Adapt dynamic question difficulty to learner Elo

2026-07-23 16:18:44 -05:00
parent 5b5741de37
commit fae38d2ded
13 changed files with 519 additions and 33 deletions
@@ -0,0 +1,69 @@
+using QuestionsApi.Models;
+
+namespace QuestionsApi.Services;
+
+public static class DynamicDifficultyPolicy
+{
+    public const int MinimumElo = 600;
+    public const int MaximumElo = 1800;
+    public const int TargetOffset = 70;
+    public static readonly IReadOnlyDictionary<string, int> TierElos =
+        new Dictionary<string, int>(StringComparer.Ordinal)
+        {
+            ["foundation"] = 850,
+            ["standard"] = 1050,
+            ["advanced"] = 1250,
+            ["expert"] = 1450
+        };
+
+    public static int EffectiveAbility(
+        int overallElo,
+        int categoryElo,
+        DynamicObjectiveMastery? objective)
+    {
+        var bankAbility = (int)Math.Round((overallElo + categoryElo) / 2.0);
+        if (objective is null || objective.Attempts <= 0)
+            return Clamp(bankAbility);
+        var objectiveWeight = Math.Min(0.8, objective.Attempts * 0.08);
+        return Clamp((int)Math.Round(bankAbility * (1.0 - objectiveWeight) + objective.Elo * objectiveWeight));
+    }
+
+    public static int TargetFamilyElo(int effectiveAbility) => Clamp(effectiveAbility - TargetOffset);
+
+    public static double ExpectedScore(int playerElo, int familyElo) =>
+        1.0 / (1.0 + Math.Pow(10, (familyElo - playerElo) / 400.0));
+
+    public static int LearnerDelta(int playerElo, int familyElo, bool correct, int attempts) =>
+        (int)Math.Round((attempts < 5 ? 40 : 24)
+            * ((correct ? 1.0 : 0.0) - ExpectedScore(playerElo, familyElo)));
+
+    public static int FamilyDelta(int playerElo, int familyElo, bool correct, int attempts) =>
+        (int)Math.Round((attempts < 20 ? 32 : 24)
+            * (ExpectedScore(playerElo, familyElo) - (correct ? 1.0 : 0.0)));
+
+    public static DynamicCaseFamily SelectFamily(
+        IReadOnlyList<DynamicCaseFamily> families,
+        IReadOnlyDictionary<string, DynamicFamilyRating> ratings,
+        int targetElo,
+        ISet<string> recentFamilyIds,
+        int tieBreaker)
+    {
+        if (families.Count == 0) throw new InvalidOperationException("No case families are available.");
+        var eligible = families.Where(value => !recentFamilyIds.Contains(value.Id)).ToList();
+        if (eligible.Count == 0) eligible = families.ToList();
+        var ranked = eligible
+            .Select(value => new
+            {
+                Family = value,
+                Elo = ratings.TryGetValue(value.Id, out var rating) ? rating.Elo : value.NominalElo
+            })
+            .OrderBy(value => Math.Abs(value.Elo - targetElo))
+            .ThenBy(value => value.Family.Id, StringComparer.Ordinal)
+            .ToList();
+        var bestDistance = Math.Abs(ranked[0].Elo - targetElo);
+        var tied = ranked.Where(value => Math.Abs(value.Elo - targetElo) == bestDistance).ToList();
+        return tied[Math.Abs(tieBreaker) % tied.Count].Family;
+    }
+
+    public static int Clamp(int elo) => Math.Clamp(elo, MinimumElo, MaximumElo);
+}