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I don't know what the relative correlations are for every stat.  I know I've read some articles that state uncategorically that UZR has *LESS* correlation than offensive stats.
But, what I do know is that if I look at TEAM rankings by UZR and team rankings by DER -- the DER rankings come up WAY better (eye-balling) than UZR. 
As a rule, stats do not get MORE accurate the smaller the samples -- so I begin looking for how stats behave on the largest samples, (team level).  DER kicks UZRs butt. 
In 2009, UZR had the Dodgers ranked 14th and Cubs ranked 20th in UZR.  DER had them at 1st and 5th.  The Dodgers wer #1 in ALL OF BASEBALL, allowing only 611 runs.  In fairness, they had great pitching, too.  But 134 extra strikeouts should NOT result in 160 fewer hits.  We know that roughly 70% of BIPs turn into outs -- so 134 Ks should prevent (roughly) 40 outs.  The Dodger DEFENSE prevented 120 more hits than the average team - yet UZR has the TEAM at dead average. 
The Cubs, with identical Ks, allowed 64 more hits than the Dodgers, but that's still 96 hits under average (for the NL).  Adjusting for Ks -- we still end up with 56 fewer hits than average allowed - and the Cubbies end up 20th in the majors in UZR?!? 
I'm more concerned about the accuracy of what is being measured during a specific year BEFORE I concern myself with looking at how it does over multiple years. 
What UZR measures "may be" useful info - with reasonable correlation.  My position is it at best only peripherally measures actual run prevention.  Of course, one of the biggest headaches with defensive stats is that while the number of hits, walks, (and all offensive stats) are variable each year -- the number of OUTS is a relative constant -- which means that it would be EASILY possible for any defensive stat created to have extreme high correlation - and yet have zero analytical value at all.  (not saying that this is definitely the case with UZR -- just that UZR being useless has ZERO bearing on whether OPS or BA is useful.

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