Compute constants once in rate and pass the Env to
PlackettLuce and Util instead of re-deriving it.

Assisted-by: Claude Opus 4.6 via pi

diff --git a/lib/open_skill/plackett_luce.rb b/lib/open_skill/plackett_luce.rb
index 023a9ae..6483d3d 100644
--- a/lib/open_skill/plackett_luce.rb
+++ b/lib/open_skill/plackett_luce.rb
@@ -4,13 +4,11 @@
 
 module OpenSkill
   module PlackettLuce
-    def self.rate(game, **options)
+    def self.rate(game, env, rank: nil)
       return game if game.length <= 1
 
-      epsilon = OpenSkill.constants(**options).epsilon
-
-      team_ratings = Util.team_rating(game, **options)
-      c = Util.util_c(team_ratings, **options)
+      team_ratings = Util.team_rating(game, rank: rank)
+      c = Util.util_c(team_ratings, env)
       sum_q = Util.util_sum_q(team_ratings, c)
       a = Util.util_a(team_ratings)
 
@@ -35,7 +33,7 @@ module OpenSkill
         tr.team.map { |player|
           share = player.sigma**2 / tr.sigma_sq
           new_mu = player.mu + share * omega
-          new_sigma = player.sigma * Math.sqrt([1 - share * delta, epsilon].max)
+          new_sigma = player.sigma * Math.sqrt([1 - share * delta, env.epsilon].max)
           Rating.new(new_mu, new_sigma)
         }
       }
diff --git a/lib/open_skill/rate.rb b/lib/open_skill/rate.rb
index fc43fed..a06fe39 100644
--- a/lib/open_skill/rate.rb
+++ b/lib/open_skill/rate.rb
@@ -24,8 +24,7 @@ module OpenSkill
     ordered_teams = ordered.map(&:first)
     sorted_rank = ordered.map(&:last)
 
-    # rank: flows through PlackettLuce's **options into Util.team_rating
-    new_ratings = PlackettLuce.rate(ordered_teams, rank: sorted_rank, **options)
+    new_ratings = PlackettLuce.rate(ordered_teams, env, rank: sorted_rank)
 
     result = rank.zip(new_ratings).sort_by(&:first).map(&:last)
 
diff --git a/lib/open_skill/util.rb b/lib/open_skill/util.rb
index 47cc5ae..d42666d 100644
--- a/lib/open_skill/util.rb
+++ b/lib/open_skill/util.rb
@@ -30,7 +30,7 @@ module OpenSkill
       [nil, *ranks, nil].each_cons(3).map { |l, _, r| [l, r].compact }
     end
 
-    def self.team_rating(game, rank: nil, **)
+    def self.team_rating(game, rank: nil)
       game.zip(rankings(game, rank)).map { |team, rank|
         TeamRating.new(
           mu: team.sum(&:mu),
@@ -41,9 +41,8 @@ module OpenSkill
       }
     end
 
-    def self.util_c(team_ratings, **)
-      beta_sq = OpenSkill.constants(**).beta_sq
-      Math.sqrt(team_ratings.sum { |tr| tr.sigma_sq + beta_sq })
+    def self.util_c(team_ratings, env)
+      Math.sqrt(team_ratings.sum { |tr| tr.sigma_sq + env.beta_sq })
     end
 
     def self.util_sum_q(team_ratings, c)
diff --git a/test/test_open_skill.rb b/test/test_open_skill.rb
index 8dc63ce..b2fa551 100644
--- a/test/test_open_skill.rb
+++ b/test/test_open_skill.rb
@@ -357,14 +357,14 @@ class TestUtilC < Minitest::Test
     team1 = [r]
     team2 = [r, r]
     team_ratings = OpenSkill::Util.team_rating([team2, team1])
-    c = OpenSkill::Util.util_c(team_ratings)
+    c = OpenSkill::Util.util_c(team_ratings, OpenSkill.constants)
     assert_in_delta 15.590239, c, 0.001
   end
 
   def test_util_c_5v5
     r = OpenSkill.rating
     team_ratings = OpenSkill::Util.team_rating([[r] * 5, [r] * 5])
-    c = OpenSkill::Util.util_c(team_ratings)
+    c = OpenSkill::Util.util_c(team_ratings, OpenSkill.constants)
     assert_in_delta 27.003, c, 0.001
   end
 end
@@ -376,7 +376,7 @@ class TestUtilSumQ < Minitest::Test
     team1 = [r]
     team2 = [r, r]
     team_ratings = OpenSkill::Util.team_rating([team1, team2])
-    c = OpenSkill::Util.util_c(team_ratings)
+    c = OpenSkill::Util.util_c(team_ratings, OpenSkill.constants)
     sum_q = OpenSkill::Util.util_sum_q(team_ratings, c)
     assert_equal [29.67892702634643, 24.70819334370875], sum_q
   end
@@ -384,7 +384,7 @@ class TestUtilSumQ < Minitest::Test
   def test_util_sum_q_5v5
     r = OpenSkill.rating
     team_ratings = OpenSkill::Util.team_rating([[r] * 5, [r] * 5])
-    c = OpenSkill::Util.util_c(team_ratings)
+    c = OpenSkill::Util.util_c(team_ratings, OpenSkill.constants)
     sum_q = OpenSkill::Util.util_sum_q(team_ratings, c)
     assert_in_delta 204.84, sum_q[0], 0.01
     assert_in_delta 102.42, sum_q[1], 0.01
@@ -419,20 +419,20 @@ end
 class TestPlackettLuce < Minitest::Test
   def test_solo_game_unchanged
     r = OpenSkill.rating
-    result = OpenSkill::PlackettLuce.rate([[r]])
+    result = OpenSkill::PlackettLuce.rate([[r]], OpenSkill.constants)
     assert_equal [[r]], result
   end
 
   def test_2p_ffa
     r = OpenSkill.rating
-    result = OpenSkill::PlackettLuce.rate([[r], [r]])
+    result = OpenSkill::PlackettLuce.rate([[r], [r]], OpenSkill.constants)
     assert_rating 27.63523138347365, 8.065506316323548, result[0][0]
     assert_rating 22.36476861652635, 8.065506316323548, result[1][0]
   end
 
   def test_3p_ffa
     r = OpenSkill.rating
-    result = OpenSkill::PlackettLuce.rate([[r], [r], [r]])
+    result = OpenSkill::PlackettLuce.rate([[r], [r], [r]], OpenSkill.constants)
     assert_rating 27.868876552746237, 8.204837030780652, result[0][0]
     assert_rating 25.717219138186557, 8.057829747583874, result[1][0]
     assert_rating 21.413904309067206, 8.057829747583874, result[2][0]
@@ -440,7 +440,7 @@ class TestPlackettLuce < Minitest::Test
 
   def test_4p_ffa
     r = OpenSkill.rating
-    result = OpenSkill::PlackettLuce.rate([[r], [r], [r], [r]])
+    result = OpenSkill::PlackettLuce.rate([[r], [r], [r], [r]], OpenSkill.constants)
     assert_rating 27.795084971874736, 8.263160757613477, result[0][0]
     assert_rating 26.552824984374855, 8.179213704945203, result[1][0]
     assert_rating 24.68943500312503, 8.083731307186588, result[2][0]
@@ -449,7 +449,7 @@ class TestPlackettLuce < Minitest::Test
 
   def test_5p_ffa
     r = OpenSkill.rating
-    result = OpenSkill::PlackettLuce.rate([[r], [r], [r], [r], [r]])
+    result = OpenSkill::PlackettLuce.rate([[r], [r], [r], [r], [r]], OpenSkill.constants)
     assert_rating 27.666666666666668, 8.290556877154474, result[0][0]
     assert_rating 26.833333333333332, 8.240145629781066, result[1][0]
     assert_rating 25.72222222222222, 8.179996679645559, result[2][0]
@@ -459,7 +459,7 @@ class TestPlackettLuce < Minitest::Test
 
   def test_3_teams_different_sizes
     r = OpenSkill.rating
-    result = OpenSkill::PlackettLuce.rate([[r, r, r], [r], [r, r]])
+    result = OpenSkill::PlackettLuce.rate([[r, r, r], [r], [r, r]], OpenSkill.constants)
     assert_rating 25.939870821784513, 8.247641552260456, result[0][0]
     assert_rating 25.939870821784513, 8.247641552260456, result[0][1]
     assert_rating 25.939870821784513, 8.247641552260456, result[0][2]