http://www.fangraphs.com/library/defense/uzr/ 'For the details on how UZR is calculated — i.e. how we can attach a run value to defensive events — see the FanGraphs UZR Primer. It’s very thorough. The specifics can be a little overwhelming, but at it’s most basic level, it’s a measure of the average amount of damage that batted ball would do and how often it is converted into an out, relative to average at the position. So if the average left fielder makes a player 40% of the time on the ball in question and that batted ball (based on location, speed, etc) is worth 0.8 runs on average, fielding it cleanly earns you 0.48 runs toward your UZR (0.8*0.6). It’s a little more nuanced than that, but that’s the view from 30,000 feet.' And if one wants to read the primer http://www.fangraphs.com/blogs/the-fangraphs-uzr-primer/ 'Now, let’s say that we want to compute a UZR for every player in 2009. For every batted ball, either it is caught by a fielder and turned into an out (either the batter or a base runner is out, or both of course), it is scored as a hit, or the batter reaches on an error or a fielder’s choice (and no out is made). One or more fielders will receive positive or negative credit depending on the outcome of the play and depending on how often that same batted ball in that same situation (outs, base runners, attributes of the batter, etc.) was successfully fielded by each fielder from 2004-2009. Let’s say that that same batted ball in the example above was caught by the CF’er on the first play of a game. Since typically someone will catch that same ball only 25% of the time (see above), this particular CF’er will get credit for an extra .75 plays – 100% minus 25%. We then convert .75 plays into runs by multiplying .75 by the difference between an average hit in that location and the average value of an air ball out. A typical outfield hit is worth around .56 runs and any batted ball out is worth around -.27 runs, so the difference between a hit and an out is worth around .83 runs. (We don’t vary the value of the hit or out based on the outs or base runners because we want “game situation-neutral” defensive evaluations.) Since our fielder gets credit for .75 extra plays, we give him credit for .75 times .83 runs, or +.6255 runs for that play.'