Overall Luck Bell Curve disagrees with Flopped Sets Report

[skyjo]

The amount of luck shown in my Overall Luck Bell Curve does not seem to match my observed results, unless I am misunderstanding something. Below is my bell curve:

Bell Curve.png

Overall Luck Bell Curve

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Note that I am nearly two standard deviations above average when it comes to flopping sets. Here are my observed results, as shown in the Flopped Sets report created by kraada (well I guess created by AlonAlbert but upadted for use in PT4 by kraada).

Flopped Sets.PNG

Flopped Sets Report

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I have been dealt a pocket pair 1,410 times, and flopped a set 172 times. I think this is less than one standard deviation above average.

The probability of flopping a set (counting quads and boats) is: 1 - (48/50) * (47/49) * (46/48) = 0.117551. If I have been dealt a pocket pair 1,410 times, my expected number of sets is 1410 * 0.117551 = 165.7. The standard deviation for a binomial distribution is: sqrt( n * p * (1 - p)). Setting n=1410 and p=0.117551, the SD = 12.1. This means the 1 SD bounds should be 165.7 +/- 12.1 = (153.6, 177.8). My observed number of flopped sets (172) is within these bounds.

Why does bell curve show me as nearly 2 SD above average?

Thanks!

[Flag_Hippo]

The 'Flopped Sets' statistic in that report doesn't include full houses or four of a kind so you will need to add those to your calculations. You can manually get the figures you need using filters, by editing the existing custom statistic or downloading and importing the 'Pocket Pair Hit Flop' PokerTracker 3 report from the Download Warehouse.