How many games does it take to accurately determine a player's UZR/150 defensive rating?

Question: How many games does it take to accurately determine a player's UZR/150 defensive rating? (Link to explanation of of UZR and UZR/150)?

Why I asked the question: In The Hardball Times 2009 Baseball Annual, Coco Crisp was given a defensive grade of F-. It seems that he was not the worst possible center fielder and his ranking was unfair. I need to find out how close a single season's value corresponds to a player's lifetime value.

Analysis: For the study, I needed to find at what levels are seasonal UZR/150 reflective of lifetime skills. I chose to use the data for the 43 Center Fielders who had a combined 1000 innings played in center field since 2004 (year that UZR/150 goes back to). This data was obtained from wwwl.FanGraphs.com.

Note on Data: I wished to increase the sample size, but being able only being able to copy and paste each player's stats, so I limited the scope on this initial look. Also the data only goes back to 2004 for UZR and it is only divided into single season data. I understand that there is some definite issue about lack and quality of the data, but I feel I used the best that is available.

For these 43 players, I wanted to compare the player's available lifetime UZR/150 to the UZR/150 the player had for each year. I used standard deviation to compare the difference of the two values. I also divided the data for the number of games played in a season. From the research I got the following results:

Minimum Games Played	Minimum Innings Played	Standard Deviation
0	0	19.98
25	225	6.56
50	450	5.95
75	675	5.81
100	900	5.24
125	1125	5.36
150	1350	6.45

So generally, a 66% (1 standard deviation measure that value that 66% of all available values fall in) of all players will have have their UZR/150 vary from 0 to 6 runs while 95% of all players will have their UZR/150 vary from ~ 0 to 12 runs.

Also I looked at how a player's lifetime UZR1/150 compares to the UZR/150 at each time in the player's career. Again I used standard deviation to measure the variation:

Minimum Games Played	Minimum Innings Played	Standard Deviation
0	0	22.92
50	450	3.45
100	900	3.07
150	1350	2.65
200	1800	2.78
250	2250	2.74
300	2700	2.14
350	3150	2.09
400	3600	1.88
450	4050	1.67
500	4500	1.39
550	4950	1.18
600	5400	1.05
650	5850	0.80
700	6300	0.60
750	6750	0.76

As you can see, over a player's career they get within 2 points of their final UZR/150 within 400 games or ~3 years of time. The reason these numbers have less variation vice the yearly data is that with so few of years worth of data, and with some players only having a couple years in majors, the final value me be closer to the current value.

To make sure the previous data isn't too far off, I took the 24 players that had 5 or more years in center field and compared their UZR average from the first 3 years to the their final. They had a standard deviation of 2.62 runs over 1028 innings which compares close to the preceding graph.

Next, I need to find how UZR/150 changed as the players aged. I grouped the players depending on their age and got the following information:

Age	UZR/150
22	0.02
23	-0.06
24	0.48
25	0.97
26	0.92
27	0.01
28	1.08
29	0.64
30	0.54
31	-0.06
32	0.00
33	-0.62
34	-0.22
35+	-0.88

It seems that defensive the center fielders peak between the ages of 25 and 28 (not sure what they are doing in their 27^th year) and seem to decline to the league average at the age 31. Not great information here, there does seem to be an ~2 point swing in UZR/150 over a player's career.

Finally, did Coco deserve better than his F- ranking. To begin with her is a look at Coco's available defensive stats over the years he has played center field:

Season	Team	Position	Innings	Lifetime Games	UZR	UZR/150	Lifetime total UZR	Lifetime UZR/150
2002	Indians	CF	269	30	-0.2	-1	-0.2	-1
2003	Indians	CF	462	81	-2.2	-6.43	-2.4	-4.43
2004	Indians	CF	807	171	6.6	11.04	4.2	3.69
2005	Indians	CF	79	180	-1.7	-28.98	2.5	2.09
2006	Red Sox	CF	900	280	0	0	2.5	1.34
2007	Red Sox	CF	1216	415	22	24.42	24.5	8.86
2008	Red Sox	CF	886	513	-8.9	-13.56	15.6	4.56
Totals			4620		15.6

Since the data in the annual was base on just the 2008 season, his score of -13.56 corresponds to their grade of F- . The problem is that 1 year's worth of data is not enough to determine how well a player plays defense over his career. Coco's defensive numbers have been all over the place over his career (much more then the average center fielder), but his lifetime value of 4.56 for UZR/150 pretty close to his ability (average center fielder – Grade: C). In 2008 he was about 18 runs off his lifetime average, which is about 3 standard deviations (18/3) off. Only 5% of all players will vary is much in a season, but it is not totally out of the norm. In my opinion a respectable publication like the Hardball Times should included, besides the seasonal defensive grade, is a lifetime or 3-year grade.