Exact (more or less) impact of defense on staff ERA?

Might be the wrong place to ask this and if so mods please shift it around.

I have seen some calculations done of defensive value often in terms of outs allowed or runners saved per 108 (or 216) plate appearances, i.e. once around the hitter card.

What I'd like to know is whether anyone has attempted to quantify the effect on staff ERA?

For instance if I have a "3-e25" at 2B for 1450 innings and my staff ERA was 4.00 (implying 644 ER allowed). What would my team ERA have been if I had used a "2-e15" fielder instead, all other things equal?

And then the follow ups:

Would that scale exactly again to a "1" or "4" fielder? In other words, if a "2" would save six runs compared to a "3", would a "1" then save 12 runs in comparison, and a "4" cost an additional six runs?

And would all that scale based on the SS/2B/CF-3B/LF-RF/1B X frequency?

Just wondering how much better Bill Doran ("1") might make my kind of shaky 1986 pitching staff compared to Bobby Grich ("3") and whether it would be cheaper to get a better defender or try to get several better pitchers?

Food for thought:

http://andrew-stevens.tripod.com/index/stratfield.html

Dean Carrano did this. Just google strat defensive ratings and it will come up.It's done per 108 at bats on batter's card and that's about a third of a season. The example you gave--a 3e25 at 2b vs a 2e15--would be about a 16 run difference under his ratings.

Just figure your team ERA with 16 fewer runs.

This:

http://www.mfooz.com/bblog/wp-content/u ... efense.pdf