"I waved in my outfielders. When they got in around me, I said, 'Sit down there on the grass right behind me. I'm pitching this last guy without an outfield.'" -- Satchel

Outfielder positioning has been a hot topic over at The Book Blog recently. Max Marchi has done some great research on the topic of defense positioning.

Using MLBAM data, which reports the location of where the ball was fielded, as well as Peter Jensen's Gameday translations, I queried the hit locations of balls in the air that left the infield but stayed in the ballpark. I restricted my sample to only hitters who had at least 100 balls in the air from one side of the plate through 2008-2009. I then ran a k-means algorithm that split the spray chart into three different clusters. I wouldn't say that the centers of each cluster indicate where a fielder might be positioned, since a lot more than just getting to balls goes into positioning, but one might put it that they indicate the middle of a fielder's area of responsibility. I think of it as a tidy way to quantify someone's spray chart.

For example, Joe Mauer hits the ball in the air the other way a lot. The left-fielder is responsible for three times as many fly balls off Mauer's bat as the right fielder. Conversely, Carlos Pena pulls a fair share of his fly balls. Assigning each ball to a fielder yields the following chart:

Logically, a fielder would get to the most balls the fastest by standing in the middle of his zone. Again, that often doesn't align with the actual job of the fielder, which is to prevent runs. Averaging the clusters produces the following centers:

So the difference in the average hit locations between a great pull hitter and a great opposite-field hitter comes out to around 30 feet.

The most interesting and informative chart is probably the one that splits batters by handedness.

On average, corner outfielders have to move 15-20 feet depending on the handedness of the batter. This is the result of pulled balls traveling farther than opposite-field balls. The center fielder only moves five feet in general. Grouping by pitcher handedness didn't produce any visibly different results.

Now, I'll look at some of the most extreme differences in cluster centers. While Pena and Mauer have an extreme difference in the rate of balls they put in play to each field, their clusters were in close proximity as compared to Scott Podsednik and Ray Durham, whose centers were 50-100 feet apart.

As for right-handed batters, Derek Jeter is the only player who hits a higher rate of balls in the air to the opposite field than Joe Mauer. Jeter leaves the right fielder responsible for over half of his fly balls, and he forces the right fielder to play closer to the line than any other right-handed batter. I'll compare him to Jesus Flores.

All of the previous charts have dealt with fly ball angle, but fly ball distance is just as important in outfield positioning. The first pair I noticed was Cody Ross and Gregor Blanco

Here, we see some of the unreliability in either the GameDay location data or the pixels-to-feet. Cody Ross has power, and power to center, but something is off. He doesn't routinely hit 400-foot flies that stay in the ballpark. Oh, well.

Looking at pull power to left, there's a more realistic difference between Chris Iannetta and Ryan Roberts.

And the obvious choice for the final coupling is Luis Gonzalez and Paul Bako.

The only player for whom my clustering algorithm spat out something funky was Clete Thomas. His spray chart is unusual in that he appears to have decent power to left-center, but not so much to right-center, which creates a distinct region in left-center where no fielder would ever play, and leaves a neighboring vacancy where the center fielder is traditionally positioned.