A metric that determines how effective a fielder is at making plays in various areas of the field. The resulting value is an indication of how many runs a certain fielder has gained or lost for his team compared to what an "average" fielder would do on plays in the same area of the field.
To calculate UZR, we must break the baseball field into various zones (there are 64 zones used in the UZR formula). The percentage of outs for balls hit into the various zones is determined, and compared to the percentage of outs in those zones for a particular player. We can then subtract the league average performance from a player's individual performance to yield that player's UZR.
As an example, let's use zone I, which is essentially left-center field. We'll say that of all balls hit into zone I, 50 percent of them end up as outs. When we examine the data for a particular player, however, it turns out his percentage of outs in zone I is 56 percent. Since he is performing above the league average, his UZR for this zone will be a positive number.