Re: Luck Metric
I'm not sure I fully understand. Are you trying to adjust the results of your play? For example, if you lost money over the 4,958 hands, but discovered that your luck had been extremely bad you wouldn't worry as much as if your luck had been good over the interval. Is this the kind of thing you want to do?
In that case it makes some sense to me, although obviously you'd need to choose more metrics than just pairs flopping sets. Your basic calculation is reasonable, although you could get there more simply using a Normal approxmation.
When you have a pair, you should flop a set or better 144 times out of 1,225 (a bit less than 1 in 8). Out of 288 pairs, you should have 33.85 sets. The standard deviation of that is 5.47, so your 28 was 1.07 standard deviations below the mean. The probability of this is 0.16 (not the 0.087 you computed using 1/8). There's no reason to divide by 0.54, you can just regard the probability as a number between 0 and 1 with 0.5 meaning average luck.
The measure is definitely not linear. 0.07 difference between 0.54 and 0.47 costs you one set, from 34 to 33. The same 0.07 gets you from 20 sets to 0, which would cost you a lot more money.
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