Everything You Always Wanted to Know About UZR But Were Afraid to Ask

The ability to substantiate defensive performance in an analytical form has become, in essence, almost a necessity for sabermetricians in need of verification of whether a fielder is a solid defender or not. Since 2002, UZR (Ultimate Zone Rating) has been the most commonly used defensive metric for those who have cognition of it's importance. Heck, the majority of people that have the time, patience, and an abundance of baseball comprehension are aware of the difference between UZR and highly flawed statistics such as fielding percentage and errors. Even with one's ability to bestow his or her knowledge of UZR, many don't seem fully aware of it's background or the ways a certain fielder can improve or negate his Ultimate Zone Rating. Before we dig in to that, confabulating the background of UZR sounds like a grand idea, wouldn't you say?

Founded by Baseball Think Factory's Michael Litchman, Ultimate Zone Rating is best defined by -- sans the pitcher and catcher -- a fielder's ability to get to balls in 64 of the 78 zones. It's not all batted balls, however, as outfield balls hit foul, infield line drives, and infield pop flies are not considered in the formula. In simplest form, Ultimate Zone Rating is the amount of runs above or below average a fielder costs or earns his team within certain zones using four metrics, well actually, three:

1. ARM (Outfield Arm Runs): First and foremost, keep in mind that ARM is only used for outfielders while DPR is only used for infielders, hence the reason why I suggested it's really three components, not four. ARM basically speaks for itself. It's the amount of runs an outfielder saves by throwing out the expected amount of runners. The more runners he throws out, the better his ARM will be.
   
2. RngR (Range Runs): This denotes the amount of runs above or below average a fielder is (infield & outfield) by determining the ability of a fielder to get to the expected batted balls in his zones. As you'll see below, UZR is larglely dependent on RngR.
   
3. ErrR (Error Runs): Given the same amount of batted balls hit to a certain fielder, ErrR determines the amount of runs he saves by his ability to prevent errors compared to an average fielder at the same position.
   
4. DPR (Double Play Runs): Again, this is solely used for infielders. Taking "handedness" in to account, DPR determines the amount of double play outs at second against the league average. Of course, this is primarily and more significantly used for middle infielders, but it applies to the whole infield quad as well, which you'll also see in the charts below...

In advanced form, you might want to take a glance at the wonderfully composed lengthy definition of UZR by Big League Stew's Alex Remington.This was what he had to say regarding the most beneficial way to formalize UZR:

Here's what is calculated for each zone: the out rate and the percentage of balls in that zone that turn into outs. The league average out rate is then subtracted from the player's out rate — if this number is negative, it means the player is worse than league average. If it's positive, it means he's better than league average.

That rate is then multiplied by the number of balls that hit in that player's zone. This yields a Zone Rating. To obtain the run value, it's multiplied by the Zone Ratings that are calculated for each zone the fielder covers, and then summed. This sum is a simple, unadjusted UZR. It is then further adjusted for park factors, batted ball speed, which side of the plate the batter was hitting from, the pitcher's groundball/flyball ratio and the number of baserunners and outs at the time. The adjustments are made because each of these variables can significantly affect the average out rate in a particular zone. Using run expectancy charts, these rates can be converted to runs.

Alas, with respect to the Alex Remington article I mentioned (and the fact that I want to break UZR down, not define it as much as I already have), I took this in to context with a goal of determining the breakdown of UZR. For instance, I asked myself these questions:

1. What is the most prominent and substantial component of UZR?
2. Which constituent of UZR is the most misleading?
3. Are there certain components of UZR that have a greater impact on UZR than others?
4. Which position is the hardest to defend?
5. What makes a good defender?
6. Should we be looking at RngR, ErrR, DPR, and ARM individually opposed to UZR as a whole?

Since the inception of UZR in 2002, there have been 22 players that have amassed 10,000 innings in the outfield. Just 10 of them have positive UZR's. Unfortunately for the sake of this post, many of those players were around prior to the commencement of UZR, thus it would be irresponsible to judge their career value as a defender with UZR and nothing but. However, we can go position by position. The data below lists the best and worst 20 qualified players since 2002 using ARM, DPR, RngR, ErrR, and of course, UZR. The reason I'm using top 20 and worst 20 is to determine the extremity of the players, assuming the boilerplated defender has "average" range, arm, and what have you. It also gives you a more clear version of the data that you're to trying to work with. Here we go...

Top 20 outfielders

Worst 20 outfielders

Top 20 first-baseman

Worst 20 first-baseman

Top 20 second-baseman

Worst 20 second-baseman

Top 20 shortstops

Worst 20 shortstops

Best & Worst 20 third-baseman

Not surprisignly, range is the prime component of UZR for outfielders. As the first two charts display, if you are unable to get to as many or more balls than the league average, hec, if you simply suck at getting to balls, it will affect your UZR more than your arm would. On the field negligence comes from the ineptness of one to track down fly balls. You can imagine what an outfielder's UZR would look like if you subtract his RngR from the equation.

For one, Carl Crawford boasts a career 120 UZR. The prime reason it's that high is due to his 113 RngR so you can imagine what his UZR would appear as should his range in the outfield be less superior than it is. Alas, his career ARM is -0.1, so he's basically surviving on his dexterity to get to batted balls better than any other outfielder in baseball. So you can certainly see that component "A" of someone's UZR (in Crawford's case, RngR) can create a misleading UZR since you add the three components up.

Almost always, a fielder's UZR will not feature an even scale of all three components, thus another reason why looking at each component instead of UZR simply by itself is more beneficial if you're trying to avoid misleading information. In other words, a fielder is never proportionately skilled or depleted at all three components, so there will be some extremities. Heck, Juan Pierre is another fine example. The "Juan Pierre Lesson" says that one should look at ARM, DPR, RngR, and ErrR before looking at UZR. Why? Well, the former Marlins and Cubs outfielder boasts a 78.2 RngR while his ARM, which is notoriously atrocious, has cost his respective teams 45.4 runs. Of course, one doing their due diligence would typically only look at Pierre's UZR which is 39.2. I guess that someone would then declare "star status" on Pierre.

Outfielders aside, range still has the most prominent impact on defenders for the most part. The exceptions are slim, but shortstops rely on prevention of errors as well the double play (ErrR & DPR). However, the shortstop position almost equally relies on range. First-baseman fall in to a similar category as well. As you can see, things get a ton busier when discussing infielders. However, like I said, range is the most substantial factor of them all.

Often you'll hear a couple of anti-sabermetric baseball fans neglect advanced metrics such as UZR, WAR, FIP, and other three or four letter words that sound creepy when you say them aloud. It doesn't take a genius to understand that getting to baseballs, preventing runs with your arm, and going the extra step to prevent a baseball from escaping your grasp is imperative to a team's success. While UZR, in this case, is commonly known as the most accurate way to judge defense (EDIT: that was a hyperbole. h/t Colin Wyers & JD Sussman for pointing that out.), it's worth being aware of the ingredients that create such a metric. As each chart shows differences and similarities between defenders at each position, the message being parlayed is that while UZR is a fantastic metric to judge defense by, it's essential to understand the elements in the recipe that go in to using such an important statistic.