Initial rating implementation
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avitex
parent
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defmodule Glicko do
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alias __MODULE__.{
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Player,
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GameResult,
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}
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@epsilon 0.0000001
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@default_system_constant 0.8
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@doc """
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Generate a new Rating from an existing rating and a series of results.
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"""
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@spec new_rating(player :: Player.t, results :: list(GameResult.t), sys_constant :: float) :: Player.t
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def new_rating(player, results, sys_constant \\ @default_system_constant)
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def new_rating(player = %Player{version: :v1}, results, sys_constant) do
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player
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|> Player.to_v2
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|> do_new_rating(results, sys_constant)
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|> Player.to_v1
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end
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def new_rating(player = %Player{version: :v2}, results, sys_constant) do
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do_new_rating(player, results, sys_constant)
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end
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defp do_new_rating(player = %Player{version: :v2}, results, sys_constant) do
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results = Enum.map(results, fn result ->
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opponent = Player.to_v2(result.opponent)
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%{
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score: result.score,
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opponent: opponent,
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opponent_rating_deviation_g: calc_g(opponent.rating_deviation),
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}
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end)
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ctx =
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Map.new
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|> Map.put(:system_constant, sys_constant)
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|> Map.put(:results, results)
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|> Map.put(:player, player)
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|> Map.put(:player_rating_deviation_squared, :math.pow(player.rating_deviation, 2))
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# Step 3
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ctx = Map.put(ctx, :variance_estimate, calc_variance_estimate(ctx))
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# Step 4
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ctx = Map.put(ctx, :delta, calc_delta(ctx))
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# Step 5.1
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ctx = Map.put(ctx, :alpha, calc_alpha(ctx))
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# Step 5.2
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{initial_a, initial_b} = iterative_algorithm_initial(ctx)
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ctx = Map.put(ctx, :initial_a, initial_a)
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ctx = Map.put(ctx, :initial_b, initial_b)
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# Step 5.3
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ctx = Map.put(ctx, :initial_fa, calc_f(ctx, ctx.initial_a))
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ctx = Map.put(ctx, :initial_fb, calc_f(ctx, ctx.initial_b))
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# Step 5.4
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ctx = Map.put(ctx, :a, iterative_algorithm_body(
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ctx, ctx.initial_a, ctx.initial_b, ctx.initial_fa, ctx.initial_fb
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))
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# Step 5.5
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ctx = Map.put(ctx, :new_player_volatility, calc_new_player_volatility(ctx))
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# Step 6
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ctx = Map.put(ctx, :prerating_period, calc_prerating_period(ctx))
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# Step 7
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ctx = Map.put(ctx, :new_player_rating_deviation, calc_new_player_rating_deviation(ctx))
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ctx = Map.put(ctx, :new_player_rating, calc_new_player_rating(ctx))
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Player.new_v2([
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rating: ctx.new_player_rating,
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rating_deviation: ctx.new_player_rating_deviation,
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volatility: ctx.new_player_volatility,
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])
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end
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# Calculation of the estimated variance of the player's rating based on game outcomes
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defp calc_variance_estimate(%{player: player, results: results}) do
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Enum.reduce(results, 0.0, fn result, acc ->
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tmp_e = calc_e(player, result)
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acc + :math.pow(result.opponent_rating_deviation_g, 2) * tmp_e * (1 - tmp_e)
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end)
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|> :math.pow(-1)
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end
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defp calc_delta(ctx) do
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calc_results_effect(ctx) * ctx.variance_estimate
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end
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defp calc_f(ctx, x) do
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:math.exp(x) *
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(:math.pow(ctx.delta, 2) - :math.exp(x) - ctx.player_rating_deviation_squared - ctx.variance_estimate) /
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(2 * :math.pow(ctx.player_rating_deviation_squared + ctx.variance_estimate + :math.exp(x), 2)) -
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(x - ctx.alpha) / :math.pow(ctx.system_constant, 2)
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end
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defp calc_alpha(%{player: player}) do
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:math.log(:math.pow(player.volatility, 2))
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end
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defp calc_new_player_volatility(%{a: a}) do
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:math.exp(a/2)
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end
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defp calc_results_effect(%{player: player, results: results}) do
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Enum.reduce(results, 0.0, fn result, acc ->
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acc + result.opponent_rating_deviation_g * (result.score - calc_e(player, result))
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end)
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end
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defp calc_new_player_rating(ctx) do
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ctx.player.rating + :math.pow(ctx.new_player_rating_deviation, 2) * calc_results_effect(ctx)
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end
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defp calc_new_player_rating_deviation(ctx) do
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1/:math.sqrt(1/:math.pow(ctx.prerating_period, 2) + 1/ctx.variance_estimate)
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end
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defp calc_prerating_period(ctx) do
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:math.sqrt((:math.pow(ctx.new_player_volatility, 2) + ctx.player_rating_deviation_squared))
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end
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defp iterative_algorithm_initial(ctx) do
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initial_a = ctx.alpha
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initial_b =
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if :math.pow(ctx.delta, 2) > ctx.player_rating_deviation_squared + ctx.variance_estimate do
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:math.log(:math.pow(ctx.delta, 2) - ctx.player_rating_deviation_squared - ctx.variance_estimate)
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else
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ctx.alpha - calc_k(ctx, 1) * ctx.system_constant
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end
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{initial_a, initial_b}
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end
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defp iterative_algorithm_body(ctx, a, b, fa, fb) do
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if abs(b - a) > @epsilon do
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c = a + (a - b) * fa / (fb - fa)
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fc = calc_f(ctx, c)
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{a, fa} =
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if fc * fb < 0 do
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{b, fb}
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else
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{a, fa / 2}
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end
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iterative_algorithm_body(ctx, a, c, fa, fc)
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else
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a
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end
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end
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defp calc_k(ctx, k) do
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if calc_f(ctx, (ctx.alpha - k * ctx.system_constant)) < 0 do
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calc_k(ctx, k + 1)
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else
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k
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end
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end
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# g function
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defp calc_g(rating_deviation) do
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1 / :math.sqrt(1 + 3 * :math.pow(rating_deviation, 2) / :math.pow(:math.pi, 2))
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end
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# E function
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defp calc_e(player, result) do
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1 / (1 + :math.exp(-1 * result.opponent_rating_deviation_g * (player.rating - result.opponent.rating)))
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end
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end
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8
mix.lock
8
mix.lock
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@ -1,4 +1,4 @@
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%{"bunt": {:hex, :bunt, "0.2.0", "951c6e801e8b1d2cbe58ebbd3e616a869061ddadcc4863d0a2182541acae9a38", [], [], "hexpm"},
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"credo": {:hex, :credo, "0.8.8", "990e7844a8d06ebacd88744a55853a83b74270b8a8461c55a4d0334b8e1736c9", [], [{:bunt, "~> 0.2.0", [hex: :bunt, repo: "hexpm", optional: false]}], "hexpm"},
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"earmark": {:hex, :earmark, "1.2.3", "206eb2e2ac1a794aa5256f3982de7a76bf4579ff91cb28d0e17ea2c9491e46a4", [], [], "hexpm"},
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"ex_doc": {:hex, :ex_doc, "0.18.1", "37c69d2ef62f24928c1f4fdc7c724ea04aecfdf500c4329185f8e3649c915baf", [], [{:earmark, "~> 1.1", [hex: :earmark, repo: "hexpm", optional: false]}], "hexpm"}}
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%{"bunt": {:hex, :bunt, "0.2.0", "951c6e801e8b1d2cbe58ebbd3e616a869061ddadcc4863d0a2182541acae9a38", [:mix], []},
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"credo": {:hex, :credo, "0.8.8", "990e7844a8d06ebacd88744a55853a83b74270b8a8461c55a4d0334b8e1736c9", [:mix], [{:bunt, "~> 0.2.0", [hex: :bunt, optional: false]}]},
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"earmark": {:hex, :earmark, "1.2.3", "206eb2e2ac1a794aa5256f3982de7a76bf4579ff91cb28d0e17ea2c9491e46a4", [:mix], []},
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"ex_doc": {:hex, :ex_doc, "0.18.1", "37c69d2ef62f24928c1f4fdc7c724ea04aecfdf500c4329185f8e3649c915baf", [:mix], [{:earmark, "~> 1.1", [hex: :earmark, optional: false]}]}}
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@ -0,0 +1,29 @@
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defmodule GlickoTest do
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use ExUnit.Case
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alias Glicko.{
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Player,
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GameResult,
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}
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doctest Glicko
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@player Player.new_v1([rating: 1500, rating_deviation: 200])
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@results [
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GameResult.new(Player.new_v1([rating: 1400, rating_deviation: 30]), :win),
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GameResult.new(Player.new_v1([rating: 1550, rating_deviation: 100]), :loss),
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GameResult.new(Player.new_v1([rating: 1700, rating_deviation: 300]), :loss),
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]
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@valid_player_rating_after_results 1464.06
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@valid_player_rating_deviation_after_results 151.52
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test "new rating" do
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%Player{rating: new_rating, rating_deviation: new_rating_deviation} =
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Glicko.new_rating(@player, @results, 0.5)
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assert_in_delta new_rating, @valid_player_rating_after_results, 0.1
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assert_in_delta new_rating_deviation, @valid_player_rating_deviation_after_results, 0.1
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end
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end
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