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# I'll Rearrange It 'Till It Looks Just Right Today: Can't Believe I'm Saying It, But Jo-Jo Reyes Doesn't Suck

In discussing Joseph (Jo-jo) Reyes's trade-value today, it was brought up that, although he's generally considered back-of-the-rotation fodder, there may be some value in that at the trade deadline.  The point of this exercise is not so much to determine how much Jojo will bring back in a trade as it is to determine how good Jojo's been relative to the average starting pitcher.  There are numerous factors at play here, of course.

The first issue at hand is deciding which pitching stats to use as most descriptive of Jojo's performance.  Next, we need to determine how the average starting pitcher rates according to that metric.  It is tempting -- but misleading (!) -- to simply take the MLB average for that stat and go from there.  If our goal is to see how Jojo has performed relative to how the "average starter" would, we need to make sure that we're comparing him to how that "average starter" would perform given the context in which Jojo has pitched.  So how well has Jojo pitched?

How good is the average MLB Starter?

Note that, while FIP is scaled to ERA, xFIP and tERA are scaled a bit higher.  Unfortunately, as many of the splits we will be using to determine what average starter xFIP and tRA are unavailable in-season for those stats, we will convert them based on how they differed from league ERA in 2010.  This method is imperfect but it at least tries to account for the difference in league-wide performance and allows us to scale the average values to the context in which Jojo has had to pitch.

Scaling xFIP and tRA to ERA

In order to scale league-average xFIP for 2011, when offence seems to be down from 2010 MLB-wide, we can do some quick algebra.  As mean xFIP in 2010 was 4.23, mean FIP (ERA) in 2010 was 4.08, and mean FIP (ERA) this season is 3.80, we estimate mean xFIP in 2011 as 3.94.

We will do the same with tRA.  Mean tRA in 2010 was 4.22, very similar to mean xFIP.  As expected, our estimate for MLB-wide mean tRA, 3.93, is very similar to our estimate for xFIP.

Determining League Average ERA in the Context of Jo-jo Reyes

However, Jojo pitches in the American League, so he does not get to face the pitcher two or three times per game.  As such, we should compare him to the AL average, 3.87.  Furthermore, Jojo has been a starter.  The average starter is going to have a higher ERA than the average reliever, so we should be comparing Jojo to the average AL starter.  Average AL starter ERA in 2011 is 3.91, which brings our xFIP estimate up to 4.05.  Even this, however, is a bit unfair to Jojo because he has made six of his 16 starts against AL East opponents.  To be fair to Jojo, we will estimate league-average ERA based on league average ERA against the opponents he's faced: OAK, LAA, BOS, TBR, TEX, TBR, DET, MIN, HOU, NYY, CLE, BAL, BOS, CIN, ATL, PIT.  Unfortunately, as it is very difficult to find ERA-against stats, we are forced to convert Runs/Game to ERA.  The mean R/G across MLB is 4.19, so to convert from R/G to ERA (3.80) we will use a factor of 0.91 (since not all runs are earned).  Although not every game is exactly nine innings, MLB average game this season is 8.98 ip/g, so we do not need to convert R/G to IP.  Given these numbers, we will estimate what the average ERA should be against the teams Jojo has faced (appropriately weighted for teams he has faced more than once): 3.95.  As we have already found that the ratio of AL starter ERA to AL ERA overall is 3.91  / 3.87, we further adjust our competition-adjusted value of 3.95 to 3.99.

Park Effects

All that remains to determine league-average ERA is to correct for effects of the parks in which Jojo pitched.  For simplicity of calculation, we will assume road park effects cancel out and adjust seven of Jojo's 16 starts based on the effects of the Skydome, one of the hitter-friendliest parks in the league this season, with a park factor of 1.250.  This seems quite high -- in 2010, the Dome played as a hitter's park, but not as one of the best in baseball (park factor of 1.058) and in 2009 it actually played as a fairly extreme pitcher's park (0.937).  We will use the 2010 value and estimate the park as hitter-friendly, but only slightly.  If this is the case, average ERA should be 4.22 in the home starts and 3.99 in the nine road starts.  As such, the average ERA across all 16 starts should be 4.09.

Scaling average ERA to xFIP and tERA

Now that we have our ERA at 4.09, we can estimate average xFIP, given the competition Jojo has faced, his seven starts in a somewhat hitter-friendly park, and the fact that he's a starter, as 4.24.

Doing the same for tERA, we find that the average tERA, given Jojo's context, should be 4.23 (again, roughly the same as his xFIP).

Jojo's actual xFIP this season is 4.40 and his actual tERA this season is 4.62, meaning that Jojo grades out to be worse than a league-average starter.  However, a league-average starter is actually quite valuable because many starters must be worse than league average.  So how much worse is Jojo Reyes than a league-average starter?

First, we will adjust Jojo's actual xFIP to reflect what it would be in a neutral context by determining the difference between league-average xFIP in a neutral context and league-average xFIP in Jojo's context.  In 2011, our estimate for mean xFIP MLB-wide was 3.94 in a neutral context and 4.24 in Jojo's context, so our factor should be 0.93.  Modifying Jojo's actual xFIP (4.40) by this factor, we find that his adjusted xFIP is 4.09, which puts him in this company (some comparable starters: Brian Deunsing, Jeff Francis, Clay Buchholz, Jake Westbrook, Bronson Arroyo, Colby Lewis, Kyle McClellan, Matt Harrison, Carlos Zambrano).

Jojo does not grade as well by tERA.  However, when adjusted for context, he grades out acceptably there as well, with an adjusted tERA of 4.30, which puts him in the company of Carl Pavano, Mark Buehrle, Jeremy Hellickson, Edwin Jackson, Jonathan Sanchez, Mike Leake, Ervin Santana, and Paul Maholm.

While I would not say any of these pitchers are elite starters by any means (notwithstanding Buchholz maintaining BABIP below .275), they are all useful major league pitchers who certainly belong in a major league rotation.  Entering the 2011 season, I would not have expected Jojo Reyes to, but I guess he does as well.

UPDATE:

xFIP and tERA quartiles:

xFIP:     1st Quartile: 2.13 - 3.40
2nd Quartile: 3.40 - 3.78
3rd Quartile: 3.78 - 4.11
4th Quartile: 4.11 - 5.20

tERA:   1st Quartile: 2.29 - 3.53
2nd Quartile: 3.54 - 4.11
3rd Quartile: 4.11 - 4.63
4th Quartile: 4.65 - 6.38

As we see, the spread of each of these is quite different.  So far in 2011, tERA ends up scaling higher than xFIP, so this will alter our calculations a bit.  Essentially, this means that Reyes actually grades out better by tERA standards than he does by xFIP standards -- While his adjusted xFIP is on the lower end of the third quartile, his adjusted tERA is squarely in the third quartile of MLB starters.  He is not quite average, but he does not quite so bad, either.