Quote:
Originally Posted by chazzycat
The 20-80 scale was devised for exactly the reasons you describe - the standard statistical bell curve. 50 is average, and each standard deviation is 10 points. That's why it only goes up to 80, because three standard deviations capture 99.7% of data.
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Using 100% accuracy my potential ratings data looks like this:
98 players at 68+ (blue)
419 players at 53-67 (green)
846 at 43-52 (gold?)
1,559 at 33-42 (orange?)
1,281 at 21-32 (red)
2,000 at 1-20 (red)
This appears to me to be a rough approximation of a one-sided distribution with a mean of zero and a std dev of ~32.
1-20 is 41.3% of my players which correlates to the 40% that would included up to .55 sigma on a 1-sided normalized curve (20/32 = .63; compare to .55)
1-32 is 67.8% which correlates to the 68% that would be up to 1 sigma (32/32 = 1.00 compares to 1.0)
1-42 is 82.5% which correlates to the 80% that would be up to 1.3 sigma (42/32 = 1.31 compares to 1.3)
1-52 is 91.3% which correlates to the 91% that would be up to 1.7 sigma (52/32 = 1.63 compares to 1.7)
1-67 is 98.0% which correlates to the 95.4% that would be up to 2.0 sigma (67/32 = 2.09 compares to 2.0)
1-80 includes outliers that are capped at 80 for display, but are actually rated over 80, so it includes sigma 3.
Moreover, if my assumptions are correct, it might not be entirely coincidental that 1 sigma is where red ends and 2 sigma is where blue begins.
I have not done these kinds of stats in forever, so I'm far from certain, but it appears that way to me.
Thoughts?