Working on a team defense statistic

I am by no means an accomplished statistician, much less a sabermetrician, but I do like to dabble in statistics and pitch f/x material. For the past 2 years, I've tinkered with the idea of creating something that tries to quantify how much work a defense is doing out in the field. Quite simply, all pitching (among other factors) is not created equal; that's the mantra I've let guide my work. I know there's lots of other materials out there (UZR, +/-, etc.), some that I know about fairly well, others not so much, that try to quantify defense in a much more sophisticated manner. I think it's possible, however, to get a much simpler view of how much work a team is doing out in the field.

I'll post what I've come up with so far, but this is also a call for ideas, thoughts, etc. If you think what I'm doing is pointless, please feel free to say it, I won't be offended. 

Now then, I mentioned UZR and +/- previously, but I'm really not interested or educated enough to try and do anything with those stats. Defensive efficiency (DE) on the other hand, is something a bit more on my level. DE is simply (1 - BABIP) for a team. So far, the Rangers have a DE of 0.712, tied for 2nd in MLB. Tampa Bay leads the league at 0.714, Houston is last at 0.661. We know BABIP fluctuates quite a bit with luck and other factors, but typically if you have a high DE, you have a good defense.

As Ranger fans, we know that are pitching the last couple of years has looked better than it is in large part because of the defense. But the reverse can also be true, and that's what I've tried to quantify. Let's look at an example.

This year, the San Francisco Giants have a pretty good pitching staff and have a DE of .706, good for 7th in MLB. The Cleveland Indians on the other hand, have had a rough year with pretty bad pitching and a DE of .685 (21st in MLB) to go with it. Obviously that's partly because of worse pitching in front of the defense, but the defense has got nothing to show for it, everyone just thinks they suck. If we look a little deeper, we can calculate that 73.4% of all Giant-foe ABs have gone for balls in play. For the Indians, they are contending with 80.7% of all ABs ending up as playable.

Giants: 3,334 ABs against * 73.4% balls in play = 2447 balls in play

Indians: 3,331 ABs against * 80.7% balls in play = 2688 balls in play

So for practically an identical amount of ABs against them, the Indians have had to field 239 extra balls in play. It seems logically that with more chances, more misplays or frozen rope liners given up by a bad pitching staff will show up.

This is where what I've termed "work" comes in.

By multiplying a team's defensive efficiency (or the inverse of it's batting average on balls in play) by the percentage of balls in play given up, we can get an idea of how much "work" a team is doing out in the field. It may be pretty terrible work, but it's work nonetheless.

Initially, a straight multiplication ended with only very small differences between all teams, so I've tried to normalize everything by using an equation that's basically what's used for OPS+ and ERA+.

Work = 100*(DEff/lg.avg.DEff)*(%BIP/lg.avg.%BIP)-1)

Plugging the numbers in to the equation, you get the Indians fielders have a 4.08 Work, whereas the Giants fielders have a -2.43 Work. (The equation is centered around 0, instead of 100)

Now I have no idea if this is utterly useless, but I feel like it isn't. This can give you a pretty basic idea of how much a team's defense is contributing (or not). i.e., the Giants can get away with acquiring a bad defender or 2 because apparently their pitching staff is carrying most of the load by not giving up balls in play. The Indians are the opposite, where the defense is having to handle a lot of balls hit out to them. Better fielders are a necessity.

I haven't looked in to to much else yet, but you can probably follow trends of players leaving and joining other teams and whether that effects how much "work" a team is doing. You can also apply it to individual pitchers and see whether they are doing most of the work or the defense behind them is.

I'll include a table of how the majors shakes it so far this year, with DE, % BIP, and work below.

So is there something here or am I wasting my time? All comments are appreciated. Go Rangers!