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Projecting White Sox Starting Pitcher DL Time

Jeff Zimmerman recently posted a totally excellent study on starting pitchers that modeled the likelihood a starter would make a trip to the DL in the upcoming season.  Here's what he projects for the Sox starters:


Where's Jake Peavy you ask?  Well, the study had some qualifications given the difficulty of the study matter.  He defined his population by those pitchers who had at least 20 starts and 120 IP in the previous season. To quote Jeff:

The main problem with projecting the chances of going on the DL is what pool of players to look at going into a season. All players could be lumped together, but there is definite differences in DL trips between pitchers and position players. Also, when looking just at pitchers, there are starting versus relief pitchers and their usage patterns. Finally, the injury information (Josh Hermsmeyer’s injury database for 2002 to 2009 and mine for 2010) is only for major league DL trips and doesn’t included any minor league information. For this reason, I am only trying to look at players that are established major league starters and had little chance of going to the minors during the season.

So, really, there's not too much reason to exclude Peavy other than to paint with a convenient brush given the mass of data.  He's obviously an established major league starter and he just missed the cut with 17 starts and 107 IP.  In other words, it's probable that the model applies.  According to the study we need to know whether or not Peavy was on the DL in any of the last three years (at least 1 trip in '08, '09 and '10), his age (30) and the number of starts he's made over the last three seasons (just 60).  Plugging this into the model gives a 53% chance he ends up on the DL at least once this season.  But that's not all that useful.  How many actual starts does that translate to?  What are the odds he goes on the DL twice?  Zimmerman acknowledges that's farther than he's gotten so far, but he did provide a handy chart:




I simplified this by assuming that for each bar, injuries were evenly distributed and assumed 6 days = 1 start.  So the 31 to 60 bar would be worth on average 7.5 missed stars.  If we weight each bar by the given probability, we can come up with a weighted average for starts lost for an average DL trip.  That comes out to about 10 starts.

Obviously there's a huge variance from that 10 start number.  35% or so DL trips end in 4 or so missed starts while another ~20 % ends in 20 missed starts.  On top of that, it seems rather likely that pitchers who've been hurt before are more likely to miss more starts per DL trip and vice versa.  So while using this method would spit out 28 expected starts for Peavy, his recent past is reason enough to take the under there.  Reason enough even if we knew he'd be ready for spring training.  Guy hasn't hit 28 starts since 2007.  Given everything the study shows us, I think 20 starts is a good conservative projection for Peavy, with the goal of being ready to give the Sox 33 ace-level starts in 2012.

I also decided I could see how this applies to the Sox' recent history.  It's not hard to find the numbers for starts and age and I filled in the last variable with Josh Hermsmeyer's database of MLB DL trips (free to anyone who wants it).  For instance, Mark Buehrle's injury risk bottomed out at 28% in 2004, but he's never been on the DL.  I came up with an overly simple way of figuring out how many wins keeping Buehrle off the DL was worth assuming a replacement level starter took those starts he hypothetically missed.  If he had a 50% of hitting the DL, then that's .5 DL trips expected times 10 starts missed per DL trip, or 5 missed starts expected.  There are a number of problems with this method, but I expect it gets in the vicinity of the truth.  The point is mostly just to illustrate, once again, how well the Sox have performed in this arena.

Exp-Act is expected DL trips minus actual trips.  I multiply that number by 10 to get missed starts and I assume 6 IP per start.  You don't see Dan Wright or Orlando Hernandez because I didn't feel like tracking down the numbers for guys who spent one notable season on the South Side.  Danks has one more season projected than Gavin because he hit the 120/20 threshold in '07 and Gavin didn't. 

While the results are pretty impressive, I'd guess they actually significantly understate the Coop/Herm Effect.  Any time a pitcher avoids an injury, the odds he gets injured in subsequent seasons goes down and he avoids the increase in odds that DL trip is longer than average.  It's even more impressive given that we're correcting for injury risk.  Before it wasn't exactly clear whether the Sox are good at merely picking DL-resistant players, but I think the value of Jeff's study is to correct for some of that effect.  It turns out they maintain their advantage even after adjusting for age and previous DL experience.  The current rotation consists of 3 guys in the top 15 by this metric, but they didn't get to that point without exceeding expectations in the first place.  Whatever juju KW and company are cooking up, it's significantly more complex than the few variables Zimmerman's study examines.