I'm happy with my debut in the blogosphere.
I got some feedback and - most importantly - critics and suggestions.
I'd like to thank those of you who spread the news about the new kid on the block.
I will use this post to sum up what has emerged from the comments here and at Tango's blog.
1. What my analysis shows is the best (or at least a very good) alignment for maximizing the proportions of batted balls that are caught by the seven fielders. That's not the whole picture about defense.
The first baseman has to take care of the assists by the other infielders so he's not completely free to take a position on the field; my model doesn't account for this.
2. Not all batted balls are created equal. An up-the-middle groundball usually produces a single, while a grounder down either foul line is more likely to produce an extra-base hit. My analysis treats all the batted balls the same way.
Batted balls should be weighted according to the likelihood of them becoming a single, a double and so on. Anyway such a weighting would improve a theoretical defense alignment without considering the game situation: sometimes you have to concede the single and guard the lines, in other situations a hit is all the opponent needs to win the game so you don't care about giving up a single or a double (obviously, in such a case, you wouldn't dream of leaving the left side of the infield unguarded).
On the same subject I'd like to reiterate that we have no available information on the speed of the batted balls: even if the third basemen had as much range as the shortstops, we should probably expect them to cover less ground, because balls get at them more quickly. I think that is just a matter of having the data, because cluster analysis can cope with more than two dimensions.
3. Not all hitters are created equal. A second baseman throwing from short right can easily beat the big men running to first; the specific batter I considered can move faster than Big Papi, Howard & co.
Utley's speed also makes him a bigger threat on the basepaths, should he decide to lay down a bunt to the left side.
4. Not all fielders are created equal. Defensemen have different ranges, some move better on one side, some can't run backward, and so on. Obviously they should choose their position according to their strenghts and weaknesses too.
With my first couple of posts I intended to scratch a surface, and I'm really happy that people read them with interest. I never thought that a team can look at the graphs I posted and place his fielders in the very same spots. I'm not even sure that a team can learn anything new from such charts: a few readers of my posts weren't aware about the pull tendency of Chase Utley, but the Rays were playing him shifted four months ago (actually it was their weird alignment that made me delve on the issue).
Anyway, a quick look at one of those chart, won't hurt.
A few side notes: to draw the basepaths on my charts I used the coordinates suggested by Adler in Baseball Hacks; though they are pretty close, Mike Fast provided more accurate values on Tango's blog, and Peter Jensen is expected to publish normalized values at THT, since the coordinate system varies from park to park.