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glicko-elixir
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Remove internal context

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avitex 2017-11-29 12:10:37 +11:00
parent f3c6189e4a
commit 585621b20a
1 changed files with 69 additions and 77 deletions
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146
lib/glicko.ex
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@ -50,157 +50,149 @@ defmodule Glicko do
|> Player.to_v1 |> Player.to_v1
end end
defp do_new_rating({player_rating, player_rating_deviation, player_volatility}, [], _) do defp do_new_rating({player_r, player_pre_rd, player_v}, [], _) do
player_post_rating_deviation = calc_player_pre_rating_deviation( player_post_rd = calc_player_post_base_rd(:math.pow(player_pre_rd, 2), player_v)
:math.pow(player_rating_deviation, 2),
player_volatility
)
{player_rating, player_post_rating_deviation, player_volatility} {player_r, player_post_rd, player_v}
end end
defp do_new_rating({player_rating, player_rating_deviation, player_volatility}, results, opts) do defp do_new_rating({player_pre_r, player_pre_rd, player_pre_v}, results, opts) do
ctx = sys_const = Keyword.get(opts, :system_constant, @default_system_constant)
Map.new conv_tol = Keyword.get(opts, :convergence_tolerance, @default_convergence_tolerance)
|> Map.put(:system_constant, Keyword.get(opts, :system_constant, @default_system_constant))
|> Map.put(:convergence_tolerance, Keyword.get(opts, :convergence_tolerance, @default_convergence_tolerance))
|> Map.put(:player_rating, player_rating)
|> Map.put(:player_volatility, player_volatility)
|> Map.put(:player_rating_deviation, player_rating_deviation)
|> Map.put(:player_rating_deviation_squared, :math.pow(player_rating_deviation, 2))
# Init # Init
ctx = Map.put(ctx, :results, Enum.map(results, &build_internal_result(ctx, &1))) player_pre_rd_sq = :math.pow(player_pre_rd, 2)
ctx = Map.put(ctx, :results_effect, calc_results_effect(ctx)) results = Enum.map(results, &build_internal_result(player_pre_r, &1))
results_effect = calc_results_effect(results)
# Step 3 # Step 3
ctx = Map.put(ctx, :variance_estimate, calc_variance_estimate(ctx)) variance_est = calc_variance_estimate(results)
# Step 4 # Step 4
ctx = Map.put(ctx, :delta, calc_delta(ctx)) delta = calc_delta(results_effect, variance_est)
# Step 5.1 # Step 5.1
ctx = Map.put(ctx, :alpha, calc_alpha(ctx)) alpha = calc_alpha(player_pre_v)
# Step 5.2 # Step 5.2
{initial_a, initial_b} = iterative_algorithm_initial(ctx) k = calc_k(alpha, delta, player_pre_rd_sq, variance_est, sys_const, 1)
ctx = Map.put(ctx, :initial_a, initial_a) {initial_a, initial_b} = iterative_algorithm_initial(
ctx = Map.put(ctx, :initial_b, initial_b) alpha, delta, player_pre_rd_sq, variance_est, sys_const, k
)
# Step 5.3 # Step 5.3
ctx = Map.put(ctx, :initial_fa, calc_f(ctx, ctx.initial_a)) initial_fa = calc_f(alpha, delta, player_pre_rd_sq, variance_est, sys_const, initial_a)
ctx = Map.put(ctx, :initial_fb, calc_f(ctx, ctx.initial_b)) initial_fb = calc_f(alpha, delta, player_pre_rd_sq, variance_est, sys_const, initial_b)
# Step 5.4 # Step 5.4
ctx = Map.put(ctx, :a, iterative_algorithm_body( a = iterative_algorithm_body(
ctx, ctx.initial_a, ctx.initial_b, ctx.initial_fa, ctx.initial_fb alpha, delta, player_pre_rd_sq, variance_est, sys_const, conv_tol,
)) initial_a, initial_b, initial_fa, initial_fb
)
# Step 5.5 # Step 5.5
ctx = Map.put(ctx, :new_player_volatility, calc_new_player_volatility(ctx)) player_post_v = calc_new_player_volatility(a)
# Step 6 # Step 6
ctx = Map.put(ctx, :player_pre_rating_deviation, calc_player_pre_rating_deviation( player_post_base_rd = calc_player_post_base_rd(player_pre_rd_sq, player_post_v)
ctx.player_rating_deviation_squared, ctx.new_player_volatility
))
# Step 7 # Step 7
ctx = Map.put(ctx, :new_player_rating_deviation, calc_new_player_rating_deviation(ctx)) player_post_rd = calc_new_player_rating_deviation(player_post_base_rd, variance_est)
ctx = Map.put(ctx, :new_player_rating, calc_new_player_rating(ctx)) player_post_r = calc_new_player_rating(results_effect, player_pre_r, player_post_rd)
{ctx.new_player_rating, ctx.new_player_rating_deviation, ctx.new_player_volatility} {player_post_r, player_post_rd, player_post_v}
end end
defp build_internal_result(ctx, result) do defp build_internal_result(player_pre_r, result) do
result = result =
Map.new Map.new
|> Map.put(:score, Result.score(result)) |> Map.put(:score, Result.score(result))
|> Map.put(:opponent_rating, Result.opponent_rating(result)) |> Map.put(:opponent_r, Result.opponent_rating(result))
|> Map.put(:opponent_rating_deviation, Result.opponent_rating_deviation(result)) |> Map.put(:opponent_rd, Result.opponent_rating_deviation(result))
|> Map.put(:opponent_rating_deviation_g, calc_g(Result.opponent_rating_deviation(result))) |> Map.put(:opponent_rd_g, calc_g(Result.opponent_rating_deviation(result)))
Map.put(result, :e, calc_e(ctx.player_rating, result)) Map.put(result, :e, calc_e(player_pre_r, result.opponent_r, result.opponent_rd_g))
end end
# Calculation of the estimated variance of the player's rating based on game outcomes # Calculation of the estimated variance of the player's rating based on game outcomes
defp calc_variance_estimate(ctx) do defp calc_variance_estimate(results) do
ctx.results results
|> Enum.reduce(0.0, fn result, acc -> |> Enum.reduce(0.0, fn result, acc ->
acc + :math.pow(result.opponent_rating_deviation_g, 2) * result.e * (1 - result.e) acc + :math.pow(result.opponent_rd_g, 2) * result.e * (1 - result.e)
end) end)
|> :math.pow(-1) |> :math.pow(-1)
end end
defp calc_delta(ctx) do defp calc_delta(results_effect, variance_est) do
ctx.results_effect * ctx.variance_estimate results_effect * variance_est
end end
defp calc_f(ctx, x) do defp calc_f(alpha, delta, player_pre_rd_sq, variance_est, sys_const, x) do
:math.exp(x) * :math.exp(x) *
(:math.pow(ctx.delta, 2) - :math.exp(x) - ctx.player_rating_deviation_squared - ctx.variance_estimate) / (:math.pow(delta, 2) - :math.exp(x) - player_pre_rd_sq - variance_est) /
(2 * :math.pow(ctx.player_rating_deviation_squared + ctx.variance_estimate + :math.exp(x), 2)) - (2 * :math.pow(player_pre_rd_sq + variance_est + :math.exp(x), 2)) -
(x - ctx.alpha) / :math.pow(ctx.system_constant, 2) (x - alpha) / :math.pow(sys_const, 2)
end end
defp calc_alpha(ctx) do defp calc_alpha(player_pre_v) do
:math.log(:math.pow(ctx.player_volatility, 2)) :math.log(:math.pow(player_pre_v, 2))
end end
defp calc_new_player_volatility(%{a: a}) do defp calc_new_player_volatility(a) do
:math.exp(a / 2) :math.exp(a / 2)
end end
defp calc_results_effect(ctx) do defp calc_results_effect(results) do
Enum.reduce(ctx.results, 0.0, fn result, acc -> Enum.reduce(results, 0.0, fn result, acc ->
acc + result.opponent_rating_deviation_g * (result.score - result.e) acc + result.opponent_rd_g * (result.score - result.e)
end) end)
end end
defp calc_new_player_rating(ctx) do defp calc_new_player_rating(results_effect, player_pre_r, player_post_rd) do
ctx.player_rating + :math.pow(ctx.new_player_rating_deviation, 2) * ctx.results_effect player_pre_r + :math.pow(player_post_rd, 2) * results_effect
end end
defp calc_new_player_rating_deviation(ctx) do defp calc_new_player_rating_deviation(player_post_base_rd, variance_est) do
1 / :math.sqrt(1 / :math.pow(ctx.player_pre_rating_deviation, 2) + 1 / ctx.variance_estimate) 1 / :math.sqrt(1 / :math.pow(player_post_base_rd, 2) + 1 / variance_est)
end end
defp calc_player_pre_rating_deviation(player_rating_deviation_squared, player_volatility) do defp calc_player_post_base_rd(player_pre_rd_sq, player_pre_v) do
:math.sqrt((:math.pow(player_volatility, 2) + player_rating_deviation_squared)) :math.sqrt((:math.pow(player_pre_v, 2) + player_pre_rd_sq))
end end
defp iterative_algorithm_initial(ctx) do defp iterative_algorithm_initial(alpha, delta, player_pre_rd_sq, variance_est, sys_const, k) do
initial_a = ctx.alpha initial_a = alpha
initial_b = initial_b =
if :math.pow(ctx.delta, 2) > ctx.player_rating_deviation_squared + ctx.variance_estimate do if :math.pow(delta, 2) > player_pre_rd_sq + variance_est do
:math.log(:math.pow(ctx.delta, 2) - ctx.player_rating_deviation_squared - ctx.variance_estimate) :math.log(:math.pow(delta, 2) - player_pre_rd_sq - variance_est)
else else
ctx.alpha - calc_k(ctx, 1) * ctx.system_constant alpha - k * sys_const
end end
{initial_a, initial_b} {initial_a, initial_b}
end end
defp iterative_algorithm_body(ctx, a, b, fa, fb) do defp iterative_algorithm_body(alpha, delta, player_pre_rd_sq, variance_est, sys_const, conv_tol, a, b, fa, fb) do
if abs(b - a) > ctx.convergence_tolerance do if abs(b - a) > conv_tol do
c = a + (a - b) * fa / (fb - fa) c = a + (a - b) * fa / (fb - fa)
fc = calc_f(ctx, c) fc = calc_f(alpha, delta, player_pre_rd_sq, variance_est, sys_const, c)
{a, fa} = {a, fa} =
if fc * fb < 0 do if fc * fb < 0 do
{b, fb} {b, fb}
else else
{a, fa / 2} {a, fa / 2}
end end
iterative_algorithm_body(ctx, a, c, fa, fc) iterative_algorithm_body(alpha, delta, player_pre_rd_sq, variance_est, sys_const, conv_tol, a, c, fa, fc)
else else
a a
end end
end end
defp calc_k(ctx, k) do defp calc_k(alpha, delta, player_pre_rd_sq, variance_est, sys_const, k) do
if calc_f(ctx, ctx.alpha - k * ctx.system_constant) < 0 do if calc_f(alpha, delta, player_pre_rd_sq, variance_est, sys_const, alpha - k * sys_const) < 0 do
calc_k(ctx, k + 1) calc_k(alpha, delta, player_pre_rd_sq, variance_est, sys_const, k + 1)
else else
k k
end end
end end
# g function # g function
defp calc_g(rating_deviation) do defp calc_g(rd) do
1 / :math.sqrt(1 + 3 * :math.pow(rating_deviation, 2) / :math.pow(:math.pi, 2)) 1 / :math.sqrt(1 + 3 * :math.pow(rd, 2) / :math.pow(:math.pi, 2))
end end
# E function # E function
defp calc_e(player_rating, result) do defp calc_e(player_pre_r, opponent_r, opponent_rd_g) do
1 / (1 + :math.exp(-1 * result.opponent_rating_deviation_g * (player_rating - result.opponent_rating))) 1 / (1 + :math.exp(-1 * opponent_rd_g * (player_pre_r - opponent_r)))
end end
end end