Elo rating table

Here’s a table that explains what Elo ratings mean. To find out the chance that one bot will beat another, subtract their Elo ratings and look up the difference in the table. Iron is rated 2081 and Wulibot is rated 1871. The difference is 210—look it up in the table!

The probability estimate is not perfect, but it is good on average.

rating diff	win %	rating diff	win %	rating diff	win %	rating diff	win %
0	50%	200	76%	400	91%	600	97%
10	51%	210	77%	410	91%	610	97%
20	53%	220	78%	420	92%	620	97%
30	54%	230	79%	430	92%	630	97%
40	56%	240	80%	440	93%	640	98%
50	57%	250	81%	450	93%	650	98%
60	59%	260	82%	460	93%	660	98%
70	60%	270	83%	470	94%	670	98%
80	61%	280	83%	480	94%	680	98%
90	63%	290	84%	490	94%	690	98%
100	64%	300	85%	500	95%	700	98%
110	65%	310	86%	510	95%	710	98%
120	67%	320	86%	520	95%	720	98%
130	68%	330	87%	530	95%	730	99%
140	69%	340	88%	540	96%	740	99%
150	70%	350	88%	550	96%	750	99%
160	72%	360	89%	560	96%	760	99%
170	73%	370	89%	570	96%	770	99%
180	74%	380	90%	580	97%	780	99%
190	75%	390	90%	590	97%	790	99%
200	76%	400	91%	600	97%	800	99%

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Comments

krasi0 on Friday, September 30. 2016:

In the case of bots playing the percentages are expected to be even more accurate since bots never get sick or tired which in the case of human players might affect their performance. OTOH, some bots like to experiment with more than one BO, so you never know what's going to happen.

imp on Friday, September 30. 2016:

when reasoning about average win percentage effects like humans being sick do not distort the rating, because a human who is more likely to be sick actually should have a lower rating.
Translating to bots, as long as a bot experiments with more than one BO consistently (and won't alter the likelihood to do so based on learning), then it will also yield the correct rating.
For humans and for bots holds: the average elo rating does not reflect the true average strength only when the subject is currently in a phase of improvement or getting worse. In theory a player can take advantage of this fact by mostly playing against declining players and avoiding rising players.

Jay Scott on Saturday, October 1. 2016:

What you say is mathematically true, given enough data and a small enough K factor in the Elo formula, neither of which is the case in reality. :-) Even so, real ratings are quite accurate on average.

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rating diff	win %	rating diff	win %	rating diff	win %	rating diff	win %
0	50%	200	76%	400	91%	600	97%
10	51%	210	77%	410	91%	610	97%
20	53%	220	78%	420	92%	620	97%
30	54%	230	79%	430	92%	630	97%
40	56%	240	80%	440	93%	640	98%
50	57%	250	81%	450	93%	650	98%
60	59%	260	82%	460	93%	660	98%
70	60%	270	83%	470	94%	670	98%
80	61%	280	83%	480	94%	680	98%
90	63%	290	84%	490	94%	690	98%
100	64%	300	85%	500	95%	700	98%
110	65%	310	86%	510	95%	710	98%
120	67%	320	86%	520	95%	720	98%
130	68%	330	87%	530	95%	730	99%
140	69%	340	88%	540	96%	740	99%
150	70%	350	88%	550	96%	750	99%
160	72%	360	89%	560	96%	760	99%
170	73%	370	89%	570	96%	770	99%
180	74%	380	90%	580	97%	780	99%
190	75%	390	90%	590	97%	790	99%
200	76%	400	91%	600	97%	800	99%

rating diff	win %	rating diff	win %	rating diff	win %	rating diff	win %
0	50%	200	76%	400	91%	600	97%
10	51%	210	77%	410	91%	610	97%
20	53%	220	78%	420	92%	620	97%
30	54%	230	79%	430	92%	630	97%
40	56%	240	80%	440	93%	640	98%
50	57%	250	81%	450	93%	650	98%
60	59%	260	82%	460	93%	660	98%
70	60%	270	83%	470	94%	670	98%
80	61%	280	83%	480	94%	680	98%
90	63%	290	84%	490	94%	690	98%
100	64%	300	85%	500	95%	700	98%
110	65%	310	86%	510	95%	710	98%
120	67%	320	86%	520	95%	720	98%
130	68%	330	87%	530	95%	730	99%
140	69%	340	88%	540	96%	740	99%
150	70%	350	88%	550	96%	750	99%
160	72%	360	89%	560	96%	760	99%
170	73%	370	89%	570	96%	770	99%
180	74%	380	90%	580	97%	780	99%
190	75%	390	90%	590	97%	790	99%
200	76%	400	91%	600	97%	800	99%

rating diff	win %	rating diff	win %	rating diff	win %	rating diff	win %
0	50%	200	76%	400	91%	600	97%
10	51%	210	77%	410	91%	610	97%
20	53%	220	78%	420	92%	620	97%
30	54%	230	79%	430	92%	630	97%
40	56%	240	80%	440	93%	640	98%
50	57%	250	81%	450	93%	650	98%
60	59%	260	82%	460	93%	660	98%
70	60%	270	83%	470	94%	670	98%
80	61%	280	83%	480	94%	680	98%
90	63%	290	84%	490	94%	690	98%
100	64%	300	85%	500	95%	700	98%
110	65%	310	86%	510	95%	710	98%
120	67%	320	86%	520	95%	720	98%
130	68%	330	87%	530	95%	730	99%
140	69%	340	88%	540	96%	740	99%
150	70%	350	88%	550	96%	750	99%
160	72%	360	89%	560	96%	760	99%
170	73%	370	89%	570	96%	770	99%
180	74%	380	90%	580	97%	780	99%
190	75%	390	90%	590	97%	790	99%
200	76%	400	91%	600	97%	800	99%