it’s the best allocation of resources. If you follow it through to conclusion, as BB does, you end up with elite non closers being a much better value than elite closers. The thing is, elite non closers are less likely to reach full free agency. By the time they do, if they truly are elite, they will often have become closers. IMO, relief pitcher is the one position where leverage comes into play to help determine their true value. Position players and starters are entering games at null leverage. Aside from the playoffs, they arent chosen to play based on the importance of the moment. That’s why I believe relief pitcher WAR still needs work.

  12. Phillie697

    April 27, 2012 01:26 PM

    The biggest flaw of his argument, which all of you have not picked up on, is that he multiplied the innings pitched by the elite closer by the actual LI, not the relative LI to other relievers. Most relievers don’t come into the game pitching in LI of 1. He artificially inflated the worth of closers relative to other relievers by using a LI that’s calculated using innings pitched by ALL pitchers, starters AND relievers alike, and as we all know, starters are THAT much more valuable by the virtue of pitching around x3 the amount of innings than a closer.

  13. Phillie697

    April 27, 2012 01:50 PM

    In fact, to expand upon the above, if we’re talking about someone replacing the closer, doesn’t it stand to argue that the replacement will pitch in similar situations as the closer would have, i.e. an average LI of 2.0 as well? Therefore, multiplying the innings pitched by the LI is in fact just wrong. The proper comparison still simply multiplying the innings pitched by the run difference, 1.5/9 inning * 70, or around 11.67 runs, or approximately 1.17 WAR. So yes, actually MGL, closers are VASTLY overpaid.

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