Sequencing issues? So it is pointless overthinking Shield's value if you don't know how he's going to 'sequence' with a new pitching coach in a new home park? Do we know different pitching coaches/catchers sequencing proclivities? In short: is there a stat for that?

Aside from the fact that Defensive Efficiency lumps errors and hits together into "outs not made," BABIP is just the inverse of Defensive Efficiency. Isn't it? As such, the correlation of the two measures within a sample is kind of meaningless, isn't it? A high DE and a low babip go together almost by definition so that finding doesn't really say anything about how a defense impacts a pitchers BABIP. It just says that if a pitcher has a high babip he probably also has a low DE. But who cares? What am I missing?

The actual inverse would be the quick way of 1 minus the BABIP. The way our engine computes it is 1-(H-HR)/(AB-SO-HR+SH+SF). According to our glossary, the ROE component, that was once part of the formula, is no longer.

A high DE & low BABIP have a good relationship, but it's also not impossible for a pitcher to put up a strong BABIP with a very weak DE behind him. In the sample sizes, there is a trend for the highest BABIP to be lower as the DE goes higher, but the low end remained rather static.

Thanks for pointing me to your glossary. Here are the definitions I found:

BABIP = (H - HR) / (AB - SO - HR + SF)
Defensive Efficiency = 1- (H-HR)/(AB-SO-HR+SH+SF)

So, for all intents and purposes, these two numbers are mathematical inverses (the strange omission of SH from the BABIP formula notwithstanding). Within the same set of plate, appearances, if you compute the two numbers, BABIP = 1- DE.

Each data point of your analysis includes a number for BABIP and a number for DE. But DE does not appear to be 1-BABIP (that is, the points don't all lie along y=1-x. But I don't understand why. Are you computing DE over a larger sample of PA's than the sample used to compute BABIP? Maybe one is computer for just the PA's against the pitcher and the other is computed for all of the defense's PA's? That would make sense. You can ignore this if you think I'm getting too technical but it seems like an ambiguity that obscures the whole focus of your analysis--to me. So maybe I'm not the only one wondering this. No worries either way.

This chart is the sort of analysis that gives us more information (or at least places to ask questions) about the outliers, than about the middle. Even better would be to plot a pitcher's BABIP against the DE of his team in all other PAs (that is, with the Pitcher Under Test removed from the DE). Then the outliers could be inspected to see if they are particularly well/badly suited to their teams (imagine Derek Lowe in front of Brooks Robinson, Ozzie Smith, Bill Mazeroski and Keith Hernandez {all in-their-prime versions}...) or if something else is going on.

If I play with the starting point of the X axis only, here are the r= figures

DE >=.720 - r=-0.34
DE >=.700 - r=-0.50
DE >=.680 - r=-0.56

If I tweak the table to ranges of .025 for DE, I get this mean BABIP for each range:

.675-.699 = .302 (14% of the overall sample)
.700-.724 = .284 (67% of the overall sample)
.725-.749 = .264 (19% of the overall sample)