How do we explain the Rays' remarkable transformation?

For this week's Stat of the Week, we turn to a recent question we received from a reader:

Hi John,
 I have a suggestion for an article for you that might be right up your alley, considering your recent piece on the importance of defense. Last season, the Rays allowed 273 fewer runs [actually 270] than they allowed in 2007. They scored almost the same number each year, so really their huge improvement can be traced almost wholly to better defense and pitching. The question is: who saved all those runs?
 I've been mulling over how to trace the improvement to either the pitchers or the different fielders, but as you have formulas and data that would point to runs saved by fielders, this question might be more easily answered by you and would be of interest to those of us on the Bill James site. It would be interesting to see: 
 
Was the difference in pitching more attributable to the starters or the relievers?
 
How many of those runs were saved by the fielders and how many by the pitching?
 
Which fielders (or positions) improved the most from 2007 to 2008? Which pitchers?
 
Where was the difference due to addition by subtraction—that is, by replacing a player?
 
 Thanks. I enjoy your work. Chuck Jacot

Thanks for the question, Chuck. The Rays' remarkable transformation was the story of last season and serves as an excellent example for other teams to follow.

First, Chuck asks about the breakdown between starters and relievers:

It's clear that the Rays' rotation and bullpen were both drastically improved in 2008. But how much of the overall improvement was due to an improved defense behind them?

In The Fielding Bible—Volume II, we found that the 2007 Rays' defense cost them 71 runs; they were 71 runs worse than the average fielding team. The 2008 Rays improved to 26 Runs Saved, a full 97 run improvement in one year (close to 10 wins, based on the rule of thumb that 10 runs equals one win).

The improvement on defense can be attributed to several defensive changes. Here's the position–by–position breakdown in runs saved by year:

Offseason acquisition Jason Bartlett got a lot of publicity for his defense during the World Series, and rightly so. But it's not so much that he is a spectacular shortstop. He is an average shortstop. It's the improvement at the position that is dramatic. The Rays' collection of shortstops cost them 29 runs in 2007. Bartlett only cost two runs in 2008. Including the 11 runs lost by other 2008 shortstops, that's a 16–run improvement at the shortstop position from 2007 to 2008.

Moving Akinori Iwamura to second benefitted the team in two ways: Iwamura improved on B.J. Upton's and Ty Wigginton's defense at second base in 2007, and it opened up the hot corner for 2008 Rookie of the Year Evan Longoria, who is a tremendous asset on both offense and defense. The defense improved by 17 runs at second base and by 28 runs at third. Elsewhere, both Carlos Pena at first base and Carl Crawford in leftfield improved their defensive numbers from 2007 to 2008.

Of the 270 fewer runs the Rays allowed in 2008, our metrics suggest that about 100 of those runs can be credited to the defense, with the remainder split between the rotation and the bullpen.