Refining the shift

I worked some more on the subject of last post.
First of all, as I said at the end of that post, I rerun the cluster analysis after having removed the short grounders from my data set.
Here's the resulting chart.

No more fielders behind the rubber... I like it.

Then I tried to do things separately for infielders and outfielders. In this way I have more confidence in constraining the clusters to having equal sizes. This makes sense especially for the outfielders.

Here is a first chart for infielders: I run a model for four players.

I'm sorry for the questionable choice of colors, but I haven't fully grasped how the customizations of plots works for the package I'm using (Mclust for R, for those interested).

And here are the outfielders (three for the moment).

Then I tried to move one player from the infield to the outfield. Following are the charts for three infielders and four outfielders, respectively.

Summing up.
Playing Utley shifted is the right thing to do. You don't need anybody playing near the third base bag. Putting a fielder in short right makes sense too: the statistical analysis puts him there to catch short flies, but (as managers who employ the shift know) he is mainly valuable for handling the grounders not collected by the infielders on that side.
When data on batted ball velocity are available, a new dimension will be added to the cluster analysis: balls along the lines that get quicker to the infielders would be treated appropriately, thus producing clusters of different sizes (in the spatial dimensions considered here) for third basemen and first basemen.