I don't claim to be a researcher or have a big background in statistics, so this post is going to be very "theory" heavy.  This past weekend, I spent a decent bit of time driving around, listening to the most recent FanGraphs podcast (!) and pondering about baseball.  During this time, for reasons unknown to me, my mind turned to how the heck to quantify catcher defense.  I haven't followed all the recent research on catcher defense so I don't exactly know where this thought-process came from, but I had a 4-hour drive ahead of me and that left me plenty of time alone with my thoughts.  For all I know, this article could be redundant and/or totally wrong, but I had some ideas and I wanted to share them.  Please, be liberal with the feedback.

All right, so, big picture time.  Imagine if you could graph the exact defensive ability of every major league baseball player over every season for the last 50 years.  What would that graph look like?  Well, it'd probably look something like a normal curve, right?  The majority of seasons would fall close to the average - within one or two standard deviations from the mean - with a smaller number of outlier seasons on both sides.  Determining what the average would be is easy enough (0 UZR, or a neutral defensive season) and if we wanted, the furthest limits on both ends could be easily established by looking back through historical UZR data.

Within that normal distribution, though, we'd have seasons from first basemen, second basemen, shortstops, catchers, etc.  We all know about Bill James' defensive spectrum, where he ranks the positions in order of increasing defensive difficulty (for a refresher: 1B, LF, RF, 3B, CF, 2B, SS, C). Theoretically, players land at their optimal position; poor defensive players end up at 1B or LF, while defensive stars stick at places like SS and 2B.  It doesn't always work out perfectly since there are always those players that make up for their defensive problems with their bat, and there are the Yuniesky Betancourts of the world that somehow manage to stick at key defensive positions despite any logical reason.  With this in mind, what would the graphs look like if we broke defensive ability down by position?  Would these subsets of the normal defensive distribution look like normal distributions themselves, or would they vary slightly from position to position?

The way I see it, the distribution of defensive talent could break down one of two ways.  One, it could be that talent is evenly distributed among positions with each position closely resembling a normal curve.  Two, the distribution could vary slightly from position to position.  Since players at positions higher on the defensive spectrum are valued strongly for their defensive abilities, players with less defensive skills may be moved from these positions down to a position that they can manage more easily.  This would result in positions higher on the spectrum having means higher than the overall average of defensive abilities, and make those lower on the spectrum have means lower than the average.  In statistical terms, these distributions would be skewed (although to what extent would need to be determined).

Keep in mind, this is purely theory, but I like the intuitive feel of it.  We know that bad defensive players typically end up at 1B, so wouldn't it make sense that the average defensive ability at 1B would be lower than that at SS?  And if this was the case - if we could document this trend and determine its extent as you move through the defensive spectrum - couldn't we simply extend the trend to calculate what the distribution of catching defensive ability is?  Catching is at the far end of the spectrum, so this theory would imply that catchers as a group tend to have a higher-than-league-average defensive ability, which again would make intuitive sense.  It's only rarely that players stick at catcher if they can hit but have limited defensive skills (see the argument surrounding Jesus Montero for evidence) and back-up catchers with no hitting skills whatsoever can survive around the league for years courtesy of their defensive skills alone.  Of course, it may be that this whole theory is crock and that defensive abilities are distributed randomly throughout the positions, but if that's the case, it'd be equally easy to determine the distribution of catching defensive skill - you just look at the normal curve.

Anyway, my thought is that if you can determine the typical distribution of catching defensive seasons by using the other defensive positions as a reference, you could then combine that information with scouting data in order to determine a rough estimate of a catcher's UZR from the previous season.  Say you know that the average catching season is 1 UZR (estimated from the distribution), and that Dioner Navarro was ranked by Tango's fan scouting report smack in the middle of all catchers in MLB in terms of defensive ability; from this information, you could safely assume that Navarro had approximately a 1 UZR the previous season.  You could also use this method to double-check such methods as the scouting report, to see how accurate it is and if the run estimates on how much a catcher's defensive contribution is worth.

Of course, there are a couple issues with this argument that even I can see.  The biggest hole seems to be that by extrapolating the catcher distribution from the defensive distributions for the other positions, you're assuming that catching falls on the same scale of measurement as the other positions.  For all we know, catcher defense could be twice as important as defense at shortstop...or vice versa.  It is a very different position from all the others on the field and it requires different skills, so it's tough to say for certain that this is an accurate estimate.  At the same time, though, without any data to prove one way or the other that catching is more or less valuable than that at any other position, the best estimate we can make is by using the information we already have from the other positions.  Also, playing the outfield requires much different skills than does playing the infield - different reaction time, different arm requirements, different footwork, different positioning, etc. - and all of those positions have comparable UZR scores.  Is it that far-fetched to imagine that catchers fall within a similar range?  I don't think so.

All right...phew, so there's the theory behind my concept.  I'll follow with another post that has the bit of research I've done so far, in which we'll get to see how crazy I am for writing over 1000 words on this subject and how crazy you are for reading it.  Like I said in the beginning, please be liberal with the feedback.  I'm just starting to look over articles on quantifying catcher defense and...well, I've determined I'm probably way out of my league.  Good thing I wrote this first...