Add function to calculate draw probability

lib/glicko.ex

@@ -28,6 +28,13 @@ defmodule Glicko do
 		iex> Glicko.win_probability(player, opponent)
 		0.5
 
+	Calculate the probability of a player drawing against an opponent.
+
+		iex> player = Player.new_v1
+		iex> opponent = Player.new_v1
+		iex> Glicko.draw_probability(player, opponent)
+		1.0
+
 	"""
 
 	alias __MODULE__.{
@@ -41,7 +48,7 @@ defmodule Glicko do
 	@type new_rating_opts :: [system_constant: float, convergence_tolerance: float]
 
 	@doc """
-	Calculates the probability of a player winning against an opponent from a player and an opponent.
+	Calculates the probability of a player winning against an opponent.
 
 	Returns a value between `0.0` and `1.0`.
 	"""
@@ -62,6 +69,28 @@ defmodule Glicko do
 		calc_e(player_rating, opponent_rating, calc_g(opponent_rating_deviation))
 	end
 
+	@doc """
+	Calculates the probability of a player drawing against an opponent.
+
+	Returns a value between `0.0` and `1.0`.
+	"""
+	@spec draw_probability(player :: Player.t, opponent :: Player.t) :: float
+	def draw_probability(player, opponent) do
+		draw_probability(player |> Player.rating(:v2), opponent |> Player.rating(:v2), opponent |> Player.rating_deviation(:v2))
+	end
+
+	@doc """
+	Calculates the probability of a player drawing against an opponent from a player rating, opponent rating and opponent rating deviation.
+
+	Values provided for the player rating, opponent rating and opponent rating deviation must be *v2* based.
+
+	Returns a value between `0.0` and `1.0`.
+	"""
+	@spec draw_probability(player_rating :: Player.rating, opponent_rating :: Player.rating, opponent_rating_deviation :: Player.rating_deviation) :: float
+	def draw_probability(player_rating, opponent_rating, opponent_rating_deviation) do
+		1 - abs(win_probability(player_rating, opponent_rating, opponent_rating_deviation) - 0.5) / 0.5
+	end
+
 	@doc """
 	Generate a new rating from an existing rating and a series (or lack) of results.
 

test/glicko_test.exs

@@ -22,29 +22,47 @@ defmodule GlickoTest do
 
 	@valid_player_rating_deviation_after_no_results 200.2714 |> Player.scale_rating_deviation_to(:v2)
 
-	test "new rating (with results)" do
-		player = Glicko.new_rating(@player, @results, [system_constant: 0.5])
+	describe "new rating" do
+		test "with results" do
+			player = Glicko.new_rating(@player, @results, [system_constant: 0.5])
 	
-		assert_in_delta Player.rating(player), @valid_player_rating_after_results, 1.0e-4
-		assert_in_delta Player.rating_deviation(player), @valid_player_rating_deviation_after_results, 1.0e-4
-		assert_in_delta Player.volatility(player), @valid_player_volatility_after_results, 1.0e-5
+			assert_in_delta Player.rating(player), @valid_player_rating_after_results, 1.0e-4
+			assert_in_delta Player.rating_deviation(player), @valid_player_rating_deviation_after_results, 1.0e-4
+			assert_in_delta Player.volatility(player), @valid_player_volatility_after_results, 1.0e-5
+		end
+	
+		test "no results" do
+			player = Glicko.new_rating(@player, [])
+	
+			assert_in_delta Player.rating_deviation(player), @valid_player_rating_deviation_after_no_results, 1.0e-4
+		end
 	end
 
-	test "new rating (no results)" do
-		player = Glicko.new_rating(@player, [])
+	describe "win probability" do
+		test "with same ratings" do
+			assert Glicko.win_probability(Player.new_v1, Player.new_v1) == 0.5
+		end
 	
-		assert_in_delta Player.rating_deviation(player), @valid_player_rating_deviation_after_no_results, 1.0e-4
+		test "with better opponent" do
+			assert Glicko.win_probability(Player.new_v1([rating: 1500]), Player.new_v1([rating: 1600])) < 0.5
+		end
+	
+		test "with better player" do
+			assert Glicko.win_probability(Player.new_v1([rating: 1600]), Player.new_v1([rating: 1500])) > 0.5
+		end
 	end
 	
-	test "win probability with same ratings" do
-		assert Glicko.win_probability(Player.new_v1, Player.new_v1) == 0.5
-	end
+	describe "draw probability" do
+		test "with same ratings" do
+			assert Glicko.draw_probability(Player.new_v1, Player.new_v1) == 1
+		end
 	
-	test "win probability with better opponent" do
-		assert Glicko.win_probability(Player.new_v1([rating: 1500]), Player.new_v1([rating: 1600])) < 0.5
-	end
+		test "with better opponent" do
+			assert Glicko.draw_probability(Player.new_v1([rating: 1500]), Player.new_v1([rating: 1600])) < 1
+		end
 	
-	test "win probability with better player" do
-		assert Glicko.win_probability(Player.new_v1([rating: 1600]), Player.new_v1([rating: 1500])) > 0.5
+		test "with better player" do
+			assert Glicko.draw_probability(Player.new_v1([rating: 1600]), Player.new_v1([rating: 1500])) < 1
+		end
 	end
 end