Harang and Arroyo: What a Difference a Defense Can Make

Bronson Arroyo led the Reds' starters in wins, ERA, and innings pitched in 2009.  Aaron Harang led the Reds in losses and has managed just 12 wins over the last two seasons.  What if I told you that the biggest difference between those two pitchers last year was something that is largely out of their control?

As Justin showed yesterday, the Reds were arguably the best defensive team in the National League in 2009, but oddly enough, Harang saw very little benefit from that improved defense.  Out of all qualified pitchers, Harang finished dead last in the National League in Defensive Efficiency Ratio (DER) at .669.  Arroyo on the other hand had the 5th best ratio at .735.  This means that out of every 100 balls that were put into play (not counting home runs), the Reds defense turned 6.6 more of them into outs for Arroyo than they did for Harang.  That may not seem like a ton until you realize that batters put the ball into play 514 times against Harang and 722 times against Arroyo last season.  Those numbers add up quickly.

This is not to say that none of it is Harang's fault.  The big right-hander did have the highest Line Drive allowed rate in the Majors at 24% and his ground ball rate of 34% was much lower than Arroyo's 44% GB rate.  But those numbers still don't seem like enough of a reason for the dramatic 30+ play difference in the two pitcher's numbers.  So I did a little mathematical experiment.

Using the batted ball data from Baseball Reference's splits page, let's compare each player's BABIP to the team's BABIP for each batted ball type.  We're using BABIP, which is more or less 1 - DER, because BBRef does not include reached on error within the pitcher splits.

You can see here that Arroyo has had the fortune of many more of his batted balls being turned into outs across the board.  His BABIP outperforms the rest of the Reds team in every single category except for the tiny sample of bunts, most of which are sacrifice hits.  If you subscribe to the DIPS theory that pitchers have very little control over what happens to a ball once it is put into play, then you can see that Arroyo benefited dramatically from defensive help much more than Harang did.

What's that look like from a runs perspective?  If we use wRAA (runs above average based on wOBA) for our estimator, we see that Arroyo, based on actual values, was about 9 runs better than the average pitcher while Harang was about 7 runs worse than the average pitcher.  If we adjust each pitcher's BABIP lines per batted ball type to match the Reds' team average in each type (exchanging only singles and outs, leaving all extra base hits the same), Arroyo's wRAA changes to 3.5 runs below the average pitcher while Harang moves to 7 runs better than average.  That's a -12.5 run shift for Arroyo and a +14 run shift for Harang, all simply by leveling out the defensive success behind them.  I'll admit that it was a much bigger change than I expected.

Unfortunately, I won't simply take these numbers and adjust ERA because the chain effect of converting a hit into an out and vice versa would adjust the number of innings pitched and the math is too complicated for my small brain.  Besides, the point wasn't to argue the quality of each pitcher so much as to demonstrate how two pitchers, pitching for the same team, can get very different support from their defensive teammates and what a dramatic effect that can have on their outcomes.  And that's not even mentioning run support.  No one should be surprised if Harang is the 15-game winner next year and Arroyo is struggling on a start-by-start basis.  Such is the fickle nature of depending on your teammates.