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BGonline.org Forums
Match Winning Chances per Elo formula
Posted By: Daniel Murphy
Date: Friday, 14 May 2010, at 7:53 p.m.
With reference to the lengthy thread originally titled "Article on "Mr. Bridge" Mentions Backgammon and Poker" and to the thread discussing the relationship between ELO and error rates, and the relationship between ELO and skill levels in backgammon:
This table shows the favorite's Match Winning Chances, with a given ELO rating advantage, at various match lengths, as predicted by the most commonly used rating formula (the one used on FIBS, other online servers, and live-action ranking systems).1
+ELO 1 2 3 5 7 9 11 13 15 17 25 50 51.44 52.03 52.49 53.21 53.80 54.31 54.76 55.17 55.55 55.91 57.15 100 52.88 54.06 54.97 56.40 57.56 58.44 59.43 60.23 60.97 61.65 64.01 200 55.73 58.07 59.84 62.59 64.78 66.61 68.22 69.64 70.93 72.10 75.97 300 58.55 61.97 64.53 68.40 71.38 73.81 75.87 77.65 79.21 80.60 84.90 400 61.31 65.73 68.95 73.69 77.18 79.92 82.16 84.03 85.61 86.98 90.91 500 64.01 69.30 73.05 78.37 82.10 84.90 87.09 88.85 90.29 91.48 94.68 600 66.61 72.65 76.79 82.41 86.15 88.82 90.81 92.35 93.56 94.52 96.93 700 69.12 75.76 80.15 85.84 89.40 91.82 93.54 94.81 95.78 96.52 98.25 800 71.53 78.63 83.14 88.69 91.96 94.06 95.50 96.51 97.25 97.81 99.01 900 73.81 81.24 85.75 91.03 93.94 95.72 96.88 97.67 98.22 98.62 99.44 1000 75.97 83.59 88.02 92.92 95.46 96.93 97.85 98.45 98.86 99.14 99.68 Footnote 1I believe that GamesGrid (and hence Gridgammon?) made an adjustment in the formula for 1-point and/or 2-point matches.
What's a beginning backgammon player's rating? No idea. Much higher, I'd think, after two hours of practice ;- For what it's worth, in the DBgF rating system, the all-time max/min ratings have been approx. 1330 and 600 with an entry point of 1000. That is, 1830 and 1100, with an entry point of 1500. That's about a three and one-half skill level spread, if +-200 ELO is one level. Of course, the 600 player was not a beginner. He was very experienced, but not very good. The current spread on the Gridgammon ranking list is from the highest rated 2044 to the second lowest rated 1012 -- about five skill levels. The lowest rating is 584. I've no idea if that's a legitimately earned rating.
"It's time I start getting paid for lessons, I think."
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