The Twins just made a deal trading Carlos Gomez to Milwaukee for JJ Hardy. UZR is being sited by all sides of the discussion of whether this was a good deal for the Twins. The proponents of the trade point to Hardy's UZR as evidence that scouting reports that his defense is declining are wrong. People concerned about the trade point to the Twins outfielders low UZR's as evidence that, without Gomez, the Twins pitchers are going to struggle because of poor outfield defense.
So what is UZR and how is it calculated. At its most basic UZR measures how many batted balls a player turns into outs compared to other players at his position. This is done by dividing the field into zones and then recording each ball hit to each zone. Players are then rated based on more calculations of how many runs the result represents based on how many runs are scored on average after that outcome. I am not going to go into the accuracy of this last calculation because whatever innaccuracies it introduces probably have little or no impact on the relative scores of players at the same position.
Lets look at the general idea. That you can determine a players range by where balls are hit and how often he turns them into outs. In essence, a bouncing groundball up the middle is the same as a line shot. A lazy fly ball caught at the wall is the same as Willie May's catch. The fact is, UZR ignores the most important factor in whether a fielder catches the ball which is how hard it was hit. And, as anyone who has followed the Twins ought to know, the nature of the field surface is also important. Balls hit on long grass are going to move much slower, than balls hit on the old Metrodome surface. And UZR gives no credit for cutting off a hard hit ball and holding a player to a single.
In short, UZR is all but useless in evaluating player's defense. It ignores the most important factor in whether a ball is a hit, how hard the batter hit it.