Is Defense Efficiency related to pitching or is it an independent way to measure a teams defensive ability?

Question: Is Defense Efficiency related to pitching or is it an independent way to measure a teams defensive ability?

Note: Defensive Efficiency, is the rate at which balls put into play are converted into outs by a team's defense. Def Eff can be approximated with (1 - BABIP), if all you have is BABIP, but a team's actual Def Eff is computed with (def from Baseball Prospectus http://www.baseballprospectus.com/glossary/index.php?search=def%20eff):

1 - ((H + ROE - HR) / (PA - BB - SO - HBP - HR))

Why I asked the question: On the surface, I thought Defense Efficiency would be a good way to determine how well a team is doing defensively, but I noticed is that teams with worse pitching had lower Def. Eff. Ratings. I looked to see if the two were actually correlated.

Analysis: Comparing a team's Def Eff vs. the team's ERA. I chose ERA because it is a commonly used and understood. Also it is a decent measure of team's pitching ability. Data from 2004 to 2007 was used. Here is a chart of the results:


There is definitely a direct relationship when these two are plotted against each other. Then I had Excel create a linear trend line (for ease in future calculations) and the formula is:

Expected Def Eff = -0.0163 * ERA + .7702

Finally I subtract the actual value from the expected value and get how the team is doing defensively. I know this method is not perfect, but it is better than Def Eff by itself since it takes the teams pitching into account.