Rating Histogram Comparisons

   

Table Comparing the Cumulative Histograms of Several Rating Systems

This table compares what rating you need to be in Xth percentile of the players in the four rating systems depicted on the graph.

Cumulative histogram comparison table
Percentile AGA KGS USCF EGF
1% -34.61 -24.26 444 100
2% -32.58 -22.30 531 100
5% -27.69 -19.20 663 153
10% -23.47 -15.36 793 456
20% -18.54 -11.26 964 953
30% -13.91 -8.94 1122 1200
40% -9.90 -7.18 1269 1387
50% -7.10 -5.65 1411 1557
60% -4.59 -4.19 1538 1709
70% -1.85 -2.73 1667 1884
80% 2.10 -1.28 1807 2039
90% 4.71 2.52 1990 2217
95% 6.12 3.88 2124 2339
98% 7.41 5.29 2265 2460
99% 8.15 6.09 2357 2536
99.5% 8.70 7.20 2470 2604
99.9% 9.64 pro 2643 2747
top 10.12 9p 2789 2809

Note: There is an artificial cutoff point at 20k in EGF ratings, which distorts the EGF graph line for 1% and 2%. The 99.9% and top rating for KGS have been estimated as 2850 (8.5 dan amateur) and 3000 (10 dan amateur). The superposition of the Elo (left hand side) and Dan/Kyu (right hand side) scales are based upon EGF assignments. The EGF defines 100 Elo to be 20k.


http://img40.imageshack.us/img40/3637/charto.png

The vertical axis the percentage of players at and below the level indicated along the horizontal axis, a [ext] cumulative distribution function.


http://img522.imageshack.us/img522/6735/ratingcomparisonsg5.png?alignright.png

The image to the right plots the same data in a [ext] cumulative histogram.

Usage Example: You have rating 2000 USCF, and are curious what that is equivalent to in go. Find the point where the USCF graph crosses 2000, which is at about 90%. Then move straight up to see where the other graphs cross that percentile, which is (roughly) 2200 EGF (2 dan), 3 dan KGS and 5 dan AGA.


Source:

The raw data for KGS and USCF ratings are in the form of histogram buckets. I used linear interpolation to get the more accurate numbers. Raw data for AGA and EGF was the entire list, so I simply picked out the Xth percentile player and used that player's rating.

The KGS and AGA ratings are in AGA form.

Related links


Rating Histogram Comparisons last edited by tapir on September 26, 2014 - 19:13
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