Statistical accuracy PP and difficulty scaling for the osu!taiko ruleset

osu.Game.Rulesets.Taiko/Difficulty/TaikoPerformanceAttributes.cs

@@ -20,6 +20,9 @@ public class TaikoPerformanceAttributes : PerformanceAttributes
         [JsonProperty("effective_miss_count")]
         public double EffectiveMissCount { get; set; }
 
+        [JsonProperty("estimated_ur")]
+        public double? EstimatedUR { get; set; }
+
         public override IEnumerable<PerformanceDisplayAttribute> GetAttributesForDisplay()
         {
             foreach (var attribute in base.GetAttributesForDisplay())

osu.Game.Rulesets.Taiko/Difficulty/TaikoPerformanceCalculator.cs

@@ -11,6 +11,7 @@
 using osu.Game.Rulesets.Scoring;
 using osu.Game.Rulesets.Taiko.Objects;
 using osu.Game.Scoring;
+using MathNet.Numerics;
 
 namespace osu.Game.Rulesets.Taiko.Difficulty
 {
@@ -20,7 +21,7 @@ public class TaikoPerformanceCalculator : PerformanceCalculator
         private int countOk;
         private int countMeh;
         private int countMiss;
-        private double accuracy;
+        private double? estimatedDeviation;
 
         private double effectiveMissCount;
 
@@ -37,7 +38,7 @@ protected override PerformanceAttributes CreatePerformanceAttributes(ScoreInfo s
             countOk = score.Statistics.GetValueOrDefault(HitResult.Ok);
             countMeh = score.Statistics.GetValueOrDefault(HitResult.Meh);
             countMiss = score.Statistics.GetValueOrDefault(HitResult.Miss);
-            accuracy = customAccuracy;
+            estimatedDeviation = computeEstimatedDeviation(score, taikoAttributes);
 
             // The effectiveMissCount is calculated by gaining a ratio for totalSuccessfulHits and increasing the miss penalty for shorter object counts lower than 1000.
             if (totalSuccessfulHits > 0)
@@ -64,6 +65,7 @@ protected override PerformanceAttributes CreatePerformanceAttributes(ScoreInfo s
                 Difficulty = difficultyValue,
                 Accuracy = accuracyValue,
                 EffectiveMissCount = effectiveMissCount,
+                EstimatedUR = estimatedDeviation * 10,
                 Total = totalValue
             };
         }
@@ -84,35 +86,52 @@ private double computeDifficultyValue(ScoreInfo score, TaikoDifficultyAttributes
                 difficultyValue *= 1.025;
 
             if (score.Mods.Any(m => m is ModHardRock))
-                difficultyValue *= 1.050;
+                difficultyValue *= 1.10;
 
             if (score.Mods.Any(m => m is ModFlashlight<TaikoHitObject>))
                 difficultyValue *= 1.050 * lengthBonus;
 
-            return difficultyValue * Math.Pow(accuracy, 2.0);
+            if (estimatedDeviation == null)
+                return 0;
+
+            return difficultyValue * Math.Pow(SpecialFunctions.Erf(40 / (Math.Sqrt(2) * (double)estimatedDeviation)), 2.0);
         }
 
         private double computeAccuracyValue(ScoreInfo score, TaikoDifficultyAttributes attributes)
         {
-            if (attributes.GreatHitWindow <= 0)
+            if (attributes.GreatHitWindow <= 0 || estimatedDeviation == null)
                 return 0;
 
-            double accuracyValue = Math.Pow(60.0 / attributes.GreatHitWindow, 1.1) * Math.Pow(accuracy, 8.0) * Math.Pow(attributes.StarRating, 0.4) * 27.0;
+            double accuracyValue = Math.Pow(7.5 / (double)estimatedDeviation, 1.1) * Math.Pow(attributes.StarRating / 2.7, 0.8) * 100.0;
 
             double lengthBonus = Math.Min(1.15, Math.Pow(totalHits / 1500.0, 0.3));
-            accuracyValue *= lengthBonus;
 
             // Slight HDFL Bonus for accuracy. A clamp is used to prevent against negative values
             if (score.Mods.Any(m => m is ModFlashlight<TaikoHitObject>) && score.Mods.Any(m => m is ModHidden))
-                accuracyValue *= Math.Max(1.050, 1.075 * lengthBonus);
+                accuracyValue *= Math.Max(1.0, 1.05 * lengthBonus);
 
             return accuracyValue;
         }
 
+        private double? computeEstimatedDeviation(ScoreInfo score, TaikoDifficultyAttributes attributes)
+        {
+            if (totalHits == 0)
+                return null;
+
+            double greatProbability = 1 - (countOk + countMiss + 1.0) / (totalHits + 1.0);
+
+            if (greatProbability <= 0 || greatProbability >= 1)
+            {
+                return null;
+            }
+
+            double deviation = attributes.GreatHitWindow / (Math.Sqrt(2) * SpecialFunctions.ErfInv(greatProbability));
+
+            return deviation;
+        }
+
         private int totalHits => countGreat + countOk + countMeh + countMiss;
 
         private int totalSuccessfulHits => countGreat + countOk + countMeh;
-
-        private double customAccuracy => totalHits > 0 ? (countGreat * 300 + countOk * 150) / (totalHits * 300.0) : 0;
     }
 }

osu.Game.Rulesets.Taiko/osu.Game.Rulesets.Taiko.csproj

@@ -15,4 +15,8 @@
   <ItemGroup Label="Project References">
     <ProjectReference Include="..\osu.Game\osu.Game.csproj" />
   </ItemGroup>
+
+  <ItemGroup>
+    <PackageReference Include="MathNet.Numerics" Version="5.0.0" />
+  </ItemGroup>
 </Project>