The Hardball Times has put together something called Chernoff Faces which uses stats to decide the shape/size of the different characteristics of a face. The site explains:
Size of the face—I used wOBA (height of the face), wRC (width of the face) and WAR (general shape of the face) to dictate the size of the face.
Shape of the mouth—Power makes people smile, ask Jose Bautista. I used slugging (height), isolated slugging (width) and total home runs (curve of the smile).
Shape of the eyes—Batters who walk a ton need good eyes. Therefore, walk rates (height) and on-base percentage (width) are represented here.
Shape of the hair—I couldn’t think of anything here really, but hits (height) and RBI (width) are here. I also made the “style” of the hair set to stolen bases.
Shape of the nose—A general idea about high batting average on balls in play is that they are unsustainable (not in all cases, but let’s go with this notion for a second). Thus, if a hitter had a high BABIP, he is lying about his true talent. Higher BABIP, bigger nose (think Pinocchio).
Shape of the ears—Psst…players with high strike out rates have big ears because they love to hear the sound of their bat whiffing.
Here are a couple of rows of the resulting awesomeness, but please, reward the time it must’ve taken to put this together by checking out the rest over at the site.