The Lord of the Pentagons: The Two Uses (of Pentagons)

            In my last post, I introduced my revolutionary (yes, I’m allowed to say that because I made it up) graphical invention, the Vigdergon.  Today, I’d like to go through a couple of the uses of my pet project in the context of giving less intense sports fans an opportunity to immerse themselves in “the numbers.”

Between-Player Comparison

            The Vigdergon attempts to graph multiple facets of a player’s performance on the same figure, which allows you to see a more complete picture of that player’s ability at any one time.  As we saw with the Vigdergons sampled in my last post, it is easy to graph multiple players’ Vigdergons on the same figure and compare their competencies on a more holistic scale than simply comparing numbers.  Here’s a second look at the Vigdergons of Michael Bourn, Carlos Peña, and Joey Votto included in my last post:

As I pointed out last time, the pointier graphs convey that the player is particularly good at one aspect of the game (i.e. for Bourn’s speed and Peña’s power), but is lacking in others (i.e. Peña’s speed and batting average and Bourn’s, well, mostly everything).  A more rounded graph, like Votto’s, indicates that the player is not much better or worse at a particular aspect.  However, one could imagine that a player would have a rounded Vigdergon without being very good at anything, and that’s where the next part comes in.

Computing the area of a Vigdergon

Since people always want to know which players are better than others on a general level as opposed to a specific part of the game, I had to come up with a way to reasonably make these comparisons.  A (relatively) straightforward way to do this is to compare the area contained within one player’s Vigdergon to that of another player.  That way, I can estimate a player’s overall worth compared to another even though they may be very different players in terms of the way they impact the game.

Taking the above players for an example, it should not come as much of a surprise that this season it appears that the rank order of the value of these three players is Votto, Bourn, Peña.  But how close is it? 

As it turns out, not very.  Votto’s Vigdergon fills 59% of the surrounding graph area, while Bourn’s covers 35% and Peña’s just 14%.  When it comes to hitters, whose value comes just as much from fielding as it does from hitting, it would be quite difficult to cover the entirety of the graph; even Jose Bautista’s absurd production this year only covers 84%.  On the other hand, since fielding and speed really aren't that valuable for a pitcher, it is not so unlikely for a pitcher to cover over 90% of the graph:

Not useful.

Within-Player Comparison

Speaking of Jose Bautista, another interesting way to look at players with Vigdergons is to graph a single player over multiple seasons (or parts of seasons) and observe their growth or decay.  As an example, here is a graph of Bautista’s last three seasons:

This graph tells an interesting story of Bautista’s career progression over the past couple years.  In 2009, he was a balanced (if unspectacular) player, but he had a renaissance and became the premier power hitter in the major leagues last year with 54 home runs.  Not surprisingly, his increase in hitting efficiency shifted the area within his Vigdergon towards the right, as speed and fielding declined (most likely due to a lack of attention being paid to those aspects of his game).  In 2011, he has become incredibly efficient at the plate, hitting for a very high average (.336) and drawing more walks than strikeouts, as he continues to lose effectiveness in the field and on the basepaths.  Fortunately for the Blue Jays, however, his overall worth has increased greatly in both seasons, from 27% coverage in 2009 to 47% in 2010 and 84% in 2011.  The widely used Wins Above Replacement (WAR) formula corroborates this jump in overall value, as he went from 2.1 WAR in 2009 to 6.9 in 2010, and has already garnered 6.7 WAR in 2011 through just 85 games.

I think that, besides the name, I’ve hit on an intriguing method of looking at baseball statistics in a more visually satisfying way, and if anyone who reads this has any suggestions for ways to use, change, or re-name the Vigdergon I would really appreciate it.  That means you, Matt Vogel, Mr. Big Shot Business Man.