How "fielding-independent" are baseball's true outcomes?

On May 5, 1998, Kerry Wood threw the greatest game ever pitched. A one-hit shutout with a record-tying 20 strikeouts. The one hit was a ground ball that just got under the third baseman's glove. If he makes that play, it preserves an incredible no-hitter. But it also means the game ends one batter earlier, with a Craig Biggio ground out instead of historic strikeout number 20. Wood's strikeout total, and K/9, benefited from poor fielding.

It's an anecdote that shows the way a rate statistic we think of as "fielding independent" actually does depend somewhat on the quality of your defense.

This is one area where sabermetrics might be lacking, failing to reflect how pitching rate statistics are on a per-inning (thus per-out) basis rather than per-batter faced. My issue there is that fielding can either shorten or lengthen innings and create more opportunities for the "true outcomes" (homers, walks, strikeouts) we generally consider to be fielding-independent, even on a per-inning basis. As an extreme, imagine all 7 fielders outside of the battery being literal garden gnomes and your K/9 is going to approach 27.0 because it's the only way you can record outs. Your HR/9 and BB/9 are also going to skyrocket because you're having to face so many more batters for every out.

To try to fix this, I first estimate how many batters pitchers would face per 9 innings, given their true outcome rates (per batter faced) and a defensive constant based on the average number of non-true-outcomes per "out in the field"

That thinking goes like this: Start with 27 outs. Subtract your K's. The rest of these outs are "outs in the field"---recorded by any non-true outcome. For every season between 2010 and 2014, that's about 1.3525 batters putting the ball in play to make one out in the field. It's the number of batted balls a defense needs to record one out.

So then it's pretty straightforward to figure out how many more or fewer batters every pitcher faced than they would have had to face with an average defense, or average luck, or whathaveyou, and to then figure out how that affected each pitcher's per-inning rate stats.(It comes out the same if you hold the batters faced constant and figure out how many outs, thus innings, the pitcher should have gotten with their actual results on batters faced. That's simpler mathematically, but I think it's easier to conceptualize facing fewer/extra batters than having everything happen in a different number of innings). 

Turns out, this can really affect rate stats.

Take Cliff Lee. His 72K in just 81.1IP in 2014 was good for a 7.97 K/9. But that MY-led Phillies defense made him face an extra 29 more batters in those innings than he should have. Based on his K-rate, figure he struck out 6 of them. Take those 6 K's out of his total and his K/9 falls to 7.34. That's a difference of 0.65, which is pretty substantial. 

As for current Rangers: Apparently the defense didn't really help create outs on batted balls. I wonder if that's more because of the Temple or the personnel, but Colby Lewis led the league in extra batters faced with 37. Based on his rates, that gave him an extra 6K's, 2BB, and 1HR. 

Alternatively, for those same counting stats, he should have gotten through an extra 9.1 innings. So one way of stating how much these adjustments matter is that having an average defense all year would have helped Colby Lewis' rate stats just as much as pitching a perfect game at the end of the season.

Yu Darvishand Robbie Ross tied for 18th in the league with 20 extra batters each, which meant an extra 6K for Yu and 3K for Robbie. Nick Tepesch saw 20 fewer batters than average results on balls-in-play would suggest, but it's not like it cost him many strikeouts--he's lowest in the MLB (min 60 IP) in K/9 or K/batter faced.

At the other end of all of this, NL Cy Young runner-up Johnny Cueto saw 44 fewer batters in 2014 than he should have given his rate stats. That cost him 11 strikeouts, enough to break his league-leading tie with Strasburg and put more distance between himself and Kershaw.

For FIP, which is based entirely on rate stats, the numbers don't end up changing that much--only +/- 0.10, because it balances out the differences in strikeouts with the corresponding differences in HR and BB. Cueto's FIP of 3.31 vs. 2.25 ERA pretty much captures that he had a helpful defense, but if you look at any of his per-9 rate stats in isolation, those can be misleading.