The Analysis:

Instead of rating players on a standard-deviation based system, I thought I'd try a percentile system. Also, I like the percentile-based rating system better than the standard-deviation based one for the following reason.:

Anyone who knows even a glimmering of stats can take one look at the standard-deviation themselves and construct a +/- SD chart. The percentile chart isn't quite as obvious, but it is easier to understand. I have left the Mean / Standard-Deviation / Range information for anyone interested.

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 T H E   S T A T S
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Number of cases (games): 443
Average score: 75.621 (76)
Standard deviation: 33.597 (34)
Range of scores: 9 to 176 (out of 200)

If your score ranks between the 30th and 35th percentile, that means you did better than 30% to 35% of surveyed pool players.

Given the wide range of scores in this survey, I'd say we've got everybody from the most abject beginner (with scores like 9 and 12 out of 200) to near world class players (with scores like 170 and 179). The top 16 players on the pro tour would probably regularly score between 180 and 200. (This is my guess. I've never seen Johnny Archer or Efren Reyes play Equal Offense.)

	You're probably better than 	 	if your typical 
        THIS percentage of pool players         score is
	-------------------------------		--------
				 5%		25
				10%		35
				15%		41
				20%		47
				25%		51
				30%		55
				35%		59
				40%		64
				45%		68
				50%		71
				55%		76
				60%		80
				65%		85
				70%		91
				75%		98
				80%		106
				85%		114
				90%		125
				95%		136
				99%		160

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I N T E R P R E T A T I O N
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So if a person regular scores, say, 80 to 85, why is that happening? Are they getting 5 scores of 15 or better and five lousy racks where they can't get past the first two shots? Or are they scoring 7 to 9 every inning?

Further analysis of the data offers these insights:

1) It doesn't seem that people tend to do better or worse on any particular inning. Repeated measures analysis of variance, using the ten innings as the ten repeated measures, supports this conclusion.

2) Curve-fitting regression models support the hypothesis that there is a polynomial relationship between a person's average score per inning and how much their scores vary from inning to inning. Specifically, people whose average inning scores are quite low (say, below 6) tend to do quite poorly on all ten innings. People who are averaging in the middle ranges have scores all over the map: they'll score 3, then 13, then 5, then 10, then 1, then 9, and so forth. People with high averages (say, 12 or more) tend to be pretty consistent, and so their variance is low, but not as low as people at the other end of the skill spectrum. People averageing 12 or better (or thereabouts) tend to have three or four really good innings, and then they have a dud.

Here are made-up examples of the phenomenon I'm describing:

	Below-average player: 1, 4, 3, 7, 1, 2, 4, 3, 5, 3
	Note how all the scores are quite low.

	Average player: 10, 4, 12, 7, 15, 3, 16, 4, 8, 15
	Here, there is quite a mix of high and low scores.

	Above-average player: 14, 20, 18, 6, 14, 15, 12, 20, 1, 20
	Here, 8 of 10 scores are very good, but two innings were duds. 
 	Bad innings happen--it's the nature of Equal Offense.