Before we get started, I’m excited to announce that we now have an Alphabet Soup reference page, called Sabermetrics 101! You can find it in the sidebar here on ATH, and other MLB sites will be adding it in the near future as well. It organizes the stats we’ve covered into categories, and links to the relevant section of each post, so you can use it as a handy-dandy resource for looking things up.

With that done, let’s add a few more stats to the roster. Last week we talked about the Proper Care and Feeding of Your Defense Statistics. These numbers need plenty of data before we can assume that they represent a player’s “true talent” level. Until we have about three years’ worth, we have to treat them a little more carefully.

That said, they’re still extremely useful, and a lot of analysis goes into them. Today we’ll talk about the big two: Defensive Runs Saved (DRS) and Ultimate Zone Rating (UZR). The two have a lot in common, including some crazy levels of complexity, but they don’t always agree – so when you can, look at both.

Defensive Runs Saved (DRS). DRS is based on the Dewan +/- system. The field is divided into many small zones, and batted balls are characterized by their location and velocity. The different categories of batted balls are called “buckets.” Video scouts then watch a whole mess of tape, and calculate the league averages for how often a play is made on each batted ball type.

These same beleaguered video scouts (or maybe they bring in different ones, who knows) then watch tape of each and every player on defense. The player gets credits and debits (pluses and minuses, heyyy, I get it now!) for each play that they make that another fielder didn’t (or vice versa). The size of the credit or debit depends on how often a league average player makes a play on the ball in question.

Then you add all the credits and debits up for all the buckets, add some finagling and adjusting for context, and you end up with a defense number. DRS is expressed in runs above or below average (but some Dewan numbers, which we’re not talking about here, are expressed in plays made above or below average, so make sure you know what you’re looking at).

If you’re curious, FanGraphs has a list of the other Dewan +/- statistics that they report. These further break down a defender’s game into things like preventing stolen bases, double plays, or outfield assists. All the Dewan stats that FanGraphs reports are in runs above/below average.

In 2011 (bear in mind that this is one year of data, so SAMPLE SIZE ALERT should be blaring with sirens and bells in your head) the DRS leaders were Brett Gardner, Pablo Sandoval, and Austin Jackson with 22 runs saved above the average player. At the bottom, trailing the pack by 11 runs, is Mark Reynolds with -29. (UZR didn’t like him either. We’ll get to that.)

Ultimate Zone Rating (UZR). UZR is similar to DRS in that the field is again divided into zones. League averages are calculated for how often a ball hit into a particular zone turns into an out. The difference between the league-average out rate and a player’s out rate for each zone will tell you whether the player is an above or below average fielder in that zone.

That difference is then multiplied by all the balls hit into a particular zone, to get a Zone Rating. This is done for each zone that a player covers, and when you add them all together, you get an unadjusted proto-UZR. This is then adjusted for a whole host of factors (including ballpark – UZR is park-neutral!) and for batted ball data (more people watching lots of tape!) and converted, using run expectancies, to runs above or below average.

The more playing time a defender has, the more runs above (or below, but that’s depressing) average he’ll rack up – basically, UZR is a counting stat. So FanGraphs also presents UZR pro-rated over 150 games, or a slightly arbitrary “average season.” This gives us a way to compare players with different inning totals, but it also – ALERT! ALERT! – only represents a single season’s worth of data. So, uh, use at your own risk.

In 2011, Brett Gardner also led the pack in UZR with 25.2 runs above average, which agrees pretty well with DRS above. The rest of the list, though, looks a bit different – Sandoval and Jackson are much further down. Still bringing up the rear is Mark Reynolds, at -22.8 runs. UZR/150 bears these particular bookends out, with Gardner at 31.0 and Reynolds at -30.

There are several component statistics that go into UZR that, much like the Dewan system, further break down a fielder’s performance. FanGraphs lists them here. For a very in-depth discussion on UZR, what it measures, and how it’s calculated, check out Michel Lichtman’s “FanGraphs UZR Primer.” And for a fairly snarky elaboration on the differences between UZR and DRS, check out Lichtman’s comment here.

Next week, we’ll talk more about how defensive numbers can be compared with offensive ones, and we’ll play around with some examples. Questions/corrections/fanmail goes in the comments!