Perhaps the most coveted part in Sabermetrics -- that is the study of baseball through advanced mathematics and statistics -- is quantifying defense. This isn't a new fascination, either. More than 110 years ago, a simple journalist set about to try to quantify what runs should be credited to the defense and what should be credited to the opposing offense. That man was Henry Chadwick and his newly created method? Earned Run Average. Chadwick is considered the Godfather of modern baseball statistics. After all, he did invent the box score that we use today (though, the columns recorded are different, but the format is the same).

A century later, we're still fighting that proverbial fight. In stepped in a man named Mitchel Lichtman. His creation is just a bit more complicated than what Chadwick came up with. With the craze of the Internet and the Wins Above Replacement boom that hit Fangraphs last winter, defense became quite the fashionable aspect of the game to value among the sabermetric community and Ultimate Zone Rating (UZR) became the biggest beneficiary of this new-found interest. UZR, however, is also the most misquoted and misunderstood statistic that is publicly available.

After the jump I will clear up misconceptions of UZR, shed some light on the methodology, and explain how and why you should use it.

What is Ultimate Zone Rating?

In its simplest terms: Just a statistic that values how much a player contributes to his team defensively. It's graded above/below the positional average. One thing I've seen is people comparing different positions. Average at shortstop is not the same as average in right field just like hitting a home run isn't the same in Coors Field and Comerica Park.

How does it work?

It's complicated, I won't lie. This isn't something the average fan is going to be able to calculate on the fly with an excel spreadsheet. You can, but it's a lot more work than it's worth, so-to-speak. That is why the sabermetric community is so important. Mitchel Lichtman (who goes by MGL if you see him referenced on places like Fangraphs or The Hardball Times) has already done the heavy lifting for us.

UZR splits the field into 78 different slices called zones. Don't worry, only 64 of those are used in the UZR formula. You figure out the average number of balls in play in each zone and then the rate at which plays made are recorded in each zone. This will give you a baseline average for the position. Now, you do this on an individual basis and graded against what the average fielder would do. If a player comes out with less plays made recorded in their zone compared to league average, they have a negative zone rating. As well, they'll have a positive zone rating if the player records more outs in the zone than the average defender at the position.

Do that for every zone the position you're looking at is responsible for.

But that's just a fraction of the process. You then take that unadjusted UZR and, well, adjust it. Because, like I noted above, you need to contextualize it so you can understand what may be the true talent of the player. Some pitching staffs may give a player more balls to field. For instance, Brandon Inge would likely have more grounders to him if the Tigers had a staff full of left-handed pitchers. The opposite would be true if the staff was filled with righties.

What do we need to adjust for? The ballpark (more-so for the outfielders), handedness of the pitcher and hitter, the number of outs, the number of base runners, which bases those runners are on, and batted ball speed. A long fly ball from Miguel Cabrera into the left-center gap in Comerica Park off of a right-handed pitcher is not going to be the same as a long fly ball by David Eckstein into the left-center gap in Petco Park off of a right-handed pitcher.

Once you've adjusted for all of those factors that can greatly impact  the raw, unadjusted UZR, you now have a viable defensive metric that can be misused and misquoted across the internet!

How do I use it?

The biggest thing to remember is sample size, sample size, sample size and sample size (a fourth one just for Kurt) (editor's note: will this be the last article by Mike as well as the first?). UZR is prone to large swings from year to year, let alone from just month to month. Defense, because of data sources, is still the most murky of all the advanced statistics. Some rules of thumb when using UZR:

1. 1 year of UZR data is on par with about 50-55 games worth of offense.Would you judge Miguel Cabrera's talents at the plate on just his games from April 1st through June? I wouldn't, and neither would you (or so I hope). So don't do it with defense. Personally, if I have three years of UZR data for a player, I'd rather have four. If I have four years of UZR data, I'd rather have five. I don't believe that you can have enough.
2. One full year of defensive data is at least 1200 innings worth of data.
3. Do not use UZR per 150 games (UZR/150; found on Fangraphs' player pages) if at all possible. It's way too misleading.
4. If Player A is a -10 one year, +10 the next year and then +0 the next year, he's likely an average fielder. Large swings in year-to-year data isn't out of the norm, but you should always use an average (preferably, a weighted average) and be conservative with it.
5. When possible, use multiple defensive systems to grade a player (UZR, John Dewan's Plus/Minus system, etc).

Flaws in the system

I'm making no bones about it: I'm a firm believer in the statistics of baseball. I'm also not naive. UZR does have short comings. However, it's not really due to the methodology -- it is how this sort of quantification should be handled -- as much as it's due to the data source.

We still don't have a uniform system that allows everyone to agree. We can all agree on slugging percentage because a double is a double is a double. However, a hard chopper that is booted by a second baseman is an error unless it's not; it depends on who is grading it.

UZR does have players that greatly disagree with other advanced defensive systems, like John Dewan's Plus/Minus system. As Alex Remington noted at Big League Stew, Adam Dunn has rated -64 runs defensively by UZR in 2008 and 2009.  However, Dewan's Plus/Minus data has him at -45 runs. That is still terrible, but also a 20-run swing that greatly impacts his total value as a baseball player. UZR and Dewan's system both use the same data source, which is people watching the game and recording numerical values about the play. That leaves a lot of subjectivity in the data sources and human error and biases will eventually creep in. Until HITf/x comes out (this summer, I'm hoping), this is the best we can do.

Why you should use it

This is, in my opinion, the best of the defensive systems available. And hey, you might even peruse Fangraphs regularly, so it's entirely accessible to look up. It takes the best data we can acquire and adjusts it for everything that will effect the play from the defender's point of view. Most importantly for me, however, is that it's a very important piece of the puzzle.

We're all aware that there's three phases of baseball: Offense, defense and pitching. On the individual level, though, there are even more: Offense, defense and base running. UZR is one-third of the puzzle you need to understand what the true talent level of a player is. After all, isn't that what Henry Chadwick set in motion over a century ago when he tried to separate what runs should get credited to the hitter and fielder? We're just carrying the torch.

Resources

There's much written about UZR, but the two biggest pieces of information (if you'd like to read in detail about the methods) are located in two parts here and here. Alex Remington's piece was a great jumping off point for me to write this. 

Fangraphs has all the cures to your UZR needs.