LOS Table

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After a tournament between two engines is over one can deduct the likelihood of superiority of one engine over the other by consulting the following table. The first column gives the score difference (wins - losses), the next columns give the LOS for a certain number of games. The table was calculated for a draw ratio of 32%.

Table

	10	50	100	200	500	1000
0	50.00%	50.00%	50.00%	50.00%	50.00%	50.00%
1	64.51%	56.77%	54.81%	53.41%	52.16%	51.53%
2	77.22%	63.34%	59.55%	56.80%	54.32%	53.06%
3	86.95%	69.55%	64.16%	60.14%	56.46%	54.58%
4	93.43%	75.24%	68.57%	63.40%	58.58%	56.09%
5	97.14%	80.32%	72.73%	66.57%	60.68%	57.60%
6	98.95%	84.71%	76.60%	69.63%	62.75%	59.10%
7	99.68%	88.40%	80.14%	72.55%	64.78%	60.58%
8	99.93%	91.41%	83.34%	75.33%	66.77%	62.05%
9	99.99%	93.80%	86.19%	77.96%	68.72%	63.50%
10	100.00%	95.64%	88.69%	80.41%	70.61%	64.93%
11		97.02%	90.85%	82.69%	72.45%	66.34%
12		98.01%	92.68%	84.80%	74.23%	67.73%
13		98.71%	94.23%	86.72%	75.95%	69.09%
14		99.19%	95.50%	88.48%	77.60%	70.43%
15		99.50%	96.54%	90.06%	79.19%	71.74%
16		99.71%	97.37%	91.48%	80.71%	73.02%
17		99.83%	98.03%	92.74%	82.16%	74.27%
18		99.91%	98.55%	93.85%	83.54%	75.49%
19		99.95%	98.94%	94.82%	84.85%	76.68%
20		99.97%	99.24%	95.67%	86.08%	77.84%
21		99.99%	99.46%	96.41%	87.25%	78.96%
22		99.99%	99.62%	97.03%	88.35%	80.05%
23		100.00%	99.74%	97.57%	89.38%	81.11%
24			99.82%	98.02%	90.34%	82.12%
25			99.88%	98.40%	91.23%	83.11%
26			99.92%	98.71%	92.07%	84.06%
27			99.95%	98.97%	92.84%	84.97%
28			99.97%	99.18%	93.55%	85.85%
29			99.98%	99.36%	94.21%	86.69%
30			99.99%	99.50%	94.81%	87.50%
31			99.99%	99.61%	95.36%	88.27%
32			100.00%	99.70%	95.86%	89.01%
33				99.77%	96.32%	89.71%
34				99.82%	96.74%	90.38%
35				99.87%	97.11%	91.02%
36				99.90%	97.45%	91.62%
37				99.93%	97.76%	92.20%
38				99.95%	98.03%	92.74%
39				99.96%	98.28%	93.26%
40				99.97%	98.50%	93.74%
41				99.98%	98.69%	94.20%
42				99.98%	98.86%	94.63%
43				99.99%	99.02%	95.04%
44				99.99%	99.15%	95.42%
45				99.99%	99.27%	95.78%
46				100.00%	99.37%	96.11%
47					99.46%	96.42%
48					99.54%	96.72%
49					99.61%	96.99%
50					99.67%	97.24%
51					99.72%	97.47%
52					99.76%	97.69%
53					99.80%	97.89%
54					99.83%	98.08%
55					99.86%	98.25%
56					99.88%	98.41%
57					99.90%	98.56%
58					99.92%	98.69%
59					99.93%	98.82%
60					99.94%	98.93%
61					99.95%	99.03%
62					99.96%	99.13%
63					99.97%	99.22%
64					99.97%	99.29%
65					99.98%	99.37%
66					99.98%	99.43%
67					99.99%	99.49%
68					99.99%	99.54%
69					99.99%	99.59%
70					99.99%	99.64%
71					99.99%	99.68%
72					100.00%	99.71%
73						99.74%
74						99.77%
75						99.80%
76						99.82%
77						99.84%
78						99.86%
79						99.88%
80						99.89%
81						99.91%
82						99.92%
83						99.93%
84						99.94%
85						99.94%
86						99.95%
87						99.96%
88						99.96%
89						99.97%
90						99.97%
91						99.98%
92						99.98%
93						99.98%
94						99.98%
95						99.99%
96						99.99%
97						99.99%
98						99.99%
99						99.99%
100						99.99%
101						99.99%
102						100.00%

Forum Posts

• Likelihood of superiority by Marco Costalba, CCC, November 15, 2009
• LOS calculation: Does the same result is always the same? by Marco Costalba, CCC, October 01, 2012
• LOS (again) by Ed Schröder, CCC, October 30, 2012
• Fast LOS estimation by Gary, CCC, February 18, 2013
• LOS by BB+, OpenChess Forum, March 31, 2013
• Type I error in LOS based early stopping rule by Kai Laskos, CCC, August 06, 2013

External Links

• Statistical significance from Wikipedia
• p-value from Wikipedia

References

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