Use 2 * beta instead of scaling by total player count.

Fixes #145

Signed-off-by: Vivek Joshy <[email protected]>

openskill/models/weng_lin/bradley_terry_full.py

@@ -839,7 +839,6 @@ def predict_win(self, teams: List[List[BradleyTerryFullRating]]) -> List[float]:
         self._check_teams(teams)
 
         n = len(teams)
-        total_player_count = sum(len(team) for team in teams)
 
         # 2 Player Case
         if n == 2:
@@ -848,11 +847,7 @@ def predict_win(self, teams: List[List[BradleyTerryFullRating]]) -> List[float]:
             b = teams_ratings[1]
             result = phi_major(
                 (a.mu - b.mu)
-                / math.sqrt(
-                    total_player_count * self.beta**2
-                    + a.sigma_squared
-                    + b.sigma_squared
-                )
+                / math.sqrt(2 * self.beta**2 + a.sigma_squared + b.sigma_squared)
             )
             return [result, 1 - result]
 
@@ -866,8 +861,7 @@ def predict_win(self, teams: List[List[BradleyTerryFullRating]]) -> List[float]:
             sigma_b = pair_b_subset[0].sigma_squared
             pairwise_probabilities.append(
                 phi_major(
-                    (mu_a - mu_b)
-                    / math.sqrt(total_player_count * self.beta**2 + sigma_a + sigma_b)
+                    (mu_a - mu_b) / math.sqrt(2 * self.beta**2 + sigma_a + sigma_b)
                 )
             )
 
@@ -912,11 +906,11 @@ def predict_draw(self, teams: List[List[BradleyTerryFullRating]]) -> float:
             pairwise_probabilities.append(
                 phi_major(
                     (draw_margin - mu_a + mu_b)
-                    / math.sqrt(total_player_count * self.beta**2 + sigma_a + sigma_b)
+                    / math.sqrt(2 * self.beta**2 + sigma_a + sigma_b)
                 )
                 - phi_major(
                     (mu_b - mu_a - draw_margin)
-                    / math.sqrt(total_player_count * self.beta**2 + sigma_a + sigma_b)
+                    / math.sqrt(2 * self.beta**2 + sigma_a + sigma_b)
                 )
             )
 
@@ -936,7 +930,6 @@ def predict_rank(
         self._check_teams(teams)
 
         n = len(teams)
-        total_player_count = sum(len(team) for team in teams)
         team_ratings = self._calculate_team_ratings(teams)
 
         win_probabilities = []
@@ -947,7 +940,7 @@ def predict_rank(
                     team_win_probability += phi_major(
                         (team_i.mu - team_j.mu)
                         / math.sqrt(
-                            total_player_count * self.beta**2
+                            2 * self.beta**2
                             + team_i.sigma_squared
                             + team_j.sigma_squared
                         )

openskill/models/weng_lin/bradley_terry_part.py

@@ -847,7 +847,6 @@ def predict_win(self, teams: List[List[BradleyTerryPartRating]]) -> List[float]:
         self._check_teams(teams)
 
         n = len(teams)
-        total_player_count = sum(len(team) for team in teams)
 
         # 2 Player Case
         if n == 2:
@@ -856,11 +855,7 @@ def predict_win(self, teams: List[List[BradleyTerryPartRating]]) -> List[float]:
             b = teams_ratings[1]
             result = phi_major(
                 (a.mu - b.mu)
-                / math.sqrt(
-                    total_player_count * self.beta**2
-                    + a.sigma_squared
-                    + b.sigma_squared
-                )
+                / math.sqrt(2 * self.beta**2 + a.sigma_squared + b.sigma_squared)
             )
             return [result, 1 - result]
 
@@ -874,8 +869,7 @@ def predict_win(self, teams: List[List[BradleyTerryPartRating]]) -> List[float]:
             sigma_b = pair_b_subset[0].sigma_squared
             pairwise_probabilities.append(
                 phi_major(
-                    (mu_a - mu_b)
-                    / math.sqrt(total_player_count * self.beta**2 + sigma_a + sigma_b)
+                    (mu_a - mu_b) / math.sqrt(2 * self.beta**2 + sigma_a + sigma_b)
                 )
             )
 
@@ -920,11 +914,11 @@ def predict_draw(self, teams: List[List[BradleyTerryPartRating]]) -> float:
             pairwise_probabilities.append(
                 phi_major(
                     (draw_margin - mu_a + mu_b)
-                    / math.sqrt(total_player_count * self.beta**2 + sigma_a + sigma_b)
+                    / math.sqrt(2 * self.beta**2 + sigma_a + sigma_b)
                 )
                 - phi_major(
                     (mu_b - mu_a - draw_margin)
-                    / math.sqrt(total_player_count * self.beta**2 + sigma_a + sigma_b)
+                    / math.sqrt(2 * self.beta**2 + sigma_a + sigma_b)
                 )
             )
 
@@ -944,7 +938,6 @@ def predict_rank(
         self._check_teams(teams)
 
         n = len(teams)
-        total_player_count = sum(len(team) for team in teams)
         team_ratings = self._calculate_team_ratings(teams)
 
         win_probabilities = []
@@ -955,7 +948,7 @@ def predict_rank(
                     team_win_probability += phi_major(
                         (team_i.mu - team_j.mu)
                         / math.sqrt(
-                            total_player_count * self.beta**2
+                            2 * self.beta**2
                             + team_i.sigma_squared
                             + team_j.sigma_squared
                         )

openskill/models/weng_lin/plackett_luce.py

@@ -839,7 +839,6 @@ def predict_win(self, teams: List[List[PlackettLuceRating]]) -> List[float]:
         self._check_teams(teams)
 
         n = len(teams)
-        total_player_count = sum(len(team) for team in teams)
 
         # 2 Player Case
         if n == 2:
@@ -848,11 +847,7 @@ def predict_win(self, teams: List[List[PlackettLuceRating]]) -> List[float]:
             b = teams_ratings[1]
             result = phi_major(
                 (a.mu - b.mu)
-                / math.sqrt(
-                    total_player_count * self.beta**2
-                    + a.sigma_squared
-                    + b.sigma_squared
-                )
+                / math.sqrt(2 * self.beta**2 + a.sigma_squared + b.sigma_squared)
             )
             return [result, 1 - result]
 
@@ -866,8 +861,7 @@ def predict_win(self, teams: List[List[PlackettLuceRating]]) -> List[float]:
             sigma_b = pair_b_subset[0].sigma_squared
             pairwise_probabilities.append(
                 phi_major(
-                    (mu_a - mu_b)
-                    / math.sqrt(total_player_count * self.beta**2 + sigma_a + sigma_b)
+                    (mu_a - mu_b) / math.sqrt(2 * self.beta**2 + sigma_a + sigma_b)
                 )
             )
 
@@ -912,11 +906,11 @@ def predict_draw(self, teams: List[List[PlackettLuceRating]]) -> float:
             pairwise_probabilities.append(
                 phi_major(
                     (draw_margin - mu_a + mu_b)
-                    / math.sqrt(total_player_count * self.beta**2 + sigma_a + sigma_b)
+                    / math.sqrt(2 * self.beta**2 + sigma_a + sigma_b)
                 )
                 - phi_major(
                     (mu_b - mu_a - draw_margin)
-                    / math.sqrt(total_player_count * self.beta**2 + sigma_a + sigma_b)
+                    / math.sqrt(2 * self.beta**2 + sigma_a + sigma_b)
                 )
             )
 
@@ -936,7 +930,6 @@ def predict_rank(
         self._check_teams(teams)
 
         n = len(teams)
-        total_player_count = sum(len(team) for team in teams)
         team_ratings = self._calculate_team_ratings(teams)
 
         win_probabilities = []
@@ -947,7 +940,7 @@ def predict_rank(
                     team_win_probability += phi_major(
                         (team_i.mu - team_j.mu)
                         / math.sqrt(
-                            total_player_count * self.beta**2
+                            2 * self.beta**2
                             + team_i.sigma_squared
                             + team_j.sigma_squared
                         )

openskill/models/weng_lin/thurstone_mosteller_full.py

@@ -880,7 +880,6 @@ def predict_win(
         self._check_teams(teams)
 
         n = len(teams)
-        total_player_count = sum(len(team) for team in teams)
 
         # 2 Player Case
         if n == 2:
@@ -889,11 +888,7 @@ def predict_win(
             b = teams_ratings[1]
             result = phi_major(
                 (a.mu - b.mu)
-                / math.sqrt(
-                    total_player_count * self.beta**2
-                    + a.sigma_squared
-                    + b.sigma_squared
-                )
+                / math.sqrt(2 * self.beta**2 + a.sigma_squared + b.sigma_squared)
             )
             return [result, 1 - result]
 
@@ -907,8 +902,7 @@ def predict_win(
             sigma_b = pair_b_subset[0].sigma_squared
             pairwise_probabilities.append(
                 phi_major(
-                    (mu_a - mu_b)
-                    / math.sqrt(total_player_count * self.beta**2 + sigma_a + sigma_b)
+                    (mu_a - mu_b) / math.sqrt(2 * self.beta**2 + sigma_a + sigma_b)
                 )
             )
 
@@ -953,11 +947,11 @@ def predict_draw(self, teams: List[List[ThurstoneMostellerFullRating]]) -> float
             pairwise_probabilities.append(
                 phi_major(
                     (draw_margin - mu_a + mu_b)
-                    / math.sqrt(total_player_count * self.beta**2 + sigma_a + sigma_b)
+                    / math.sqrt(2 * self.beta**2 + sigma_a + sigma_b)
                 )
                 - phi_major(
                     (mu_b - mu_a - draw_margin)
-                    / math.sqrt(total_player_count * self.beta**2 + sigma_a + sigma_b)
+                    / math.sqrt(2 * self.beta**2 + sigma_a + sigma_b)
                 )
             )
 
@@ -989,7 +983,7 @@ def predict_rank(
                     team_win_probability += phi_major(
                         (team_i.mu - team_j.mu)
                         / math.sqrt(
-                            total_player_count * self.beta**2
+                            2 * self.beta**2
                             + team_i.sigma_squared
                             + team_j.sigma_squared
                         )

openskill/models/weng_lin/thurstone_mosteller_part.py

@@ -878,7 +878,6 @@ def predict_win(
         self._check_teams(teams)
 
         n = len(teams)
-        total_player_count = sum(len(team) for team in teams)
 
         # 2 Player Case
         if n == 2:
@@ -887,11 +886,7 @@ def predict_win(
             b = teams_ratings[1]
             result = phi_major(
                 (a.mu - b.mu)
-                / math.sqrt(
-                    total_player_count * self.beta**2
-                    + a.sigma_squared
-                    + b.sigma_squared
-                )
+                / math.sqrt(2 * self.beta**2 + a.sigma_squared + b.sigma_squared)
             )
             return [result, 1 - result]
 
@@ -905,8 +900,7 @@ def predict_win(
             sigma_b = pair_b_subset[0].sigma_squared
             pairwise_probabilities.append(
                 phi_major(
-                    (mu_a - mu_b)
-                    / math.sqrt(total_player_count * self.beta**2 + sigma_a + sigma_b)
+                    (mu_a - mu_b) / math.sqrt(2 * self.beta**2 + sigma_a + sigma_b)
                 )
             )
 
@@ -951,11 +945,11 @@ def predict_draw(self, teams: List[List[ThurstoneMostellerPartRating]]) -> float
             pairwise_probabilities.append(
                 phi_major(
                     (draw_margin - mu_a + mu_b)
-                    / math.sqrt(total_player_count * self.beta**2 + sigma_a + sigma_b)
+                    / math.sqrt(2 * self.beta**2 + sigma_a + sigma_b)
                 )
                 - phi_major(
                     (mu_b - mu_a - draw_margin)
-                    / math.sqrt(total_player_count * self.beta**2 + sigma_a + sigma_b)
+                    / math.sqrt(2 * self.beta**2 + sigma_a + sigma_b)
                 )
             )
 
@@ -975,7 +969,6 @@ def predict_rank(
         self._check_teams(teams)
 
         n = len(teams)
-        total_player_count = sum(len(team) for team in teams)
         team_ratings = self._calculate_team_ratings(teams)
 
         win_probabilities = []
@@ -986,7 +979,7 @@ def predict_rank(
                     team_win_probability += phi_major(
                         (team_i.mu - team_j.mu)
                         / math.sqrt(
-                            total_player_count * self.beta**2
+                            2 * self.beta**2
                             + team_i.sigma_squared
                             + team_j.sigma_squared
                         )

tests/models/weng_lin/test_bradley_terry_full.py

@@ -531,10 +531,10 @@ def test_predict_draw():
     team_2 = [b1, b2]
 
     probability = model.predict_draw(teams=[team_1, team_2])
-    assert probability == pytest.approx(0.1694772, 0.0001)
+    assert probability == pytest.approx(0.1919967, 0.0001)
 
     probability = model.predict_draw(teams=[team_1, team_2, [a1], [a2], [b1]])
-    assert probability == pytest.approx(0.0518253, 0.0001)
+    assert probability == pytest.approx(0.0603735, 0.0001)
 
     probability = model.predict_draw(teams=[[b1], [b1]])
     assert probability == pytest.approx(0.5)

tests/models/weng_lin/test_bradley_terry_part.py

@@ -534,10 +534,10 @@ def test_predict_draw():
     team_2 = [b1, b2]
 
     probability = model.predict_draw(teams=[team_1, team_2])
-    assert probability == pytest.approx(0.1694772, 0.0001)
+    assert probability == pytest.approx(0.1919967, 0.0001)
 
     probability = model.predict_draw(teams=[team_1, team_2, [a1], [a2], [b1]])
-    assert probability == pytest.approx(0.0518253, 0.0001)
+    assert probability == pytest.approx(0.0603735, 0.0001)
 
     probability = model.predict_draw(teams=[[b1], [b1]])
     assert probability == pytest.approx(0.5)

tests/models/weng_lin/test_plackett_luce.py

@@ -529,10 +529,10 @@ def test_predict_draw():
     team_2 = [b1, b2]
 
     probability = model.predict_draw(teams=[team_1, team_2])
-    assert probability == pytest.approx(0.1694772, 0.0001)
+    assert probability == pytest.approx(0.1919967, 0.0001)
 
     probability = model.predict_draw(teams=[team_1, team_2, [a1], [a2], [b1]])
-    assert probability == pytest.approx(0.0518253, 0.0001)
+    assert probability == pytest.approx(0.0603735, 0.0001)
 
     probability = model.predict_draw(teams=[[b1], [b1]])
     assert probability == pytest.approx(0.5)

tests/models/weng_lin/test_thurstone_mosteller_full.py

@@ -538,10 +538,10 @@ def test_predict_draw():
     team_2 = [b1, b2]
 
     probability = model.predict_draw(teams=[team_1, team_2])
-    assert probability == pytest.approx(0.1694772, 0.0001)
+    assert probability == pytest.approx(0.1919967, 0.0001)
 
     probability = model.predict_draw(teams=[team_1, team_2, [a1], [a2], [b1]])
-    assert probability == pytest.approx(0.0518253, 0.0001)
+    assert probability == pytest.approx(0.0603735, 0.0001)
 
     probability = model.predict_draw(teams=[[b1], [b1]])
     assert probability == pytest.approx(0.5)

tests/models/weng_lin/test_thurstone_mosteller_part.py

@@ -542,10 +542,10 @@ def test_predict_draw():
     team_2 = [b1, b2]
 
     probability = model.predict_draw(teams=[team_1, team_2])
-    assert probability == pytest.approx(0.1694772, 0.0001)
+    assert probability == pytest.approx(0.1919967, 0.0001)
 
     probability = model.predict_draw(teams=[team_1, team_2, [a1], [a2], [b1]])
-    assert probability == pytest.approx(0.0518253, 0.0001)
+    assert probability == pytest.approx(0.0603735, 0.0001)
 
     probability = model.predict_draw(teams=[[b1], [b1]])
     assert probability == pytest.approx(0.5)