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# Team Defense

By now, I'm sure everyone is pretty familiar with the fact that the Mariners have one of the league's better defenses. As a unit, they're pretty good at getting to the ball (#8 overall Defensive Efficiency last year), and once they get there, they don't bobble it very often (#2 overall in fewest runners reached via error). But what does it really mean? Can we take this to another level, perhaps one that's a bit clearer than saying "the Mariners had a 0.702 team Def_Eff in 2005"?

I'd like to think so, so I slapped together another Wednesday afternoon spreadsheet project, with a final goal of converting defensive efficiency numbers into runs and wins saved above average. The first step? Find out just how far above (or below) average the Mariners' team defense really was.

2005 League Average Defensive Efficiency: 0.695
2005 Seattle Mariners Defensive EFficiency: 0.702
Difference: +0.007

In other words, the Mariners saved seven hits for every 1000 balls put in play against them. The pitchers allowed a total of 4,548 balls in play through the year, so we can use a little simple multiplication to figure out how many hits the defense saved:

0.007 * 4548 = 31.8 = 32

The gloves were "worth" 32 hits above the average, or roughly one hit for every five games.

How do we convert this to runs? The first thing we need to do is figure out the distribution of hit types that the defense saved. This isn't so bad:

Singles: 74.9% of all hits kept in play (homers, obviously, don't count)
Doubles: 22.8%
Triples: 2.3%

This isn't Seattle-specific - those percentages are based on league-wide numbers, and aren't adjusted for different pitching staffs (by which I mean, the Mariners as a group allowed a bunch of fly balls, which may have turned into more doubles and triples and fewer singles) - but I think it makes for a pretty handy approximation. A little more simple multiplication gives us the following numbers:

Singles: 32 * 0.749 = 24 singles saved
Doubles: ~7 doubles saved
Triples: ~1 triple saved

Now we're getting somewhere. The next step is to find out the run values for different types of hits, which you can get from Tangotiger here:

Singles: Worth 0.46 runs each
Doubles: 0.75 runs
Triples: 1.033 runs

A little more grade school math and you'll end up here:

Singles: 24 * 0.46 = 11 runs saved
Doubles: ~5 runs saved
Triples: ~1 run saved
Sum total: 17 runs saved

That last one is the key to this whole thing - the 2005 Seattle Mariners team defense was worth 17 runs above average over the course of the season. To put it another way, you could get the same kind of contribution by turning Raul Ibanez into another Richie Sexson. That's pretty significant.

How significant, you may ask? Well, the last step is to find out how many wins those 17 runs were worth, which we can do by using the Pythagorean formula for winning percentage:

WP% = Runs scored^1.83/(RS^1.83 + RA^1.83)

Given their total runs scored (699) and runs allowed (751), we find that the Mariners had a 76-86 Pythagorean expected record in 2005. If you adjust for a league-average defense, though, tacking on another 17 runs to that 751, we get a new expected record of 74-88, a two-win decrease. So, therefore, we can say that the Mariner defense was worth two wins above average in 2005.

Neat.

For your convenience and viewing pleasure, here's a chart of the same kind of stuff for the last five years. HITS = hits saved, RUNS = runs saved, and WINS = wins added.