I have a question for you knowledgeable folks about FIP. I'm not a statistical guru, but it seems to me that there's a minor improvement to be made to the calculating formula. 

As a fan of the Minnesota Twins, I had to watch Francisco Liriano give up cheap single after cheap single en route to a big inning for the Royals. His line for the day was 5 innings, 8 hits, 7 runs, 1 walk, and 4 k's, no hrs. That produced a pretty good FIP line; 4 ks in 5 innings is fine.

But Liriano faced 24 batters. He had up to 8 innings worth of batters to strike out, and he only managed to strike out four. The question I have about FIP, then, is this: Is it possible that FIP as calculated rewards pitchers playing in front of bad defenses?

Let's imagine two identical pitchers playing for different teams, one with a great defense (let's call them the "Rays"), and one with terrible defense (the "Mets"). Wouldn't the Mets pitcher get to face many more batters in the same number of innings, because more of the balls in play would turn into hits, giving him more batters to face in fewer innings? the Rays pitcher would be penalized for striking out the same number of people, but since more balls in play turned into outs, the strikeouts would come over a greater number of innings, and thus the effect of the strikeouts on FIP would be diminished.

So the way I see it,

Rays P: 28 batters faced; 8 ks; 20 balls in play; good defense produces 16 outs, for 8 ks in 8 innings.

Mets P: 28 batters faced; 8 ks; 20 balls in play; bad defense produces 11 outs, for 8 ks in 6 innings.

The Mets pitcher makes an identical line look a lot better.

Instead of considering Innings Pitched, should FIP be calculated using some other number? Preliminarily, I'd imagine that ((1 - League Average BABIP)(At bats vs. pitcher ending in balls in play)+strikeouts) / 3 would be an improvement.

Thoughts? Again, I have no statistical analysis background or experience, so please feel free to explain why I'm wrong.