30
2010
Fielding Metric – UZR
An article by XtreemIcon
I hope everyone had a great Thanksgiving weekend. I spent the whole weekend with both sides of my family and had a great time. I went shopping on Friday and did some Albert Pujols-like damage to my holiday shopping list. But now back to the grind.
I explored some of the more common offensive metrics used by sabermetricians in my first post, and I’d like to talk about defensive metrics this time, namely the most popular and widely known: UZR. Dewan Plus-Minus is another defensive metric, but let’s stick to the one most of MMO already has some level of familiarity with.
UZR stands for Ultimate Zone Rating and measures the runs above or below average saved (or given up) by a player. It combines several factors of defense that all quantifies the skill into a runs above average number: Range Runs (RngR), Outfield Arm Runs (ARM), and Error Runs (ErrR) and Double-Play Runs (DPR).
The baseball field is split into 78 zones and UZR accounts for 64 of them. Note the chart on the right from retrosheet.org for more understanding on the zones. The numerical notation for each position is used to name the zone, and the zones in holes and gaps are numbered using the two position numbers. The gap in left-center is 78. The hole between first and second is 34. The letters stand for the depth of the zone.”S” is short, “D” is deep and “XD” is extreme deep (usually only notes the deepest zones of the ballparks). A ball hit to deep right-center is zone 89D. A bloop that lands just over shortstop lands in zone is 78S. A pop fly caught by a back-tracking second baseman will likely be in zone 4D or 34D (deep second or maybe deep second shaded a bit to the first base zone. The fourteen zones not accounted for in UZR include outfield foul territory (across the league, ballparks have very little foul ground in the outfield, not enough to consider. Yankee Stadium comes to mind.), infield pop-ups and zones for catchers and pitchers, as they don’t have UZRs.
It’s a little tricky calculating range runs, but I’ll do my best to make it as easy as possible using nice, round numbers. Buckle up. For each zone, a running total is kept of the hits in that zone, the outs made in that zone and the run value of the hits in that zone. For each player, the number of hits per zone and the number of outs per zone is recorded while the player is on the field. To establish a player’s range runs, first take the percentage of balls in that zone that result in outs by all players, called the average. If 1,000 hits and 1,500 outs were made in a certain zone, the out rate for that zone is 1,500 divided by 2,500 (total chances in that zone). That zone has a 60% out rate by the average fielder. Now, since UZR rate is expressed as a fraction of 1, you can determine the extra value of the balls caught by a specific fielder in that zone by subtracting the average out rate (60% or .60) from 1 to get a .40 value on all balls caught in that zone. Because the hit rate is 40%, so that’s the value given to an out made, or hit taken away. Get it? Don’t move on till you do, it doesn’t get any easier.
Let’s go back to that part about the running total kept for each player. Let’s suppose the player in question caught 150 balls in that zone over the year. So to get the extra value of his defense, multiply the 150 balls he caught by the value of balls he caught. He’s caught 60 extra balls than the average fielder in that zone (150 times .40).
I think determining the outs was the easy part, but determining the NEGATIVE value of the hits in that zone is more difficult. You’ll have to use how many outs were made by the average player at that position and the total number of outs made in that zone by any position. If you were using zone 78D (deep left-center), for instance, outs can be made in that zone by either the left fielder or the center fielder. If our player in question was hypothetically Angel Pagan, and we already determined 1,500 outs were made on 2,500 chances in that zone, how many were Pagan responsible for, and how many was Jason Bay responsible for? Well, if of those 1,500 outs, the centerfielder made 1,000 (67%) of them and the leftfielder made 500 (33%) of them, the centerfielder is similarly as responsible for 67% of the hits, 667 in this case (67% of 1,000 hits). If there were 75 hits in that zone while Pagan was playing center, he was responsible for 50 of them against 25 chalked up to Bay (or whoever the left fielder was at the time).
We already determined the value for the caught ball is .60, so Pagan gets a hit value of 45 (75 times .60). So he’s got a value of 45 hits against 60 outs. In that zone 78D, Pagan caught 15 more balls over the season than an average centerfielder. We determine the run value of Pagan’s defense in that zone by taking the swing in average run value of each hit compared to run value of an outrecorded in that zone and multiplying it by 15.That’s tricky, I know. Let’s break it down. Let’s say the average expected run value of each hit was 0.4 runs, and the average run expectancy for an out made was -0.2. Therefore, multiply his 15 extra outs by 0.6 (the swing in run expectancy) and Pagan was 9 runs better than the average centerfielder in that zone. From there, run that same formula for every single zone in which any CF in baseball made at least one out. Add together those zone-specific range runs to get the player’s cumulative range runs to factor into UZR. You can also take specific zones to garner specific evaluations. For instance, if Pagan was +9 in 78D, +2.5 in 78, +1.5 in 78S and +2.0 in 78XD, all told, Pagan was +15 range runs above average going to his right.
To calculate the error runs, we don’t use zone-specific numbers, we use the chances across all zones. If we use the same total number of chances (the 2,500) and the total errors made in that zone across MLB we’ll get the MLB error rate. Say 100 errors were made in MLB by centerfielders for a rate of .04. If Pagan had 150 chances, as I gave you above, he SHOULD have made six errors. Let’s say he made four, for a gain of two errors (he made two fewer than he should have based on the average rate across MLB). If the run expectancy of reaching on an error is 0.5 runs, the swing is 0.7 expected runs (remember the -0.2 run expectancy for an out). So, 0.7 times the two errors gained is an error runs above average of 1.4 runs.
The same principle is used determining ARM and DPR, using the rates across all MLB and the rate of the player in question as compared to the run expectancy of the outcome. The four resulting numbers are combined to for UZR. Hooray? Not quite yet. UZR is a counting stat, just like home runs or RBIs. The more you play, the more you’ll have. To compare the defensive abilities of two players who have drastic differences in games played, UZR/150 is used, which is the number of runs above or below average a fielder is, per 150 defensive games. Now we can Hooray!
The goal of UZR/150 is to quantify runs into a total because putting a run value to defense allows one to compare with offensive metrics like wRAA (weighted runs above average, see previous post) to determine the true value of a player as a complete player, on both sides of the ball. According to Fangraphs, Joey Votto led the National League with 61.3 wRAA. Albert Pujols had 55.4. Votto also ranked higher than Pujols in UZR/150, though not by much. Votto’s UZR/150 was 2.2, edging Albert’s 1.1 by the slightest of margins. Combining UZR/150 and wRAA, it’s determined that Votto was worth exactly seven runs above average more than Pujols was in 2010 (Votto was 5.9 wRAA better and 1.1 UZR/150 better).
This and other stats make it pretty clear why Votto was a near-unanimous choice for MVP despite not leading the league in any of the traditional stats. While not leading in things like batting average, RBIs and home runs, the guy who won the MVP was first in the league in OBP, SLG%, wOBA and wRAA. The shift in thinking amongst the mainstream media who have MVP votes towards sabermetrics is a welcome change. This was also evident in King Felix winning the Cy Young Award despite 13 wins. He was clearly far and away such a better pitcher than anyone else in the league, almost in a league by himself.
After explaining offensive metrics like wOBA, which is inclusive of all outcomes of at-bats, and now UZR, I hope it’s becoming clearer why these stats are better than knowing simply the counting stats and totals. I, for one, am glad these stats already exist and are calculated already. Can you imagine the vein in your forehead if someone gave you a player’s stat line with individual numbers and asked you yourself to determine how many runs that player was worth offensively? Or someone asking you to determine Pagan’s UZR if you were given his total chances, put-outs and errors? I also hope it’s becoming clearer why sabermetrics generally quantifies statistics into runs and why that’s so important.
About the Author: Jesse Elgarten
33 Comments + Add Comment
NL East Standings
| Team | W | L | Pct. | GB |
|---|---|---|---|---|
| Braves | 26 | 17 | .605 | - |
| Nationals | 25 | 17 | .595 | 0.5 |
| Marlins | 23 | 19 | .548 | 2.5 |
| Mets | 22 | 20 | .524 | 3.5 |
| Phillies | 21 | 22 | .488 | 5.0 |
Last updated: 05/22/2012
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This is one of the best articles I have read on uzr. Great article and welcome to the team icon
Thanks, Sean.
EXCUSE ME, I’VE GOT A SCREAMING HEADACHE & AM NOW TO BLURRY EYED TO SEE THE ACTUAL GAMES BEING PLAYED…LMAO
Who has actually won anything relying on this bilge?
’62, How you doing? To me it’s a fun type of stat that allows you to back up your opinion with something other than “He covers the whole field” Last year we all watched Angel Pagan run balls down all over the place, but how much better did he do at home vs all the other CFer’s? Was his D AS vital on the road and if so was it as good as it was at home? Looking at the numbers on Fangraphs.com it say’s he was merely avg at home (CF) and substanially better than that on the road. I find that to be surprising. As far as I’m concerned he couldn’t really have played a better CF than I watched him play all year regardless of venue. Tejada also has some ugly numbers that to me just flat out fail the eye test but it does make it interesting comparing these numbers to your own ideas. Sometimes they match sometimes they don’t.
T, if I pry open my eyes & mind while considering your Pagan reference, those numbers are a tad skewed considering CF @ Citi is relatvely vast & more difficult to defend than other CFs. Break down every CFer’s #s restricted to Citifield & compare them to Angel @ home & u’ll have a more significant comarison(favoring Angel, due to familiarity with cutout quirks) than merely all CFers @ home. because not all homes are =. These stats would be much more valuable in my opinion when evaluating players of the 80s when cookiecutter fields were more in vogue, the renasaiscance movement replacing them with more unique updates devalue the comparisons beyond restraining it to just players on the same team defending the identical turf with a similarity of familiarity with specific quirks. WHEW!. Kmow what I mean?
Yeah 62, That’s what I’m getting at. How much more valuable (with the comfort of knowing Citi) is Angel to the Mets in the run prevention dept? compared to all the other CFers that have played there? Also in comparing CFers and using the method the author explains (averaging the runs saved or cost) vs how many runs the catches ACTUALLY saved would be interesting. Clutch defense anyone? Take Tommie Agee’s 2 spectacular catches in the World Series and break them both down. I don’t know what the counts were or even the pitch type (probably fastballs up) Both Hendricks and Blair were being shaded to pull. Both hit the ball the other way. Both were with 2 outs and Agee has been credited by Fans and sportswriters with saving 5 runs total. The second catch in particular would seem to be the RFers ball and I’ve read numerous times of Swoboda’s overall “rocky” defense but where was he? Where was he positioned? He couldn’t have been on the RF line AND Agee playing Blair to pull. Was he that immobile? What type of pitch winds up in each zone. This is the stuff I’d love to see Sabermetrics take a look at.
T, there u go mentioning your namesake & getting me into trouble as I must, in honesty, point to my feelings those catches, while certainly spectacular, were primrily so because Agee was renowned for his consistant bad positioning relying too heavily on his speed to correct his initial bad defensive placement.
I know ’62, But was he incorrectly positioned on those two plays? He was playing both guys to pull yet they were pitched to away. 50/50 either way. And who’s responsible for the positioning anyway?
T, back then I’m not sure; but I believe veteran players weere left to determinee their own placement as opposed to today’s environement where 2 coaches are assigned to monitor all player positionings, 1 coach for infield, the other outfield. I believe this is predicated by the stringent reduction in developmental periods being allowed prior to MLB promotions.
’62, I think your right about now but I’ll bet Gil or maybe even Pignattano or Walker had a say. We’ll probably just have to wonder.
METS62FAN, the reason this stat is useful is to compensate for the fact that we no longer have the cookie-cutter fields we used to. That’s why the field is cut up into so many different zones. It’s not prudent to compare how a right fielder plays his position in Yankee Stadium as opposed to Citi because of how drastically different the right fields are. That’s why we use smaller zones across the league, because Zone 9 in Citi is the same as Zone 9 in the Bronx. Same for Zone 9D. The difference is that Citi probably has a Zone 9XD, but few other parks do, if any. So the difference lies in maybe three or four zones out of the entire 64 used, a very small percentage. It’s easier to compare and yeilds better results.
X, while that cetrtainly makes sense “on paper” & for Fantasy Leaguers, I’m still perplexed as to, Who has actually won ANYTHING ON GRASS using Sabremetrics? Certainly not in Oakland,San Diego, Toronto, is finishing “out of the Money” more prudently(for less $$$) really the goal we should be opting for? If I look at Oakland as the Premere rep of this relativly “new school” of thought/approach & the NYY as the premre rep for the “old school” methods of “Balls to the financial wall” I see in modern era mutitudenous NYY WS totles Vs. zilch in Oakland,SD,TOR even combined. In his day, even Ted Williams was not considered a top 5 defensive player in LF, neither was Reggie in right much later on; but didn’t their performances on the turf prove worthy of being honored as complete players late in the Season despite Teddy Baseball’s unadorned digits?
I certainly can’t help; but consider the Wilpons have turned into perpertrators of a PONZI SCHEME on the fanbase.
Personally, I believe that Fantasy baseball Leagues have done wonders for reallocating baseball enthusiasm from the “Gut”ter fans on street corners & barstools everywhere to the sliderulers with pocket protectors & protractors.
Well, the Red Sox and the Yankees, to name just a couple.
Nice write up X. I’d love to read more about specific players and how they perform in specific zones vs others at the same position and whether that then costs them somewhere else (positioning) For instance Angel Pagan in the zone where he made that incredible catch last August and then started a DP. How players perform in unique area of a particular stadium. Which infielders go to their right better than the left ect. and see how these numbers match up with what we see out there. Also, I’ve heard or read somewhere that infielders don’t get credit for running down pop fly’s regardless of whether they are fair or foul. Is this true?
T, unfortunately it is some of the time. The answer is not because they’re casually dismissed, though. Just because so few happen to really have a large enough sample size, like in outfield foul territory. Fair infield flies in general are disregarded because anyone can catch it and no one really has to run very hard, or far. Infield foul territory DOES count, however. The three times Ike fell over the dugout rail was credited.
Got you X. Thanks for the reply. It’s funny you mentioned Davis’ Rail thefts I was thinking about them when I posted my comment.
Xtree — thanks for a great job. These metrics represent ‘state of the practice’ and are evolving. We’ll never be able to go back the old ways which were not transferable between alleged experts.
Prepare yourself for attacks by the unread and unwashed. They’ll be coming. Change is really hard for some folks, especially if they’ve analyzed or coached only with intuition.
you must mean Bayonne…he coached. and played.
You’re a quick study, Chris. Now if you could impart some of your knowledge to him, all would be well west of the Hudson and on Ave. C and Kennedy Boulevard.
Don’t count on an easy time.
I’m on board with +/-. Less so with UZR.
Pagan has good range laterally, but still misplays balls over his head. He catches most of those, although its an adventure. UZR doesn’t really capture that (it captures the event as an “out”, and doesn’t subjectively judge). That’s one of the things that traditionalists will point out; your “eyes” can tell you that he’s not as good as the stats suggest, while the sabermetricians are less interested in the subjective side.
Darth, you’re right about taking the subjectivity out of it. But doesn’t +/- treat defense the same way? I admit, I’m not fluent with it, just familiar. As I understand it, +/- deals only with putouts and the same principal of the rate being out of 1 applies. So if Pagan, with well above average range, makes a play that only 15% of other CFs make, he’s credited with .85 points. All his putouts are then totaled to get his +/- total. As with UZR, the higher the better.
If I’m wrong, please correct me, but doesn’t that also dismiss the adventures some have out there and focus only on the result?
If a CFer doesn’t have a few balls burn him every year than he is playing too deep and not taking away a bunch of singles. My impression of Pagan is that he’s great side to side and very good going back and has just the slightest hesitation coming in, something that I believe he will eliminate this year because of the confidence he’s playing with. I’d be very interested to see these plus/minus numbers. Where on the internet are they?
X,
Thanks for the article.
I am still working at it.
For the next article, can you find something equivalent to the football’s WPA in baseball? Jets’ Holmes has the highest # in football.
Mets2012, WPA exists in baseball, too. As a matter of fact, it existed in baseball first and was received so well, it spread to other sports. In baseball, there are several offshoots of WPA, such as in expectancy and scoring expectancy. Using retrosheet data, expectancies can be computed to determine a few things. Condiser a base/out scenario, say 1st and 3rd, one out. Run expectancy can be determined two ways, the perctage of at least one run scoring AND the percentage of one run, two or three runs can score. Usually the matrix goes up to five runs.
A couple of times I’ve mentioned how a caught stealing hurts more than the stolen base helps. This is based on scoring expectancy. I’m at work and don’t have my books with exact figures, but I can still get my point across. Suppose Reyes is on first with one out. That situation, a team can be expected to score .5 runs for argument’s sake. If he steals safely, one out, man on second will score .65 runs. But is he’s caught, bases empty with two outs will only score you .2 runs. Get it? He could earn the team another .15 runs with a successful attempt, but cost his team .3 runs is he’s thrown out.
Win expectancy is more like what you’re talking about. Given a situation (say…..home team down by two in the top of the 6th inning with 2 outs and bases loaded) will yield maybe a 25% chance of the home team winning. If the next batter hits a grand slam, and the home team is now down by six, that win expectancy for the home can drop to 10%. Keep in mind I’m using hypothetical numbers, just trying to explain how they work.
To put David Wright in perspective, he was 21st in the NL in WPA in 2010.
X, Thanks.
Is 21st good or bad?
Mets2012, I won’t make that assumption, because some of the most heated arguments on this website are about David Wright’s worth. All I’ll say is that it’s a safe calculation to assume that there are 215 position players in the National League. Sixteen teams times a 25-man roster is 400, subtract 192 if each team has a twelve-man pitching staff. Some only carry eleven pitchers, so we’ll go with 215 as a very solid guestimate.
At 21st in the league, Wright was better than about 90% of the league in adding wins to his team. My personal belief is that it’s pretty darn good, but I’ve long been a proponent of David Wright. Those with different views of Wright may deride him for being worse than ten percent of the league. Just depends on how you look at it.
X that’s a great way of looking at it. unfortunately I don’t think that’s enough for the ignorant. I think they need Wright to be a robot and never make an error and get the big hit 100% of the time. That is how Mets fans think. The front office should get EVERY player that the fans think should be on the team, no matter what the cost, and ALL those players should have a 1.000 fld% and never make out in a big spot. Isn’t that how it should be?
Well, that WOULD be a hell of a team, wouldn’t it?
LOL.
Thanks.
Very good indeed. I am talking about you ,X
Thanks, Mets2012.
When rating a player defensively just statistically and sabermetrically, I prefer to add a player’s UZR (on Fangraphs)and a player’s Defensive Runs Saved Above Avg.(provided by Baseball Info Solutions on Baseball reference.com)and a player’s Total Zone Total Fielding Runs Above Avg.(provided by BaseballProjection.com on Baseball reference.com) and then subtracting from that total figure a player’s errors at a particular position for a more comprehensive saber defensive figure. Employing that formula, last yr. Angel Pagan just in CF would rate a very solid plus 26.9 and Torii Hunter again just last yr. in CF would rate a miserly minus 15.8.
Sach, can you explain more of that formula? I’ve never heard of it.
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