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Bill,

**WARNING – horribly wonkish**

I pestered a statistics oriented friend (used to be) with this.

But first, I think most, would argue that 10 for 10 IS more accurate than 7 for 7. This is because the probability of being 7 for 7 is 0.781% (1/128) and being 10 for 10 is 0.098% (1/1024).

But is being 9 for 12 (75%) more accurate than being 6 for 8 (75%). It is in my opinion because again the probabilities are 5.42% (222/4096) and 10.94% (28/256) respectively. [5.42% is the probability of being exactly 9 for 12, not 9 for 12 or better].

The adjustment is to turn the accuracy into a score which can be done by dividing the accuracy by the probability of that accuracy.

So for example: 7 for 7 is 100% with a probability of 0.781%
Score=128=1.0/0.0781
The score for 10 for 10 is 100% (1) divided by 0.000976 (1/1024)
Score=1024

OK so this skews really high on the ends - no surprise there. How does it work in the middle?

6.87 = Score for 6 for 8 [0.75/(22/256)]
13.8 = Score for 8 for 12 [0.75/(222/4096)] which is better than 6 for 8.
It works for in between sized portfolios.
The respective accuracy scores for 7 for 10 and 8 for 10 are:
5.97 = [0.7/(120/1024)] - worse than 6 for 8
18.2 = [0.8/(45/1024)] – better than 8 for 12

But it is worth noting that 11 for 12 would be better than 7 for 7 with scores of 321 and 128 respectively. Similarly being 10 for 12 (score=51.7) would be better than 7 for 8 (score 28), despite being a somewhat lower % accuracy.

Thoughts (LOL)?

Zz

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