Examining UZR

[757690]

No it doesn't because SS are only compared to other SS.

I understand this is a difficult concept to grasp, so lets just look at the math:

An average SS makes around 80 plays outside of his zone.

An average 3B makes around 40 plays outside of his zone.

This makes sense, since a SS covers twice the ground a 3B covers.

So, if a SS has 25% more range than the average SS, he will get 20 more plays out of his zone.

If a 3B has the same 25% more range than the average 3B, then he will get 10 more plays out of his zone.

So on top of the positional adjustment, the SS who has the same skill level as the 3B, will get a UZR range rating 10 points higher.


I'm not even saying this has to be a problem. But I do think it's something we should be aware of when we compare players.

[jojo]

I understand this is a difficult concept to grasp, so lets just look at the math:

An average SS makes around 80 plays outside of his zone.

An average 3B makes around 40 plays outside of his zone.

This makes sense, since a SS covers twice the ground a 3B covers.

So, if a SS has 25% more range than the average SS, he will get 20 more plays out of his zone.

If a 3B has the same 25% more range than the average 3B, then he will get 10 more plays out of his zone.

So on top of the positional adjustment, the SS who has the same skill level as the 3B, will get a UZR range rating 10 points higher.


I'm not even saying this has to be a problem. But I do think it's something we should be aware of when we compare players.

The SS and 3b don't have the same skill levels.

[757690]

The SS and 3b don't have the same skill levels.

Which is taken into account in both the positional adjustment and the extra plays a SS makes. It's double counted if the SS has above average range.

If the SS and the 3B were both average in terms of range, the extra value a SS provides is only counted once, in the positional adjustment. They would have the same UZR, zero, and WAR would give the SS a boost in value with the positional adjustment.

If they both are 25% above average in range, the SS would get a higher UZR, +20 to + 10, and a boost from the positional adjustment when using WAR.

[jojo]

Which is taken into account in both the positional adjustment and the extra plays a SS makes. It's double counted if the SS has above average range.

If the SS and the 3B were both average in terms of range, the extra value a SS provides is only counted once, in the positional adjustment. They would have the same UZR, zero, and WAR would give the SS a boost in value with the positional adjustment.

If they both are 25% above average in range, the SS would get a higher UZR, +20 to + 10, and a boost from the positional adjustment when using WAR.

It's not double counting because again, the SS is compared to other SS.

[RedsManRick]

I understand that.

My issue is that an above average SS is going to get a higher UZR than a similarly above average 3B, even after the positional adjustment. This is because a SS gets significantly more chances to make out of the zone plays than a 3B. This is only true for above average fielders at certain positions, and it's because of the way the field is constructed.

I think we're getting confused over what the positional adjustment is for.

In WAR, the basic premise is that you can't replace a part of player. You have to replace the whole guy. So there's no such thing as a replacement hitter or replacement fielder. Just replacement player.

This plays out thusly: Players are compared to the average major leaguer in each component of the game. Those differences are then added up to get a performance relative to the overall average player. That aggregate is then adjusted by a standard amount, weighted by playing time, to account for the difference between the average player and the theoretical "replacement player".

The positional adjustment on defense is done to account for the fact that each position gets a different set of opportunities which are handled by a subset of players. So you can can't compare a play to SS to an overall league average the way you can with a given plate appearance.

So to get to a comparison of a given defender to the overall league average defender, we have to do two things: measure performance relative to positional average and adjust for the difference between positional average and overall fielder average*. So you're not double-counting anything, you're just counting the whole thing in two parts.

*This is obviously the positional adjustment and the values for those were calculated by looking at how guys who played multiple positions performed in each.

[RedsManRick]

I thought maybe a graphic would help explain UZR separately from the WAR positional adjustment. So here goes:

OFFENSE
Example 1. Better than average hitter (Positive Batting Runs), Worse than average hitter (Negative Battings Runs)

	  <-----Positive Batting Runs-----|----Negative Batting Runs--->
   (Our Best Hitter)----------------(AVG Hitter)-----------(Our Worst Hitter)


DEFENSE
Example 1.  Better than average SS (Positive UZR), Worse than average 1B (Negative UZR)

      <----UZR----|       				          |---UZR---> 
  (Our SS)-----(AVG SS)-------------(AVG Fielder)-------------(AVG 1B)---(Our 1B)
	           <------PosAdj---------|---------PosAdj-------->


Example 2.  Worse than average SS (Negative UZR), Better than average 1B (Positive UZR)
  
		  |---UZR--->				<---UZR---|
               (AVG SS)--(Our SS)---(AVG Fielder)---(Our 1B)--(AVG 1B)
	           <------PosAdj---------|---------PosAdj-------->

[757690]

I think we're getting confused over what the positional adjustment is for.

In WAR, the basic premise is that you can't replace a part of player. You have to replace the whole guy. So there's no such thing as a replacement hitter or replacement fielder. Just replacement player.

This plays out thusly: Players are compared to the average major leaguer in each component of the game. Those differences are then added up to get a performance relative to the overall average player. That aggregate is then adjusted by a standard amount, weighted by playing time, to account for the difference between the average player and the theoretical "replacement player".

The positional adjustment on defense is done to account for the fact that each position gets a different set of opportunities which are handled by a subset of players. So you can can't compare a play to SS to an overall league average the way you can with a given plate appearance.

So to get to a comparison of a given defender to the overall league average defender, we have to do two things: measure performance relative to positional average and adjust for the difference between positional average and overall fielder average*. So you're not double-counting anything, you're just counting the whole thing in two parts.

*This is obviously the positional adjustment and the values for those were calculated by looking at how guys who played multiple positions performed in each.

I get all of that.

Again, the issue is that As I said in my initial post, I understand why WAR provides positional adjustment.

My issue is precise, not an overall critique of UZR. I think everyone assumes I'm trying to bash UZR. I'm not. I'm simply trying to analyze it in detail to see where there are some problems, or issues that should be noticed. I'm not even suggesting changing UZR, just pointing out precise points where it appears to overvalue or undervalue certain players.

So let me ask you this, in this example from my previous post:

An average SS makes around 80 plays outside of his zone.

An average 3B makes around 40 plays outside of his zone.

This makes sense, since a SS covers twice the ground a 3B covers.

So, if a SS has 25% more range than the average SS, he will get 20 more plays out of his zone.

If a 3B has the same 25% more range than the average 3B, then he will get 10 more plays out of his zone.

So on top of the positional adjustment, the SS who has the same skill level as the 3B, will get a UZR range rating 10 points higher.

Are you okay with that? I am not. I think when figuring out WAR for above average SS, their WAR is inflated.

[jojo]

Here's some reading from the archives for those inclined....

Somewhere in this thread, Doug posted a picture of the field cut into zones and there is a discussion about the effect of positioning:

http://www.redszone.com/forums/showt...ensive+metrics

Here's a post dug up from the archives that explains the nuts and bolts of UZR

http://www.redszone.com/forums/showp...&postcount=123

Oh come on. Just explain how defense can be so readily quantified. You or jojo or both. I really want to understand a defensive metric that can quantify runs in the way these claim to.

There is a treasure trove of information on the web about the nuts and bolts of play by play (PBP)-based defensive metrics just a google search away. I know some of it can be dry reading but if you have the time, it might change how you view defense so the effort would almost surely be rewarded.

I'll specifically focus on UZR in an effort ot answer your question because it's currently considered the gold standard. Basically, UZR uses play by play (PBP) data to determine the probability a ball in play (BIP) will be converted into an out based upon batted ball type (grounder, flyball, line drive, fliner, etc), BIP velocity (i.e. how hard it was hit), and zone into which it was hit. The field is divided into 78 zones as recorded on baseball reference website. UZR uses 64 of them. Each position has specific zones of responsibility (though some zones will overlap between two positions in which case balls within a zone are divided up proportionally i.e. if 80% of balls in a zone overlapping first and second base were caught by the second baseman, the first baseman would only be expected to field 20% of such balls).

In a nutshell a player’s UZR rating will be calculated as follows:

Player A’s “caught ball value” is determined for his specific position by using PBP data to tabulate how many put outs (PO) and hits were recorded in each zone of responsibility associated with his position while he was on the field. This value is then compared to the total number of PO and hits recorded in those zones by all players over the course of the season. It should be noted that a player could have a negative caught ball value for some zones of responsibility but a positive one for others depending upon his unique abilities (i.e. Felipe Lopez is weak to his right but actually very good to his left). If player A was below average in a zone, he’ll have a negative caught ball value for that zone compared to the league (average is zero or “neutral”). In contrast, if player A was above average in a zone his caught ball value will be a positive number.

Now to specifically address your question, Player A’s caught ball value for a zone can be fairly easily converted to a run value by multiplying it by the average run value of a hit in that zone (which has been determined by traditional linear weights hit values). Run values are totaled for each zone of responsibility for player A’s position to yield his final UZR value while playing his position.

UZR attempts to account for everything that could impact a fielder’s chances of recording an out in a zone by adjusting for a plethora of factors including environment, situation (number and position of runners and number of outs), batter’s handedness, and the pitcher’s BIP tendencies (i.e. GO/FO).

UZR is the best way I’ve seen defensive value tackled. Importantly, a majority of major league clubs are now using either this system or similar permutations of it.

Here’s some links that explain the system in much greater detail:

http://www.baseballthinkfactory.org/..._2003-03-14_0/

http://www.baseballthinkfactory.org/..._2003-03-21_0/

Here's another post from the archives discussing WAR and UZR and their relationship to runs.

http://www.redszone.com/forums/showp...&postcount=369

Re: Don't look now - Dunn having year we always hoped for

So...is anybody going to answer my question about stats relative to a roster? I would just like to know if it exists. Or is impossible to develop. Or is a dumb idea.

First, it’s not a dumb idea. Your question speaks to the heart of many debates that are had on the ORG. Intuitively you’ve put your finger on exactly what sabermetrics has been building toward since Bill James started writing about baseball. Fortunately, not only is such a system possible, it already exists! An explanation is below.

This was posted a few pages ago, and should be addressed by both sides of this argument.

I absolutely agree because this is a central point that must be addressed when discussing the proper way to valuate players-it’s the ultimate sniff test. In other words, does the approach allow meaningful discussion to be had regarding a player's true total worth and does it relate that worth to its impact on the team’s fortunes on a global scale (i.e. does that production relate to a team’s real runs?). Ultimately, that’s the gold standard concerning usefulness. Here is VP’s original question in the post referenced above:

This article actually kind of gets to the heart of a major statistical question I have. And I hope this doesn't sound too simplistic, but – are there any stats that successfully and thoroughly take into account a player's value in the context of a given team? Because when I find myself not totally agreeing with the conclusion a set of hard and fast facts put in front of me, this is usually the element that I find is missing.

The answer is absolutely there are stats that successfully and thoroughly take into account a player’s value and places it in the context of what it means to the team…. The system is WAR (wins above replacement) and its freely available at fangraphs.

WAR calculates marginal wins (wins above freely replaceable production) by using wOBA as the run estimator for offense (a metric that readily converts to runs), UZR (ultimate zone rating; a play-by-play based defensive metric) as the estimate of defensive value, and FIP (fielding independent pitching; estimates a pitcher’s true performance by isolating his peripherals, i.e. things he can control) as an estimate of pitching win value. As a matter of bookkeeping the offensive value provided by pitchers is lumped in with position players. So all phases of the game are measured as a position player's WAR consists of offensive value + defensive value and Pitching War consists of the value pitcher's provide while on the mound. Team WAR is then the sum of Position Player WAR and Pitching War. Importantly, again, both WAR and the individual component metrics are available for free at fangraphs so the whole system is readily accessible for fans to use and to test.

In several posts in this thread, I’ve explained the approach that WAR uses and why it should be considered the most appropriate way to valuate players so I won’t dwell on that aspect. Instead, I’ll focus on the part of your question that speaks to the heart of the issue-how well does WAR relate back to the team on a global level. In other words, how well does WAR correlate with “real runs”. By answering your question, such criticisms as the following can again be addressed as well:

1) defensive metrics do not correspond with reality, or
2) defensive metrics substantially inflate the value of defense, or
3) expressing player worth in terms of marginal value is inappropriate because while it may suggest something about dollar value, summing offensive runs plus or minus defensive runs does not related to the net runs that a player created/cost his team.

So in order to test whether summing offensive runs and defensive runs relates to the net runs that a player created/cost his team, I calculated the strength of the linear relationship between team WAR and pythag record (i.e. calculated the correlation coefficient) by regressing total team WAR to pythag wins for all teams from 2002 thru 2009 (the years in which WAR is available from fangraphs). Since WAR is expressed as marginal wins, 47 wins were added to the total WAR for each team so that total WAR and pythag wins could be directly compared. This is because 47 wins represents the expected number of wins for a team comprised completely of replacement level players (replacement level winning percentage=.29 so 162*.29=47 wins). Here are the results by year and for across all seasons:

WAR vs pythag Win
year corr coef
2002	0.94
2003	0.91
2004	0.93
2005	0.86
2006	0.89
2007	0.92
2008	0.93
2009	0.88

'02-'09: 0.92

These results indicate that when looking across all years for which WAR data is available, WAR gets us 92% of the way to the predicted pythag record. WAR correlates to runs better than OBP and SLG and approaches the correlation of OPS or RC to runs even though admittedly WAR still has room for improvement from a defensive standpoint. In other words, WAR correlates very, very well to “real runs”. Clearly the WAR system of player valuation adds up extremely well at the team level.

Here’s a break down of the NL central over those years providing a look at how well WAR has correlated with the fortunes of our beloved Reds at the actual run level:

	Wins '02-'09
team  Pythag	WAR
cards	707	674
cubs	660	660
astros	659	649
brewers	586	595
reds	562	550
pirates	562	551

correlation coefficient=.97

Clearly WAR has captured what has gone on in the NL central this decade very well. For instance, looking at the Reds over the last 8 seasons, WAR has gotten to within 1 win on average of their pythag record.

So WAR allows us to calculate total value for a player on a scale that permits comparison to every other player in the league in an apples to apples fashion and these player values can be used to directly gauge the player’s impact on his team at a global level as Team WAR directly correlates to a team’s RS/RA (runs scored/runs against). What’s more, WAR values also correlate directly to market values as explained in earlier posts.

The WAR system is rooted in reality, allows player valuation to occur on a scale that was previously impossible and it allows such discussion to be had in the context of market value as well. I can’t think of a better way to answer the question of player impact/worth or a better tool to evaluate roster formulation decisions.

Again, WAR and defensive metrics pass the sniff test as they reflect "real runs" pretty closely.

While defensive metrics are not prefect and they certainly will be improved as new technologies such as hit f/x allows such metrics to address the issue of quality of chances better, generally, the notions that defensive metrics do not correspond with reality or that they substantially inflate the value of defense or that the summing offensive runs and defensive runs does not relate to the net runs that a player created/cost his team have to be rejected as gross exaggerations of the weaknesses of the approach.

The WAR approach is not perfect-like all metrics, there are limitations and weaknesses. However, that said, the WAR approach not only passes the sniff test its ability to relate player worth back to the impact such individual worth has on the team makes it the best (actually the only) metric currently available for addressing many of the issues we’ve talked about in this thread and daily on the ORG.

Given the correlation of WAR to team wins, it's not compelling to argue that WAR is divorced from reality....

Here's another post from the archives illustrating these issues with an example from the Reds 2009 season:

http://www.redszone.com/forums/showp...&postcount=185

Re: Don't look now - Dunn having year we always hoped for
One significant issue raised in this thread relates to the production levels that the Reds have gotten from left field this season versus last season. Specifically, it is being debated whether the 2009 Reds have replaced the production that they got from left field last season or whether they’ve seen a substantial downgrade.

One thing that has been missing from the discussion, however, is a look at the Reds production levels from a global standpoint-a view that ought to provide a definitive answer. The table below describes the total production the Reds have gotten overall and also by position. Production was calculated using wOBA as the run estimator for offense and UZR as the estimate of defensive value. Finally, based upon these metrics, a run difference is calculated for the difference in offensive and defensive production at each position between 2008 and 2009. The difference in overall value represents the sums the offensive and defensive values. These are also given for each position and on the team level.

Here are the comparisons:

The "wOBA run difference" represents the difference in run values associated with each season’s wOBA (by position and at the team level) calculated using wOBA values as applied to the number of PAs in each category for 2009 to date (i.e. 2008 run values are normalized to 2009 playing time to allow direct comparison of production levels). The 2008 value was then subtracted from the 2009 value to show the difference in production between years. The UZR run difference is the actual UZR values for ’08 and ’09 with the ’08 values being adjusted for the number of defensive innings the Reds has thus far logged in their 140 games played this season. Again, the 2008 UZR value was then subtracted from the 2009 value to show the difference in production between years.

First using a WAR approach (offense+defense) suggests the Reds have essentially replaced the total production that they got from leftfield in ’08. In fact, they’ve surpassed it with their 2009 roster.

Left field has not been the problem with the Reds in ’09. This global look suggests that the infield has actually been a significant problem with the Reds. The production from firstbase and thirdbase has actually been worth almost 40 runs less than what the Reds got from those positions in ’08. That’s huge. Taveras was projected as a bad idea coming into the season and I think it’s fair to suggest most ORG members actually realized that Taveras would likely be a problem. Yet it’s still surprising that the Reds have managed to downgrade CF by almost a win this season relative to 2008.

So again, left field hasn’t been the problem. If one wants to point to an outfield position that needs upgrading, CF is the elephant in the living room. Leftfield production can be adequate through shrewd platooning as a WAR approach demonstrates.

Perhaps this global view of the Reds over Jocketty’s tenure also points to why Rolen was targeted by the Reds. Also, while shortstop looks like a solved problem based upon the above view, one has to remember that in ’08 shortstop was a train wreck for the Reds (so the above improvement is associated with production that is still below league average). Thus, going forward, shortstop is also a position that the Reds should look to upgrade.

Defense matters and the Reds should continue to embrace that to allow resources to be allocated toward more premium positions. Rolen is in the fold. I’d be giddy if the Reds signed Cameron short term for center and acquired Hardy for short. Dickerson/Stubbs could be a leftfield platoon with Stubbs getting further opportunities to develop by filling in at center and right when needed. That is a scenario at least that exemplifies what the Reds really need to do-get complete players i.e. ones that can play offense and defense. As it stands, the ’09 Reds went all in on defense but sacrificed offense to a point that their season amounted to being on a treadmill.

On to another issue-does the analysis above make sense outside of a spreadsheet?

and I'm not the only one that thinks some of these defensive runs saved and runs cost projections are unrealistic.

This is probably the most common criticism of defensive metrics and player valuation metrics like WAR that rely upon defensive values to estimate player worth. Often it is accompanied by statements evoking a “smell test” or conclusions that WAR-derived valuations are divorced from reality like:

The defensive stats are unproven because they do not correspond with reality. They do not correlate to the real on-field results. Defensive metrics are still in their infancy. They have some value, but can't honestly and accurately be given the same respect as offensive run metrics.

Or

When people use unproven run value metrics in combination with proven run value metrics without stating the liberty they have taken (or realizing their error) then it is only fair for their claims to be challenged by people that are familiar with the metrics.

Some have thoughtfully expressed concern about the relative reliability of such offensive and defensive metrics (which I think is a valid point though I think it overstates certain flaws):

Until it reaches that hard-data point, you simply have to weigh the offensive aspects far more greatly than the defensive. You can know, with some certainty, what a player is contributing offensively to a team and what his likely contribution will be in the future. Defensively? You're taking an educated guess based on some speculative (but standardized) "measurements."

Given some of the above comments were taken directly from this thread, lets actually test these assertions by looking at how well the above WAR approach jives globally with the reality of the Reds 2008 and 2009 seasons (in other words, lets relate them back to actual runs to see about that famous "sniff test")…..

First here’s a breakdown of what advanced metrics say about the run contributions of each phase of the Reds game (pitching/defense, offense):

	    thru 140 games
	2008	2009  Run Diff. 
FIP	4.47	4.68	-29
UZR    -37.1	36.2	 73
wOBA			-59
			
	RS= -59	RA= +44

Here’s a breakdown of the Reds actual RS/RA through 140 games of both 2008 and 2009 as well as their pythag and actual records:

	      thru 140 games	
	 RS	 RA    Pyth w-l  W-L
2008	601	698	61-79	62-78
2009	554	646	60-80	63-77
Diff	-47	 52

Analysis of wOBA predicts the Reds should have scored 59 fewer runs this season versus last. Looking the real totals, we see that the Reds only scored 47 runs less in reality. That’s a difference of 12 runs when comparing actual versus predicted (about a win over 140 games). Interestingly, the WAR summary above suggests that the Reds should have impacted their RA by 20 fewer runs based upon UZR (UZR is 73 runs better in ’09 but their RA is only 52 runs better). This would seem to suggest that UZR does indeed overestimate the impact of defense. However, when looking at the Reds fielding independent pitching (FIP) in 2009 versus 2008, the Reds pitching staff has actually performed about 30 runs worse over the course of this season versus 2008. Thus their run prevention might actually be predicted to be 44 runs better in ’09 (73 UZR-29 FIP) than it was in ’08. The actual difference is 52 runs. That’s pretty darn close.

As another sniff check, take another quick look at the table that breaks down the run contributions of each phase of the Reds game (pitching/defense, offense) using advanced metrics. That table suggests that the Reds decreased their runs scored by -59 runs between ’08 and ’09. They only improved their run prevention by 44 runs. Thus they would be expected to have negatively impacted their record by about 1.5 wins. Using the RS/RA for each year to calculate pythag records we see the Reds would indeed be expected to have won 1 fewer game in ’09 versus ’08 (2008 pythag W-L: 61-79; 2009 pythag W-L: 60-80).

So ya, WAR and defensive metrics pass the sniff test as they reflect "real runs" pretty closely. This isn't really that surprising since such metrics use run expectancy-derived linear weights to estimate run values of events.

While defensive metrics are not prefect and they certainly will be improved as new technologies such as hit f/x allows such metrics to address the issue of quality of chances better, generally, the notions that defensive metrics do not correspond with reality or that they substantially inflate the value of defense have to be rejected as gross exaggerations of the weaknesses of the approach.

Here's some numbers showing an example of how defensive value can actually make the difference between a platoon player ans an every day starter using Gomes as the guinea pig:

http://www.redszone.com/forums/showp...&postcount=651

Here's the argument for why Gomes is a platoon player:

First here's his career splits (major league average is a wOBA=.330):
vs L: wOBA=.387
vs R: wOBA=.329

Pausing for a second, overall, that's an above average bat. We shouldn't forget that. Gomes is a legit major league bat.

But he's also a poor defender. We can argue about the magnitude of his defensive value but defensive metrics match my eyes, his reputation and scouting reports. He's not adequate. He's bad. I'll conservatively cap his negative value at -15 runs over a full season. Again argue about it, but really, it's a tough argument to win IMHO.

So what does this mean relative to his value on a platoon basis (assuming 600 PAs woth of playing time from each side)?

                  vLH         vRH
bat               30         -1.5
glove            -15         -15
replacement       20          20
position         -7.5        -7.5

total:           27.5         -4

In a season's worth of playing time against lefties, he's almost 1 WAR above average. In a season's worth of playing time against righties, he basically replacement level. Unfortunately everyday players see righthanders a lot more than lefties

If he could play defense, he wouldn't be a platoon player.

[RedsManRick]

So let me ask you this, in this example from my previous post:

An average SS makes around 80 plays outside of his zone.

An average 3B makes around 40 plays outside of his zone.

This makes sense, since a SS covers twice the ground a 3B covers.

So, if a SS has 25% more range than the average SS, he will get 20 more plays out of his zone.

If a 3B has the same 25% more range than the average 3B, then he will get 10 more plays out of his zone.

So on top of the positional adjustment, the SS who has the same skill level as the 3B, will get a UZR range rating 10 points higher.

Are you okay with that? I am not. I think when figuring out WAR for above average SS, their WAR is inflated.

I am absolutely OK with that and am not quite sure why you're not. I see a few possible issues:

Firstly, you're just talking about UZR values in a funny way. UZR is "rating" their defensive ability in the abstract sense; it is a counting statistic of actual performance, like Batting Runs. We're not talking about 10 generic "points" of defensive ability. We're talking runs worth of production.

Secondly, you actually pulled a bit of a bait & switch, accidentally I imagine.

This: "a SS has 25% more range than the average SS"..."3B has the same 25% more range than the average 3B" is NOT the same thing as this: "the SS who has the same skill level as the 3B". In the original situation you described, the SS is a more skilled defender in absolute terms than the 3B, because the average SS is more skilled than the average 3B. In the second situation, they are equally skilled. This is one of the things that makes measuring defense different. With hitters, a PA is a PA, everybody can get compared to the same "average Hitter". But with fielding, you have different subsets of people fielding different subsets of unique opportunities. So you have to first compare to just the guys at the position and then you have to adjust for the positional average being better or worse than the league average. But you say you get this part; I believe you.

I think it's probably this:

Thirdly, each player has a different amount of opportunities and they get credit accordingly, the exact same way hitters of equal skill who have a different number of plate appearances would end up with proportionately different batting run totals. UZR is simply a tally of how you performed relative to average in the opportunities you had. If you have more opportunities, you have the possibility to accrue more UZR. Just like a hitter with more PA has more opportunities to accrue more batting runs.

For example, if Hitter A has 600 PA and Hitter B has 500 PA, but both guys were 25% better than the the league average hitter, should they have the same total number of batting runs? Of course not! Player A has 20% more opportunities and would accrue 20% more batting runs. So why would you expect it to play out differently on defense?

That defensive opportunities are distributed differently than offensive ones doesn't make them wrong. It just makes it that much more important to play your best defenders at the spots where the greatest amount of defensive value can be produced. Just like it's silly to bat your best hitter 5th, it would be silly to play your best defender at 3B.

Of course, this is all in the context of tallying up production. If you want to start trying to look at which defenders are the most skilled, the most talented, I can see your point about needing to account for the difference in the number of opportunities they've each had, as the SS has had more opportunities.

[757690]

I am absolutely OK with that and am not quite sure why you're not.

We're not rating their abilities in the abstract sense, we're measuring their actual performance.

We're not talking about 10 generic "points" of defensive ability. We're talking runs worth of production.

Each player had a different set of opportunities and they get credit accordingly.

If one hitter had 600 PA and another had 500 PA, but both guys were 25% better than the the average hitter, should they have the same total number of batting runs? Of course not! So why would you expect it to play out that way on defense?

We calculate the 600 PA guy's batting runs one PA a time and add them up, leaving him with a total number of batting runs based on what he did relative to what a league average hitter does in 600 PA. We do the same with the 500 PA guy. And if they both hit the same way, at the end of the day, the 600 PA guy is going to have 20% more batting runs.

That defensive opportunities are distributed differently than offensive ones doesn't make them wrong. It just makes it that much more important to play your best defenders at the spots where the greatest amount of defensive value can be produced. Just like it's silly to bat your best hitter 5th, it would be silly to play your best defender at 3B.

Only we don't add any adjustment to the player's offense numbers.

I understand that a SS is more valuable defensivley than a 3B. The issue is how much more impoartant.

Again, this extra bump doesn't exist for players who are average or below average defensively. But it does exist for those who are above average. To me that's an issue,

[757690]

Secondly, you actually pulled a bit of a bait & switch, accidentally I imagine.

This: "a SS has 25% more range than the average SS"..."3B has the same 25% more range than the average 3B" is NOT the same thing as this: "the SS who has the same skill level as the 3B". In the original situation you described, the SS is a more skilled defender in absolute terms than the 3B, because the average SS is more skilled than the average 3B. In the second situation, they are equally skilled. This is one of the things that makes measuring defense different. With hitters, a PA is a PA, everybody can get compared to the same "average Hitter". But with fielding, you have different subsets of people fielding different subsets of unique opportunities. So you have to first compare to just the guys at the position and then you have to adjust for the positional average being better or worse than the league average. But you say you get this part; I believe you.

It's not a bait and switch.

Look at it this way.

A 3B who is 25% better than average should not have the same UZR as a SS who is 25% better than average... And the positional adjustment should account for all of that. It does account for all of that with average and below average fielders. For above average fielders, both the positional adjustment and the extra balls a SS fields is accounted for. So above average range SS, gets a boost twice, which means above average SS, are overvalued by WAR.

[RedsManRick]

Only we don't add any adjustment to the player's offense numbers.

I understand that a SS is more valuable defensivley than a 3B. The issue is how much more impoartant.

Again, this extra bump doesn't exist for players who are average or below average defensively. But it does exist for those who are above average. To me that's an issue,

I'm sorry, but I really don't understand the claim you're making in the bolded part. There's no special "extra bump" being made for anybody based on their skill level. The bump you seem to be referring to isn't an arbitrary "bump" being given to good fielders based on SS being special, or harder, or anything. It's simply a function of the nature of the position resulting in their being more opportunities for defensive production.

The net result scales in both directions. A range limited SS is going to have more plays missed than the a similarly ranged limited 3B for the exact same reason -- more opportunities to make (or not make) those plays.

We don't have to adjust players offensive numbers because for the purposes of measuring batting runs, all PA are created equal. A PA for the #2 hitter has the same run potential as a PA for the #7. There's no offensive version of specific opportunities that only some hitters get like there is with balls batted on a certain vector, height and velocity. RF get a completely different set of defensive opportunities than 3B on defense. They get the same set of offensive opportunities when hitting. Thus, no adjustment is needed.

The funny thing with defense though is that you can move guys around to minimize how much they suck. It's the equivalent of batting your worst hitters at the bottom of the lineup. Only the difference there is what, 100 plate appearances and thus ~20% more or less opportunity for production? The difference in the amount and run value of the opportunities at SS or CF compared to that of a 1B are quite a bit larger. The result is that it is much easier to "hide" a bad glove than a bad bat. If you stink at hitting, you still have to hit every time through the lineup and each plate appearance affords the same opportunity to produce runs (and thus the same cost of failure). But if you have a lead glove and no range, you can get put over at 1B and you'll never ever have to field a ball in the hole or a liner in the gap and even the defensive opportunities that are similar to those at SS, grounders hit near you, will be significantly less frequent (and easier to convert in to outs since no throw is required).

[jojo]

I can't explain it any more succinctly than this. Hopefully, this is helpful to move the discussion forward.

UZR is a rate stat. The position adjustment should NOT account for chances.

The position adjustment accounts for the relative value of a shortstop and third baseman if they had the SAME number of chances. In other words, the position adjustment allows an apples to apples comparison concerning scarcity. WAR doesn't care if a player has a similar number of defensive chances or a similar number of PA's. It's a stat that tells one the marginal value of a player given his playing time.

Frazier will get fewer defensive chances than Cozart. But you know what? Frazier will get fewer PAs than Choo.

[RedsManRick]

It's not a bait and switch.

Look at it this way.

A 3B who is 25% better than average should not have the same UZR as a SS who is 25% better than average... And the positional adjustment should account for all of that. It does account for all of that with average and below average fielders. For above average fielders, both the positional adjustment and the extra balls a SS fields is accounted for. So above average range SS, gets a boost twice, which means above average SS, are overvalued by WAR.

No. This is wrong. There are always two sources of difference. The difference between the defender and his positional average. And the difference between the positional average and the average generic defender (e.g. what the positional average would be if all position players played that position).

The positional adjustment is the same regardless of the quality of the fielders involved. The positional adjustment does not account for the difference in the number of opportunities. It accounts for the difference in the ability of the players who tend to play that position. It accounts for the problem of SS being compared to a different group of players than 3B.

When we look at the rate at which a given defensive play is made, we are inherently looking at the rate at which that play is made by a subset of defenders who have been selected based on their skill level to have that opportunity. We can't compare how frequently Zack Cozart fields a ball in the hole to how often Albert Pujols makes that play. Players' of Pujols' general skill level never are asked to field those balls because they are stuck over at 1B -- the only guys who field those balls are the subset of guys who are asked to play to SS. And that is a group who is more skilled than the average defender. The positional adjustment is there to account for this problem of having different positional baseline comparison groups. By adding a positional adjustment, you can compare Zack Cozart not just to other SS, but to the average of the entire pool of other fielders at every (non-catcher/pitcher) position.

But with hitters, everybody hits. And when they hit, they face the same conditions. There's nothing inherently different about a PA for the #3 hitter than one for the #7 hitter. Both are facing the same pitcher, the same conditions, the same set of pitches, etc. On net, it's the same kind of opportunity. 500 PA provide the same opportunity for production, the same level of difficulty, the same challenge whether you accrue them batting 3rd or batting 7th. Bat a typical #3 hitter in the 7 hole and he's going to put up the same batter outcomes. No adjustment necessary. So when analyze hitting production, we can easily compare any given hitter to the average of the entire pool of other hitters.

[757690]

Let me try one more way to explain it.

Lets say Zack Cozart plays four seasons. 2 as SS, 2 as 3B.

In his first year as a SS and a 3B, he plays with average range. Now assume he's league average in everything else, this is how his WAR would look in each year:

Season 1: Average SS - +.7 WAR
Season 2: Average 3B - +.2 WAR

The +.7 and +.2 are his positional adjustments.

Now he plays a season at each position, but this time, he has 25% more range than the average SS or 3B. His WAR would be:

Season 3 SS Above Average - +2.7
Season 4 3B Above Average - +1.2

He gets the +.7 and +.2 for positional adjustment, but he gets also gets 1 more WAR at SS, because his zone is bigger and he can get to 10 more balls out of his zone.

So the issue I have is, that the difference in value between Cozart as a SS and Cozart at 3B should be the same whether he's average, or above average. That .5 difference should stay the same, if he improves the same, whether he's playing SS or 3B.