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The Arroyo contract extension: another look

The Reds recently made two major contact extensions: one to Bronson Arroyo, and the other to Jay Bruce.  Charlie Scrabbles already penned a good overview of the Arroyo deal here, and came to the conclusion that the deal is unlikely to work out in the Reds favor (Dave Cameron at FanGraphs came to a similar conclusion, though these posts were made before details of the deferments were announced).  And more recently, RijoSaboCaseyWKRP gave a nice overview of the Jay Bruce signing.  I wanted to follow up on those pieces with a best-guess sabermetric take on the contracts.  I'll start with Arroyo, but will hopefully get something up on Bruce within the next few days.

Let's start with an overview of Arroyo's past performances.  I'm going to focus exclusively on his numbers from 2004 onward, which includes his first full season in the rotation with Boston at age 27, but not the roughly 200 innings of ineffectiveness prior to that point.  Why ignore those early years?  Because it was a long time ago, and I think it's reasonable to assume, given Arroyo's success after that point, that he is not the same pitcher he was then.  2004 onward still gives us a sample of 1471 1/3 innings to work from, which seems pretty big to me...and that's important given some of the peculiarities of Bronson's performance.  

Year Age Team IP ERA* FIP* xFIP BABIP ParkFactor TeamFielding K/9 BB/9 HR/9
2004 27 BOS 178.7 3.81 3.86 4.21 0.299 1.02 -27 7.2 2.4 0.9
2005 28 BOS 205.3 4.31 4.47 5.08 0.285 1.02 -20 4.4 2.4 1.0
2006 29 CIN 240.7 3.16 4.03 4.15 0.279 1.01 -18 6.9 2.4 1.2
2007 30 CIN 210.7 4.07 4.43 4.74 0.318 1.01 -22 6.7 2.7 1.2
2008 31 CIN 200.0 4.61 4.34 4.12 0.321 1.02 -13 7.3 3.1 1.3
2009 32 CIN 220.3 3.93 4.60 4.56 0.270 1.04 41 5.2 2.7 1.3
2010 33 CIN 215.7 4.02 4.45 4.60 0.246 1.03 41 5.1 2.5 1.2
Totals -- BOS/CIN 1471.3 3.97 4.32 4.49 0.287 1.02 -18
6.1 2.6 1.1

Note: In all of the stats above (except IP and BABIP), I've tried to adjust for both park and fielding behind Bronson.  FIP and xFIP do the fielding implicitly (though I park-adjust HR rates for FIP), but for ERA I've tried to adjust based on published team UZR, DRS, and (in recent years) fan scouting data.  I'm aware there are potentially significant problems in the fielding data we currently have available (though the magnitude of the problems are not yet confirmed), but we have to use what we have because that's all we have!  I'm reporting what I'm using so that you can adjust accordingly should you disagree.

The interesting thing about Arroyo is that he seems to routinely outperform his peripherals.  That is, if Arroyo were a "normal" pitcher, we'd expect that his ERA would converge on his FIP and xFIP at a large sample.  And yet, for 2004-2010, his park- and fielding- adjusted ERA is 0.35 runs better than his FIP and a whopping 0.5 runs better than his xFIP.  You could argue that this is "luck," but we're talking about almost 1500 innings here!  I tend to think that much of this is real.  Arroyo is a crafty sort of pitcher, pitches backwards, etc, etc.  If any type of pitcher is likely to beat his peripherals, Arroyo's the kind of guy I'd expect to do it.  But you might disagree, which is fine.  We'll keep both possibilities alive, because I don't know what is actually correct.  Here are his WAR totals, based on four different estimates of performance:  

Year Age Team WAR-R/9* WAR-BsR* WAR-FIP* WAR-xFIP
2004 27 BOS 3.1 4.6 4.2 3.5
2005 28 BOS 2.7 4.0 2.8 1.5
2006 29 CIN 6.5 6.3 4.0 3.6
2007 30 CIN 3.1 2.6 2.4 1.7
2008 31 CIN 1.4 1.7 2.1 2.6
2009 32 CIN 3.2 2.9 1.4 1.5
2010 33 CIN 3.2 4.4 1.5 1.1
Totals -- BOS/CIN 23.3 26.4 18.4 15.6

Basically, each column gives Arroyo progressively less and less credit for what has happened in the game around him:

WAR-R/9 is based strictly on his actual runs allowed, as recorded by the official scorer.  So this gives Arroyo full credit for all events, including any "lucky" outs or lucky sequencing of events.  It does include an adjustment for park (which benefits Arroyo) and an adjustment for fielding (which helps or hurts him in a given year, but overall helps him).  By this measure, Arroyo has averaged 2.6 WAR over the past three years.

WAR-BsR uses all events that occurred with Arroyo on the mound--singles, homers, strikeouts, errors, etc--but it removes sequencing by assuming they occured at random by plugging them into a base runs equation that I use.  For many pitchers sequencing does seem more or less random, but some probably do have some sequencing skill.  I don't know if Arroyo does or not.  But anyway, Arroyo has averaged 3.0 WAR over the past three years by this measure.

WAR-FIP measures Arroyo only by his innings, strikeouts, walks, and home runs allowed (though I park-adjust these).  This can be thought of as another way to remove fielding from the picture, but it also recognizes that many pitchers have limited control over the outcome of batted balls in play.  By this meaure, Arroyo has averaged 1.7 WAR over the past three years.

WAR-xFIP is the same as FIP, except that instead of using actual home run rates, it assumes all deviations from HR/FB% to be random and not skill based.  By this measure, Arroyo has averaged 1.8 WAR over the past three years.

This is hard thing about assessing Arroyo--these are all reasonable approaches, and yet we're getting that he's been produced anywhere from 1.7 to 3 WAR per season over the last three years.  Therefore, if we add in some aging and regression, we might project Arroyo to be anywhere from a 1.2 WAR to a 2.5 WAR player in 2011!  That's an enormous range, but it's honestly about as well as I can do.  I wouldn't argue with any projection in that range.

Now, what are we paying him to do?  Arroyo is now signed for three more years for $35 million, but because so much of the money is deferred and thus its impact is minimized due to baseball inflation, the players' union estimates his contract is only worth $28.9 million.  I am thankful that they produced this number, because I couldn't figure out how to properly discount the impact of the deferred money.  It's not entirely fungible, though it amounts to less than a half-win "burdon" on the club from 2014-2021.  Anyway, copying an approach by Tom Tango, here's a schedule that justifies that sum:

Year Age $/WAR WAR Payout
2011 34 $5.00 2.3 $11.5
2012 35 $5.40 1.8 $9.7
2013 36 $5.83 1.3 $7.6
Total $28.8

So based on some reasonable assumptions of aging and future market value (not to mention current $/WAR, which is not at all certain), this contract basically identifies him as close to, though not at the top of, the range of "reasonable" true talent WARs that we came up with above.  That, to me, makes it a bit on the high side, but still very much a reasonable and justifiable deal.

...and just to throw more uncertainty into the mix, what if we basically assume that the deferred money is inconsequential since it's just a few million per year.  If that's true, then Arroyo is really only making around $20 M (according to Cot's).  Let's run that one:

Year Age $/WAR WAR Payout
2011 34 $5.00 1.75 $8.8
2012 35 $5.40 1.25 $6.8
2013 36 $5.83 0.75 $4.4
Total $19.9

So now we're down closer to the bottom end of our projection range.  And I could be convinced that this is a reasonable way to look at it...though I tend to favor the players union number since there has to be some penalty to all of those deferred dollars off in the future.


And that's where I'll leave it.  I never did really come to some grand final number on what the guy SHOULD HAVE been paid.  And so you may, at this point, think that this post was all a whole lot of nothing.  But I guess my point is to illustrate how much uncertainty there is in projecting (and paying) a guy like Arroyo.  He has a long track record, but he also consistently has behaved in a manner that defies how we typically judge pitchers statistically. 

The Reds are convinced that he's a good bet to be on the high end of the range of reasonable projections.  But they have smart people and good scouts (not mutually exclusive) working for them, so they probably have good reason for thinking that.  The key point is that the contract is in line with a reasonable projection for Arroyo, and so I feel pretty good about it.  And this is coming from someone who has been against extending Arroyo from the start!