Update UCI_Elo parameterization #4341
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The old parameterization (https://github.com/official-stockfish/Stockfish/pull/2225/files) has now become quite inaccurate. This updates the formula based on updated results with master. The formula is based on a fit of the Elo results for games played between master at various skill levels, and various versions of the Stash engine, which have been ranked at CCRL. ``` # PLAYER : RATING ERROR POINTS PLAYED (%) 1 master-skill-19 : 3191.1 40.4 940.0 1707 55 2 master-skill-18 : 3170.3 39.3 1343.0 2519 53 3 master-skill-17 : 3141.3 37.8 2282.0 4422 52 4 master-skill-16 : 3111.2 37.1 2773.0 5423 51 5 master-skill-15 : 3069.5 37.2 2728.5 5386 51 6 master-skill-14 : 3024.8 36.1 2702.0 5339 51 7 master-skill-13 : 2972.9 35.4 2645.5 5263 50 8 master-skill-12 : 2923.1 35.0 2653.5 5165 51 9 master-skill-11 : 2855.5 33.6 2524.0 5081 50 10 master-skill-10 : 2788.3 32.0 2724.5 5511 49 11 stash-bot-v25.0 : 2744.0 31.5 1952.5 3840 51 12 master-skill-9 : 2702.8 30.5 2670.0 5018 53 13 master-skill-8 : 2596.2 28.5 2669.5 4975 54 14 stash-bot-v21.0 : 2561.2 30.0 1338.0 3366 40 15 master-skill-7 : 2499.5 28.5 1934.0 4178 46 16 stash-bot-v20.0 : 2452.6 27.7 1606.5 3378 48 17 stash-bot-v19.0 : 2425.3 26.7 1787.0 3365 53 18 master-skill-6 : 2363.2 26.4 2510.5 4379 57 19 stash-bot-v17.0 : 2280.7 25.4 2209.0 4378 50 20 master-skill-5 : 2203.7 25.3 2859.5 5422 53 21 stash-bot-v15.3 : 2200.0 25.4 1757.0 4383 40 22 stash-bot-v14 : 2145.9 25.5 2890.0 5167 56 23 stash-bot-v13 : 2042.7 25.8 2263.5 4363 52 24 stash-bot-v12 : 1963.4 25.8 1769.5 4210 42 25 master-skill-4 : 1922.9 25.9 2690.0 5399 50 26 stash-bot-v11 : 1873.0 26.3 2203.5 4335 51 27 stash-bot-v10 : 1783.8 27.8 2568.5 4301 60 28 master-skill-3 : 1742.3 27.8 1909.5 4439 43 29 master-skill-2 : 1608.4 29.4 2064.5 4389 47 30 stash-bot-v9 : 1582.6 30.2 2130.0 4230 50 31 master-skill-1 : 1467.6 31.3 2015.5 4244 47 32 stash-bot-v8 : 1452.8 31.5 1953.5 3780 52 33 master-skill-0 : 1320.1 32.9 651.5 2083 31 ``` Skill 0 .. 19, now covers CCRL Blitz Elo from 1320 to 3190, approximately. Indeed, the Elo of stash in this analysis is only to within +- 100 Elo of CCRL, probably because it depends quite a bit on the opponent pool. To obtain a skill level for a given Elo number, the above data is fit as a 3rd degree polynomial Skill(Elo). A quick test confirms the correspondence to the above table: ``` Score of master-elo-2721 vs stash-bot-v21.0: 51 - 16 - 19 [0.703] 86 Elo difference: 150.1 +/- 70.2, LOS: 100.0 %, DrawRatio: 22.1 % ``` No functional change.
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This is a graph of the data and fit used to translate Elo in the needed skill level. |
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There isn't even a 100 elo difference between the 4 highest skill levels 😕 |
This has been computed on the 8moves_v3.pgn with 120+1TC, so high draw rate and small Elo differences to be expected at the highest level. |
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The old parameterization (https://github.com/official-stockfish/Stockfish/pull/2225/files) has now become quite inaccurate. This updates the formula based on updated results with master. The formula is based on a fit of the Elo results for games played between master at various skill levels, and various versions of the Stash engine, which have been ranked at CCRL.
Skill 0 .. 19, now covers CCRL Blitz Elo from 1320 to 3190, approximately. Indeed, the Elo of stash in this analysis is only to within +- 100 Elo of CCRL, probably because it depends quite a bit on the opponent pool.
To obtain a skill level for a given Elo number, the above data is fit as a 3rd degree polynomial Skill(Elo). A quick test confirms the correspondence to the above table:
No functional change.