Update UCI_Elo parameterization

vondele · vondele · commit a08b8d4e9711 · 2023-01-22T10:54:15.000+01:00
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 % ``` closes #4341 No functional change.
diff --git a/README.md b/README.md
@@ -102,7 +102,7 @@ change them via a chess GUI. This is a list of available UCI options in Stockfis
 
   * #### UCI_Elo
     If enabled by UCI_LimitStrength, aim for an engine strength of the given Elo.
-    This Elo rating has been calibrated at a time control of 60s+0.6s and anchored to CCRL 40/4.
+    This Elo rating has been calibrated at a time control of 120s+1.0s and anchored to +- 100 Elo to CCRL Blitz.
 
   * #### Skill Level
     Lower the Skill Level in order to make Stockfish play weaker (see also UCI_LimitStrength).
diff --git a/src/search.cpp b/src/search.cpp
@@ -96,7 +96,10 @@ namespace {
   struct Skill {
     Skill(int skill_level, int uci_elo) {
         if (uci_elo)
-            level = std::clamp(std::pow((uci_elo - 1346.6) / 143.4, 1 / 0.806), 0.0, 20.0);
+        {
+            double e = double(uci_elo - 1320) / (3190 - 1320);
+            level = std::clamp((((37.2473 * e - 40.8525) * e + 22.2943) * e - 0.311438), 0.0, 19.0);
+        }
         else
             level = double(skill_level);
     }
diff --git a/src/ucioption.cpp b/src/ucioption.cpp
@@ -73,7 +73,7 @@ void init(OptionsMap& o) {
   o["UCI_Chess960"]          << Option(false);
   o["UCI_AnalyseMode"]       << Option(false);
   o["UCI_LimitStrength"]     << Option(false);
-  o["UCI_Elo"]               << Option(1350, 1350, 2850);
+  o["UCI_Elo"]               << Option(1320, 1320, 3190);
   o["UCI_ShowWDL"]           << Option(false);
   o["SyzygyPath"]            << Option("<empty>", on_tb_path);
   o["SyzygyProbeDepth"]      << Option(1, 1, 100);
