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 Originally Posted by MadMojoMonkey
Not only do the units match, but the value is directly cooperative with our mean.
So, if our mean value is 20 with a stdev of 5, then that's easy to immediately read off:
That's 20 +/- 5 @ ~68% CI and 20 +/- 10 @ ~95% CI
Sorry. This part is pretty bad on my part. These numbers assume we're talking about a random variable that follows the normal distribution, which I've repeatedly pointed out is of little-to-no use for us.
However, the fact that +/- 1 stdev is ~68% CI is the constant thing here. The distribution may not be symmetrical with the plusses and minuses. For stats like VPIP and PFR, we would distrust them if they were symmetrical.
If we have 1.01% PFR after 99 hands, and we fold the next hand, then we have 1.00% PFR. However, if we had raised the hand, then we'd have 2.00% PFR.
So a fold causes a change of -0.01%, but a bet yields a change of +0.99%.
If our error bars around the 1.01% were symmetrical, we'd be very suspicious about them. Well, some mathematicians were a while ago, and they figured out some workarounds... like the Wilson Score interval... which gives stable results and is not symmetrical.
So the plusses will be bigger than the minuses for a stat with frequency less than 50%, and vice versa for a stat with freq. greater than 50%.
Only a stat that is exactly 50% will have a symmetrical distribution.
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