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Run mix format (#1)

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Add formatter configuration and run `mix format`.

Additionally, manually replace leading tabs in documentation examples
with four spaces.
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Mikael Muszynski 2020-01-19 14:58:40 +01:00 committed by James
parent 8612b2aa97
commit e22c34f2ff
8 changed files with 641 additions and 536 deletions
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3
.formatter.exs Normal file
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[
inputs: ["{mix,.formatter}.exs", "{config,lib,test}/**/*.{ex,exs}"]
]

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lib/glicko.ex
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defmodule Glicko do
@moduledoc """
Provides the implementation of the Glicko rating system.
@moduledoc """
Provides the implementation of the Glicko rating system.
See the [specification](http://www.glicko.net/glicko/glicko2.pdf) for implementation details.
See the [specification](http://www.glicko.net/glicko/glicko2.pdf) for implementation details.
## Usage
## Usage
Get a player's new rating after a series of matches in a rating period.
Get a player's new rating after a series of matches in a rating period.
iex> results = [Result.new(Player.new_v1([rating: 1400, rating_deviation: 30]), :win),
...> Result.new(Player.new_v1([rating: 1550, rating_deviation: 100]), :loss),
...> Result.new(Player.new_v1([rating: 1700, rating_deviation: 300]), :loss)]
iex> player = Player.new_v1([rating: 1500, rating_deviation: 200])
iex> Glicko.new_rating(player, results, [system_constant: 0.5])
{1464.0506705393013, 151.51652412385727}
iex> results = [Result.new(Player.new_v1([rating: 1400, rating_deviation: 30]), :win),
...> Result.new(Player.new_v1([rating: 1550, rating_deviation: 100]), :loss),
...> Result.new(Player.new_v1([rating: 1700, rating_deviation: 300]), :loss)]
iex> player = Player.new_v1([rating: 1500, rating_deviation: 200])
iex> Glicko.new_rating(player, results, [system_constant: 0.5])
{1464.0506705393013, 151.51652412385727}
Get a player's new rating when they haven't played within a rating period.
Get a player's new rating when they haven't played within a rating period.
iex> player = Player.new_v1([rating: 1500, rating_deviation: 200])
iex> Glicko.new_rating(player, [], [system_constant: 0.5])
{1.5e3, 200.27141669877065}
iex> player = Player.new_v1([rating: 1500, rating_deviation: 200])
iex> Glicko.new_rating(player, [], [system_constant: 0.5])
{1.5e3, 200.27141669877065}
Calculate the probability of a player winning against an opponent.
Calculate the probability of a player winning against an opponent.
iex> player = Player.new_v1
iex> opponent = Player.new_v1
iex> Glicko.win_probability(player, opponent)
0.5
iex> player = Player.new_v1
iex> opponent = Player.new_v1
iex> Glicko.win_probability(player, opponent)
0.5
Calculate the probability of a player drawing against an opponent.
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
iex> player = Player.new_v1
iex> opponent = Player.new_v1
iex> Glicko.draw_probability(player, opponent)
1.0
"""
"""
alias __MODULE__.{
Player,
Result,
}
alias __MODULE__.{
Player,
Result
}
@default_system_constant 0.8
@default_convergence_tolerance 1.0e-7
@default_system_constant 0.8
@default_convergence_tolerance 1.0e-7
@type new_rating_opts :: [system_constant: float, convergence_tolerance: float]
@type new_rating_opts :: [system_constant: float, convergence_tolerance: float]
@doc """
Calculates the probability of a player winning against an opponent.
@doc """
Calculates the probability of a player winning against an opponent.
Returns a value between `0.0` and `1.0`.
"""
@spec win_probability(player :: Player.t, opponent :: Player.t) :: float
def win_probability(player, opponent) do
win_probability(player |> Player.rating(:v2), opponent |> Player.rating(:v2), opponent |> Player.rating_deviation(:v2))
end
Returns a value between `0.0` and `1.0`.
"""
@spec win_probability(player :: Player.t(), opponent :: Player.t()) :: float
def win_probability(player, opponent) do
win_probability(
player |> Player.rating(:v2),
opponent |> Player.rating(:v2),
opponent |> Player.rating_deviation(:v2)
)
end
@doc """
Calculates the probability of a player winning against an opponent from a player rating, opponent rating and opponent rating deviation.
@doc """
Calculates the probability of a player winning 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.
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 win_probability(player_rating :: Player.rating, opponent_rating :: Player.rating, opponent_rating_deviation :: Player.rating_deviation) :: float
def win_probability(player_rating, opponent_rating, opponent_rating_deviation) do
calc_e(player_rating, opponent_rating, calc_g(opponent_rating_deviation))
end
Returns a value between `0.0` and `1.0`.
"""
@spec win_probability(
player_rating :: Player.rating(),
opponent_rating :: Player.rating(),
opponent_rating_deviation :: Player.rating_deviation()
) :: float
def win_probability(player_rating, opponent_rating, opponent_rating_deviation) do
calc_e(player_rating, opponent_rating, calc_g(opponent_rating_deviation))
end
@doc """
Calculates the probability of a player drawing against an opponent.
@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
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.
@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.
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
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.
@doc """
Generate a new rating from an existing rating and a series (or lack) of results.
Returns the updated player with the same version given to the function.
"""
@spec new_rating(player :: Player.t, results :: list(Result.t), opts :: new_rating_opts) :: Player.t
def new_rating(player, results, opts \\ [])
def new_rating(player, results, opts) when tuple_size(player) == 3 do
do_new_rating(player, results, opts)
end
def new_rating(player, results, opts) when tuple_size(player) == 2 do
player
|> Player.to_v2
|> do_new_rating(results, opts)
|> Player.to_v1
end
Returns the updated player with the same version given to the function.
"""
@spec new_rating(player :: Player.t(), results :: list(Result.t()), opts :: new_rating_opts) ::
Player.t()
def new_rating(player, results, opts \\ [])
defp do_new_rating({player_r, player_pre_rd, player_v}, [], _) do
player_post_rd = calc_player_post_base_rd(:math.pow(player_pre_rd, 2), player_v)
def new_rating(player, results, opts) when tuple_size(player) == 3 do
do_new_rating(player, results, opts)
end
{player_r, player_post_rd, player_v}
end
defp do_new_rating({player_pre_r, player_pre_rd, player_pre_v}, results, opts) do
sys_const = Keyword.get(opts, :system_constant, @default_system_constant)
conv_tol = Keyword.get(opts, :convergence_tolerance, @default_convergence_tolerance)
def new_rating(player, results, opts) when tuple_size(player) == 2 do
player
|> Player.to_v2()
|> do_new_rating(results, opts)
|> Player.to_v1()
end
# Initialization (skips steps 1, 2 and 3)
player_pre_rd_sq = :math.pow(player_pre_rd, 2)
{variance_est, results_effect} = result_calculations(results, player_pre_r)
# Step 4
delta = calc_delta(results_effect, variance_est)
# Step 5.1
alpha = calc_alpha(player_pre_v)
# Step 5.2
k = calc_k(alpha, delta, player_pre_rd_sq, variance_est, sys_const, 1)
{initial_a, initial_b} = iterative_algorithm_initial(
alpha, delta, player_pre_rd_sq, variance_est, sys_const, k
)
# Step 5.3
initial_fa = calc_f(alpha, delta, player_pre_rd_sq, variance_est, sys_const, initial_a)
initial_fb = calc_f(alpha, delta, player_pre_rd_sq, variance_est, sys_const, initial_b)
# Step 5.4
a = iterative_algorithm_body(
alpha, delta, player_pre_rd_sq, variance_est, sys_const, conv_tol,
initial_a, initial_b, initial_fa, initial_fb
)
# Step 5.5
player_post_v = calc_new_player_volatility(a)
# Step 6
player_post_base_rd = calc_player_post_base_rd(player_pre_rd_sq, player_post_v)
# Step 7
player_post_rd = calc_new_player_rating_deviation(player_post_base_rd, variance_est)
player_post_r = calc_new_player_rating(results_effect, player_pre_r, player_post_rd)
defp do_new_rating({player_r, player_pre_rd, player_v}, [], _) do
player_post_rd = calc_player_post_base_rd(:math.pow(player_pre_rd, 2), player_v)
{player_post_r, player_post_rd, player_post_v}
end
{player_r, player_post_rd, player_v}
end
defp result_calculations(results, player_pre_r) do
{variance_estimate_acc, result_effect_acc} =
Enum.reduce(results, {0.0, 0.0}, fn result, {variance_estimate_acc, result_effect_acc} ->
opponent_rd_g =
result
|> Result.opponent_rating_deviation
|> calc_g
defp do_new_rating({player_pre_r, player_pre_rd, player_pre_v}, results, opts) do
sys_const = Keyword.get(opts, :system_constant, @default_system_constant)
conv_tol = Keyword.get(opts, :convergence_tolerance, @default_convergence_tolerance)
win_probability = calc_e(player_pre_r, Result.opponent_rating(result), opponent_rd_g)
# Initialization (skips steps 1, 2 and 3)
player_pre_rd_sq = :math.pow(player_pre_rd, 2)
{variance_est, results_effect} = result_calculations(results, player_pre_r)
# Step 4
delta = calc_delta(results_effect, variance_est)
# Step 5.1
alpha = calc_alpha(player_pre_v)
# Step 5.2
k = calc_k(alpha, delta, player_pre_rd_sq, variance_est, sys_const, 1)
{
variance_estimate_acc + :math.pow(opponent_rd_g, 2) * win_probability * (1 - win_probability),
result_effect_acc + opponent_rd_g * (Result.score(result) - win_probability)
}
end)
{initial_a, initial_b} =
iterative_algorithm_initial(
alpha,
delta,
player_pre_rd_sq,
variance_est,
sys_const,
k
)
{:math.pow(variance_estimate_acc, -1), result_effect_acc}
end
# Step 5.3
initial_fa = calc_f(alpha, delta, player_pre_rd_sq, variance_est, sys_const, initial_a)
initial_fb = calc_f(alpha, delta, player_pre_rd_sq, variance_est, sys_const, initial_b)
# Step 5.4
a =
iterative_algorithm_body(
alpha,
delta,
player_pre_rd_sq,
variance_est,
sys_const,
conv_tol,
initial_a,
initial_b,
initial_fa,
initial_fb
)
defp calc_delta(results_effect, variance_est) do
results_effect * variance_est
end
# Step 5.5
player_post_v = calc_new_player_volatility(a)
# Step 6
player_post_base_rd = calc_player_post_base_rd(player_pre_rd_sq, player_post_v)
# Step 7
player_post_rd = calc_new_player_rating_deviation(player_post_base_rd, variance_est)
player_post_r = calc_new_player_rating(results_effect, player_pre_r, player_post_rd)
defp calc_f(alpha, delta, player_pre_rd_sq, variance_est, sys_const, x) do
:math.exp(x) *
(:math.pow(delta, 2) - :math.exp(x) - player_pre_rd_sq - variance_est) /
(2 * :math.pow(player_pre_rd_sq + variance_est + :math.exp(x), 2)) -
(x - alpha) / :math.pow(sys_const, 2)
end
{player_post_r, player_post_rd, player_post_v}
end
defp calc_alpha(player_pre_v) do
:math.log(:math.pow(player_pre_v, 2))
end
defp result_calculations(results, player_pre_r) do
{variance_estimate_acc, result_effect_acc} =
Enum.reduce(results, {0.0, 0.0}, fn result, {variance_estimate_acc, result_effect_acc} ->
opponent_rd_g =
result
|> Result.opponent_rating_deviation()
|> calc_g
defp calc_new_player_volatility(a) do
:math.exp(a / 2)
end
win_probability = calc_e(player_pre_r, Result.opponent_rating(result), opponent_rd_g)
defp calc_new_player_rating(results_effect, player_pre_r, player_post_rd) do
player_pre_r + :math.pow(player_post_rd, 2) * results_effect
end
{
variance_estimate_acc +
:math.pow(opponent_rd_g, 2) * win_probability * (1 - win_probability),
result_effect_acc + opponent_rd_g * (Result.score(result) - win_probability)
}
end)
defp calc_new_player_rating_deviation(player_post_base_rd, variance_est) do
1 / :math.sqrt(1 / :math.pow(player_post_base_rd, 2) + 1 / variance_est)
end
{:math.pow(variance_estimate_acc, -1), result_effect_acc}
end
defp calc_player_post_base_rd(player_pre_rd_sq, player_pre_v) do
:math.sqrt((:math.pow(player_pre_v, 2) + player_pre_rd_sq))
end
defp calc_delta(results_effect, variance_est) do
results_effect * variance_est
end
defp iterative_algorithm_initial(alpha, delta, player_pre_rd_sq, variance_est, sys_const, k) do
initial_a = alpha
initial_b =
if :math.pow(delta, 2) > player_pre_rd_sq + variance_est do
:math.log(:math.pow(delta, 2) - player_pre_rd_sq - variance_est)
else
alpha - k * sys_const
end
defp calc_f(alpha, delta, player_pre_rd_sq, variance_est, sys_const, x) do
:math.exp(x) *
(:math.pow(delta, 2) - :math.exp(x) - player_pre_rd_sq - variance_est) /
(2 * :math.pow(player_pre_rd_sq + variance_est + :math.exp(x), 2)) -
(x - alpha) / :math.pow(sys_const, 2)
end
{initial_a, initial_b}
end
defp calc_alpha(player_pre_v) do
:math.log(:math.pow(player_pre_v, 2))
end
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) > conv_tol do
c = a + (a - b) * fa / (fb - fa)
fc = calc_f(alpha, delta, player_pre_rd_sq, variance_est, sys_const, c)
{a, fa} =
if fc * fb < 0 do
{b, fb}
else
{a, fa / 2}
end
iterative_algorithm_body(alpha, delta, player_pre_rd_sq, variance_est, sys_const, conv_tol, a, c, fa, fc)
else
a
end
end
defp calc_new_player_volatility(a) do
:math.exp(a / 2)
end
defp calc_k(alpha, delta, player_pre_rd_sq, variance_est, sys_const, k) do
if calc_f(alpha, delta, player_pre_rd_sq, variance_est, sys_const, alpha - k * sys_const) < 0 do
calc_k(alpha, delta, player_pre_rd_sq, variance_est, sys_const, k + 1)
else
k
end
end
defp calc_new_player_rating(results_effect, player_pre_r, player_post_rd) do
player_pre_r + :math.pow(player_post_rd, 2) * results_effect
end
# g function
defp calc_g(rd) do
1 / :math.sqrt(1 + 3 * :math.pow(rd, 2) / :math.pow(:math.pi, 2))
end
defp calc_new_player_rating_deviation(player_post_base_rd, variance_est) do
1 / :math.sqrt(1 / :math.pow(player_post_base_rd, 2) + 1 / variance_est)
end
# E function
defp calc_e(player_pre_r, opponent_r, opponent_rd_g) do
1 / (1 + :math.exp(-1 * opponent_rd_g * (player_pre_r - opponent_r)))
end
defp calc_player_post_base_rd(player_pre_rd_sq, player_pre_v) do
:math.sqrt(:math.pow(player_pre_v, 2) + player_pre_rd_sq)
end
defp iterative_algorithm_initial(alpha, delta, player_pre_rd_sq, variance_est, sys_const, k) do
initial_a = alpha
initial_b =
if :math.pow(delta, 2) > player_pre_rd_sq + variance_est do
:math.log(:math.pow(delta, 2) - player_pre_rd_sq - variance_est)
else
alpha - k * sys_const
end
{initial_a, initial_b}
end
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) > conv_tol do
c = a + (a - b) * fa / (fb - fa)
fc = calc_f(alpha, delta, player_pre_rd_sq, variance_est, sys_const, c)
{a, fa} =
if fc * fb < 0 do
{b, fb}
else
{a, fa / 2}
end
iterative_algorithm_body(
alpha,
delta,
player_pre_rd_sq,
variance_est,
sys_const,
conv_tol,
a,
c,
fa,
fc
)
else
a
end
end
defp calc_k(alpha, delta, player_pre_rd_sq, variance_est, sys_const, k) do
if calc_f(alpha, delta, player_pre_rd_sq, variance_est, sys_const, alpha - k * sys_const) < 0 do
calc_k(alpha, delta, player_pre_rd_sq, variance_est, sys_const, k + 1)
else
k
end
end
# g function
defp calc_g(rd) do
1 / :math.sqrt(1 + 3 * :math.pow(rd, 2) / :math.pow(:math.pi(), 2))
end
# E function
defp calc_e(player_pre_r, opponent_r, opponent_rd_g) do
1 / (1 + :math.exp(-1 * opponent_rd_g * (player_pre_r - opponent_r)))
end
end

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lib/glicko/player.ex
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defmodule Glicko.Player do
@moduledoc """
Provides convenience functions that handle conversions between Glicko versions one and two.
@moduledoc """
Provides convenience functions that handle conversions between Glicko versions one and two.
## Usage
## Usage
Create a *v1* player with the default values for an unrated player.
Create a *v1* player with the default values for an unrated player.
iex> Player.new_v1
{1.5e3, 350.0}
iex> Player.new_v1
{1.5e3, 350.0}
Create a *v2* player with the default values for an unrated player.
Create a *v2* player with the default values for an unrated player.
iex> Player.new_v2
{0.0, 2.014761872416068, 0.06}
iex> Player.new_v2
{0.0, 2.014761872416068, 0.06}
Create a player with custom values.
Create a player with custom values.
iex> Player.new_v2([rating: 3.0, rating_deviation: 2.0, volatility: 0.05])
{3.0, 2.0, 0.05}
iex> Player.new_v2([rating: 3.0, rating_deviation: 2.0, volatility: 0.05])
{3.0, 2.0, 0.05}
Convert a *v2* player to a *v1*. Note this drops the volatility.
Convert a *v2* player to a *v1*. Note this drops the volatility.
iex> Player.new_v2 |> Player.to_v1
{1.5e3, 350.0}
iex> Player.new_v2 |> Player.to_v1
{1.5e3, 350.0}
Convert a *v1* player to a *v2*.
Convert a *v1* player to a *v2*.
iex> Player.new_v1 |> Player.to_v2(0.06)
{0.0, 2.014761872416068, 0.06}
iex> Player.new_v1 |> Player.to_v2(0.06)
{0.0, 2.014761872416068, 0.06}
Note calling `to_v1` with a *v1* player or likewise with `to_v2` and a *v2* player
will pass-through unchanged. The volatility arg in this case is ignored.
Note calling `to_v1` with a *v1* player or likewise with `to_v2` and a *v2* player
will pass-through unchanged. The volatility arg in this case is ignored.
iex> player_v2 = Player.new_v2
iex> player_v2 == Player.to_v2(player_v2)
true
iex> player_v2 = Player.new_v2
iex> player_v2 == Player.to_v2(player_v2)
true
"""
"""
@magic_version_scale 173.7178
@magic_version_scale_rating 1500.0
@magic_version_scale 173.7178
@magic_version_scale_rating 1500.0
@type t :: v1 | v2
@type t :: v1 | v2
@type v1 :: {rating, rating_deviation}
@type v2 :: {rating, rating_deviation, volatility}
@type v1 :: {rating, rating_deviation}
@type v2 :: {rating, rating_deviation, volatility}
@type version :: :v1 | :v2
@type rating :: float
@type rating_deviation :: float
@type volatility :: float
@type version :: :v1 | :v2
@type rating :: float
@type rating_deviation :: float
@type volatility :: float
@doc """
The recommended initial rating value for a new player.
"""
@spec initial_rating(version) :: rating
def initial_rating(_version = :v1), do: 1500.0
def initial_rating(_version = :v2), do: :v1 |> initial_rating |> scale_rating_to(:v2)
@doc """
The recommended initial rating value for a new player.
"""
@spec initial_rating(version) :: rating
def initial_rating(_version = :v1), do: 1500.0
def initial_rating(_version = :v2), do: :v1 |> initial_rating |> scale_rating_to(:v2)
@doc """
The recommended initial rating deviation value for a new player.
"""
@spec initial_rating_deviation(version) :: rating_deviation
def initial_rating_deviation(_version = :v1), do: 350.0
def initial_rating_deviation(_version = :v2), do: :v1 |> initial_rating_deviation |> scale_rating_deviation_to(:v2)
@doc """
The recommended initial rating deviation value for a new player.
"""
@spec initial_rating_deviation(version) :: rating_deviation
def initial_rating_deviation(_version = :v1), do: 350.0
@doc """
The recommended initial volatility value for a new player.
"""
@spec initial_volatility :: volatility
def initial_volatility, do: 0.06
def initial_rating_deviation(_version = :v2),
do: :v1 |> initial_rating_deviation |> scale_rating_deviation_to(:v2)
@doc """
Creates a new v1 player.
@doc """
The recommended initial volatility value for a new player.
"""
@spec initial_volatility :: volatility
def initial_volatility, do: 0.06
If not overriden, will use the default values for an unrated player.
"""
@spec new_v1([rating: rating, rating_deviation: rating_deviation]) :: v1
def new_v1(opts \\ []) when is_list(opts), do: {
Keyword.get(opts, :rating, initial_rating(:v1)),
Keyword.get(opts, :rating_deviation, initial_rating_deviation(:v1)),
}
@doc """
Creates a new v1 player.
@doc """
Creates a new v2 player.
If not overriden, will use the default values for an unrated player.
"""
@spec new_v1(rating: rating, rating_deviation: rating_deviation) :: v1
def new_v1(opts \\ []) when is_list(opts),
do: {
Keyword.get(opts, :rating, initial_rating(:v1)),
Keyword.get(opts, :rating_deviation, initial_rating_deviation(:v1))
}
If not overriden, will use default values for an unrated player.
"""
@spec new_v2([rating: rating, rating_deviation: rating_deviation, volatility: volatility]) :: v2
def new_v2(opts \\ []) when is_list(opts), do: {
Keyword.get(opts, :rating, initial_rating(:v2)),
Keyword.get(opts, :rating_deviation, initial_rating_deviation(:v2)),
Keyword.get(opts, :volatility, initial_volatility()),
}
@doc """
Creates a new v2 player.
@doc """
Converts a v2 player to a v1.
If not overriden, will use default values for an unrated player.
"""
@spec new_v2(rating: rating, rating_deviation: rating_deviation, volatility: volatility) :: v2
def new_v2(opts \\ []) when is_list(opts),
do: {
Keyword.get(opts, :rating, initial_rating(:v2)),
Keyword.get(opts, :rating_deviation, initial_rating_deviation(:v2)),
Keyword.get(opts, :volatility, initial_volatility())
}
A v1 player will pass-through unchanged.
@doc """
Converts a v2 player to a v1.
Note the volatility field used in a v2 player will be lost in the conversion.
"""
@spec to_v1(player :: t) :: v1
def to_v1({rating, rating_deviation}), do: {rating, rating_deviation}
def to_v1({rating, rating_deviation, _}), do: {
rating |> scale_rating_to(:v1),
rating_deviation |> scale_rating_deviation_to(:v1),
}
A v1 player will pass-through unchanged.
@doc """
Converts a v1 player to a v2.
Note the volatility field used in a v2 player will be lost in the conversion.
"""
@spec to_v1(player :: t) :: v1
def to_v1({rating, rating_deviation}), do: {rating, rating_deviation}
A v2 player will pass-through unchanged with the volatility arg ignored.
"""
@spec to_v2(player :: t, volatility :: volatility) :: v2
def to_v2(player, volatility \\ initial_volatility())
def to_v2({rating, rating_deviation, volatility}, _volatility), do: {rating, rating_deviation, volatility}
def to_v2({rating, rating_deviation}, volatility), do: {
rating |> scale_rating_to(:v2),
rating_deviation |> scale_rating_deviation_to(:v2),
volatility,
}
def to_v1({rating, rating_deviation, _}),
do: {
rating |> scale_rating_to(:v1),
rating_deviation |> scale_rating_deviation_to(:v1)
}
@doc """
A version agnostic method for getting a player's rating.
"""
@spec rating(player :: t, as_version :: version) :: rating
def rating(player, as_version \\ nil)
def rating({rating, _}, nil), do: rating
def rating({rating, _, _}, nil), do: rating
def rating({rating, _}, :v1), do: rating
def rating({rating, _}, :v2), do: rating |> scale_rating_to(:v2)
def rating({rating, _, _}, :v1), do: rating |> scale_rating_to(:v1)
def rating({rating, _, _}, :v2), do: rating
@doc """
Converts a v1 player to a v2.
@doc """
A version agnostic method for getting a player's rating deviation.
"""
@spec rating_deviation(player :: t, as_version :: version) :: rating_deviation
def rating_deviation(player, as_version \\ nil)
def rating_deviation({_, rating_deviation}, nil), do: rating_deviation
def rating_deviation({_, rating_deviation, _}, nil), do: rating_deviation
def rating_deviation({_, rating_deviation}, :v1), do: rating_deviation
def rating_deviation({_, rating_deviation}, :v2), do: rating_deviation |> scale_rating_deviation_to(:v2)
def rating_deviation({_, rating_deviation, _}, :v1), do: rating_deviation |> scale_rating_deviation_to(:v1)
def rating_deviation({_, rating_deviation, _}, :v2), do: rating_deviation
A v2 player will pass-through unchanged with the volatility arg ignored.
"""
@spec to_v2(player :: t, volatility :: volatility) :: v2
def to_v2(player, volatility \\ initial_volatility())
@doc """
A version agnostic method for getting a player's volatility.
"""
@spec volatility(player :: t, default_volatility :: volatility) :: volatility
def volatility(player, default_volatility \\ initial_volatility())
def volatility({_, _}, default_volatility), do: default_volatility
def volatility({_, _, volatility}, _), do: volatility
def to_v2({rating, rating_deviation, volatility}, _volatility),
do: {rating, rating_deviation, volatility}
@doc """
A convenience function for summarizing a player's strength as a 95%
confidence interval.
def to_v2({rating, rating_deviation}, volatility),
do: {
rating |> scale_rating_to(:v2),
rating_deviation |> scale_rating_deviation_to(:v2),
volatility
}
The lowest value in the interval is the player's rating minus twice the RD,
and the highest value is the player's rating plus twice the RD.
The volatility measure does not appear in the calculation of this interval.
@doc """
A version agnostic method for getting a player's rating.
"""
@spec rating(player :: t, as_version :: version) :: rating
def rating(player, as_version \\ nil)
def rating({rating, _}, nil), do: rating
def rating({rating, _, _}, nil), do: rating
def rating({rating, _}, :v1), do: rating
def rating({rating, _}, :v2), do: rating |> scale_rating_to(:v2)
def rating({rating, _, _}, :v1), do: rating |> scale_rating_to(:v1)
def rating({rating, _, _}, :v2), do: rating
An example would be if a player's rating is 1850 and the RD is 50,
the interval would range from 1750 to 1950. We would then say that we're 95%
confident that the player's actual strength is between 1750 and 1950.
@doc """
A version agnostic method for getting a player's rating deviation.
"""
@spec rating_deviation(player :: t, as_version :: version) :: rating_deviation
def rating_deviation(player, as_version \\ nil)
def rating_deviation({_, rating_deviation}, nil), do: rating_deviation
def rating_deviation({_, rating_deviation, _}, nil), do: rating_deviation
def rating_deviation({_, rating_deviation}, :v1), do: rating_deviation
When a player has a low RD, the interval would be narrow, so that we would
be 95% confident about a player’s strength being in a small interval of values.
"""
@spec rating_interval(player :: t) :: {rating_low :: float, rating_high :: float}
def rating_interval(player, as_version \\ nil), do: {
rating(player, as_version) - rating_deviation(player, as_version) * 2,
rating(player, as_version) + rating_deviation(player, as_version) * 2,
}
def rating_deviation({_, rating_deviation}, :v2),
do: rating_deviation |> scale_rating_deviation_to(:v2)
@doc """
Scales a player's rating.
"""
@spec scale_rating_to(rating :: rating, to_version :: version) :: rating
def scale_rating_to(rating, _version = :v1), do: (rating * @magic_version_scale) + @magic_version_scale_rating
def scale_rating_to(rating, _version = :v2), do: (rating - @magic_version_scale_rating) / @magic_version_scale
def rating_deviation({_, rating_deviation, _}, :v1),
do: rating_deviation |> scale_rating_deviation_to(:v1)
@doc """
Scales a player's rating deviation.
"""
@spec scale_rating_deviation_to(rating_deviation :: rating_deviation, to_version :: version) :: rating_deviation
def scale_rating_deviation_to(rating_deviation, _version = :v1), do: rating_deviation * @magic_version_scale
def scale_rating_deviation_to(rating_deviation, _version = :v2), do: rating_deviation / @magic_version_scale
def rating_deviation({_, rating_deviation, _}, :v2), do: rating_deviation
@doc """
A version agnostic method for getting a player's volatility.
"""
@spec volatility(player :: t, default_volatility :: volatility) :: volatility
def volatility(player, default_volatility \\ initial_volatility())
def volatility({_, _}, default_volatility), do: default_volatility
def volatility({_, _, volatility}, _), do: volatility
@doc """
A convenience function for summarizing a player's strength as a 95%
confidence interval.
The lowest value in the interval is the player's rating minus twice the RD,
and the highest value is the player's rating plus twice the RD.
The volatility measure does not appear in the calculation of this interval.
An example would be if a player's rating is 1850 and the RD is 50,
the interval would range from 1750 to 1950. We would then say that we're 95%
confident that the player's actual strength is between 1750 and 1950.
When a player has a low RD, the interval would be narrow, so that we would
be 95% confident about a player’s strength being in a small interval of values.
"""
@spec rating_interval(player :: t) :: {rating_low :: float, rating_high :: float}
def rating_interval(player, as_version \\ nil),
do: {
rating(player, as_version) - rating_deviation(player, as_version) * 2,
rating(player, as_version) + rating_deviation(player, as_version) * 2
}
@doc """
Scales a player's rating.
"""
@spec scale_rating_to(rating :: rating, to_version :: version) :: rating
def scale_rating_to(rating, _version = :v1),
do: rating * @magic_version_scale + @magic_version_scale_rating
def scale_rating_to(rating, _version = :v2),
do: (rating - @magic_version_scale_rating) / @magic_version_scale
@doc """
Scales a player's rating deviation.
"""
@spec scale_rating_deviation_to(rating_deviation :: rating_deviation, to_version :: version) ::
rating_deviation
def scale_rating_deviation_to(rating_deviation, _version = :v1),
do: rating_deviation * @magic_version_scale
def scale_rating_deviation_to(rating_deviation, _version = :v2),
do: rating_deviation / @magic_version_scale
end

101
lib/glicko/result.ex
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@ -1,68 +1,69 @@
defmodule Glicko.Result do
@moduledoc """
Provides convenience functions for handling a result against an opponent.
@moduledoc """
Provides convenience functions for handling a result against an opponent.
## Usage
## Usage
iex> opponent = Player.new_v2
iex> Result.new(opponent, 1.0)
{0.0, 2.014761872416068, 1.0}
iex> Result.new(opponent, :draw) # With shortcut
{0.0, 2.014761872416068, 0.5}
iex> opponent = Player.new_v2
iex> Result.new(opponent, 1.0)
{0.0, 2.014761872416068, 1.0}
iex> Result.new(opponent, :draw) # With shortcut
{0.0, 2.014761872416068, 0.5}
"""
"""
alias Glicko.Player
alias Glicko.Player
@type t :: {Player.rating, Player.rating_deviation, score}
@type t :: {Player.rating(), Player.rating_deviation(), score}
@type score :: float
@type score_shortcut :: :loss | :draw | :win
@type score :: float
@type score_shortcut :: :loss | :draw | :win
@score_shortcut_map %{loss: 0.0, draw: 0.5, win: 1.0}
@score_shortcuts Map.keys(@score_shortcut_map)
@score_shortcut_map %{loss: 0.0, draw: 0.5, win: 1.0}
@score_shortcuts Map.keys(@score_shortcut_map)
@doc """
Creates a new result from an opponent rating, opponent rating deviation and score.
@doc """
Creates a new result from an opponent rating, opponent rating deviation and score.
Values provided for the opponent rating and opponent rating deviation must be *v2* based.
Values provided for the opponent rating and opponent rating deviation must be *v2* based.
Supports passing either `:loss`, `:draw`, or `:win` as shortcuts.
"""
@spec new(Player.rating, Player.rating_deviation, score | score_shortcut) :: t
def new(opponent_rating, opponent_rating_deviation, score) when is_number(score) do
{opponent_rating, opponent_rating_deviation, score}
end
def new(opponent_rating, opponent_rating_deviation, score_type) when is_atom(score_type) and score_type in @score_shortcuts do
{opponent_rating, opponent_rating_deviation, Map.fetch!(@score_shortcut_map, score_type)}
end
Supports passing either `:loss`, `:draw`, or `:win` as shortcuts.
"""
@spec new(Player.rating(), Player.rating_deviation(), score | score_shortcut) :: t
def new(opponent_rating, opponent_rating_deviation, score) when is_number(score) do
{opponent_rating, opponent_rating_deviation, score}
end
@doc """
Creates a new result from an opponent and score.
def new(opponent_rating, opponent_rating_deviation, score_type)
when is_atom(score_type) and score_type in @score_shortcuts do
{opponent_rating, opponent_rating_deviation, Map.fetch!(@score_shortcut_map, score_type)}
end
Supports passing either `:loss`, `:draw`, or `:win` as shortcuts.
"""
@spec new(opponent :: Player.t, score :: score | score_shortcut) :: t
def new(opponent, score) do
new(Player.rating(opponent, :v2), Player.rating_deviation(opponent, :v2), score)
end
@doc """
Creates a new result from an opponent and score.
@doc """
Convenience function for accessing an opponent's rating.
"""
@spec opponent_rating(result :: Result.t) :: Player.rating
def opponent_rating(_result = {rating, _, _}), do: rating
Supports passing either `:loss`, `:draw`, or `:win` as shortcuts.
"""
@spec new(opponent :: Player.t(), score :: score | score_shortcut) :: t
def new(opponent, score) do
new(Player.rating(opponent, :v2), Player.rating_deviation(opponent, :v2), score)
end
@doc """
Convenience function for accessing an opponent's rating deviation.
"""
@spec opponent_rating_deviation(result :: Result.t) :: Player.rating_deviation
def opponent_rating_deviation(_result = {_, rating_deviation, _}), do: rating_deviation
@doc """
Convenience function for accessing an opponent's rating.
"""
@spec opponent_rating(result :: Result.t()) :: Player.rating()
def opponent_rating(_result = {rating, _, _}), do: rating
@doc """
Convenience function for accessing the score.
"""
@spec score(result :: Result.t) :: score
def score(_result = {_, _, score}), do: score
@doc """
Convenience function for accessing an opponent's rating deviation.
"""
@spec opponent_rating_deviation(result :: Result.t()) :: Player.rating_deviation()
def opponent_rating_deviation(_result = {_, rating_deviation, _}), do: rating_deviation
@doc """
Convenience function for accessing the score.
"""
@spec score(result :: Result.t()) :: score
def score(_result = {_, _, score}), do: score
end

51
mix.exs
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@ -1,30 +1,33 @@
defmodule Glicko.Mixfile do
use Mix.Project
use Mix.Project
@description """
Implementation of the Glicko rating system
"""
@description """
Implementation of the Glicko rating system
"""
def project, do: [
app: :glicko,
version: "0.6.0",
elixir: "~> 1.5",
start_permanent: Mix.env == :prod,
deps: deps(),
package: package(),
description: @description,
]
def project,
do: [
app: :glicko,
version: "0.6.0",
elixir: "~> 1.5",
start_permanent: Mix.env() == :prod,
deps: deps(),
package: package(),
description: @description
]
defp deps, do: [
{:inch_ex, "~> 0.5", only: :docs},
{:ex_doc, "~> 0.16", only: :dev, runtime: false},
{:credo, "~> 0.8", only: [:dev, :test], runtime: false},
]
defp deps,
do: [
{:inch_ex, "~> 0.5", only: :docs},
{:ex_doc, "~> 0.16", only: :dev, runtime: false},
{:credo, "~> 0.8", only: [:dev, :test], runtime: false}
]
defp package, do: [
name: :glicko,
maintainers: ["James Dyson"],
licenses: ["MIT"],
links: %{"GitHub" => "https://github.com/avitex/elixir-glicko"},
]
defp package,
do: [
name: :glicko,
maintainers: ["James Dyson"],
licenses: ["MIT"],
links: %{"GitHub" => "https://github.com/avitex/elixir-glicko"}
]
end

125
test/glicko_test.exs
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@ -1,68 +1,77 @@
defmodule GlickoTest do
use ExUnit.Case
use ExUnit.Case
alias Glicko.{
Player,
Result,
}
alias Glicko.{
Player,
Result
}
doctest Glicko
doctest Glicko
@player [rating: 1500, rating_deviation: 200] |> Player.new_v1 |> Player.to_v2
@player [rating: 1500, rating_deviation: 200] |> Player.new_v1() |> Player.to_v2()
@results [
Result.new(Player.new_v1([rating: 1400, rating_deviation: 30]), :win),
Result.new(Player.new_v1([rating: 1550, rating_deviation: 100]), :loss),
Result.new(Player.new_v1([rating: 1700, rating_deviation: 300]), :loss),
]
@results [
Result.new(Player.new_v1(rating: 1400, rating_deviation: 30), :win),
Result.new(Player.new_v1(rating: 1550, rating_deviation: 100), :loss),
Result.new(Player.new_v1(rating: 1700, rating_deviation: 300), :loss)
]
@valid_player_rating_after_results 1464.06 |> Player.scale_rating_to(:v2)
@valid_player_rating_deviation_after_results 151.52 |> Player.scale_rating_deviation_to(:v2)
@valid_player_volatility_after_results 0.05999
@valid_player_rating_after_results 1464.06 |> Player.scale_rating_to(:v2)
@valid_player_rating_deviation_after_results 151.52 |> Player.scale_rating_deviation_to(:v2)
@valid_player_volatility_after_results 0.05999
@valid_player_rating_deviation_after_no_results 200.2714 |> Player.scale_rating_deviation_to(:v2)
@valid_player_rating_deviation_after_no_results 200.2714
|> Player.scale_rating_deviation_to(:v2)
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
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
describe "new rating" do
test "with results" do
player = Glicko.new_rating(@player, @results, system_constant: 0.5)
describe "win probability" do
test "with same ratings" do
assert Glicko.win_probability(Player.new_v1, Player.new_v1) == 0.5
end
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
describe "draw probability" do
test "with same ratings" do
assert Glicko.draw_probability(Player.new_v1, Player.new_v1) == 1
end
test "with better opponent" do
assert Glicko.draw_probability(Player.new_v1([rating: 1500]), Player.new_v1([rating: 1600])) < 1
end
test "with better player" do
assert Glicko.draw_probability(Player.new_v1([rating: 1600]), Player.new_v1([rating: 1500])) < 1
end
end
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
describe "win probability" do
test "with same ratings" do
assert Glicko.win_probability(Player.new_v1(), Player.new_v1()) == 0.5
end
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
describe "draw probability" do
test "with same ratings" do
assert Glicko.draw_probability(Player.new_v1(), Player.new_v1()) == 1
end
test "with better opponent" do
assert Glicko.draw_probability(Player.new_v1(rating: 1500), Player.new_v1(rating: 1600)) < 1
end
test "with better player" do
assert Glicko.draw_probability(Player.new_v1(rating: 1600), Player.new_v1(rating: 1500)) < 1
end
end
end

88
test/player_test.exs
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@ -1,60 +1,62 @@
defmodule Glicko.PlayerTest do
use ExUnit.Case
use ExUnit.Case
alias Glicko.Player
alias Glicko.Player
doctest Player
doctest Player
@valid_v1_base {1.0, 2.0}
@valid_v2_base {1.0, 2.0, 3.0}
@valid_v1_base {1.0, 2.0}
@valid_v2_base {1.0, 2.0, 3.0}
test "create v1" do
assert @valid_v1_base == Player.new_v1([rating: 1.0, rating_deviation: 2.0])
end
test "create v1" do
assert @valid_v1_base == Player.new_v1(rating: 1.0, rating_deviation: 2.0)
end
test "create v2" do
assert @valid_v2_base == Player.new_v2([rating: 1.0, rating_deviation: 2.0, volatility: 3.0])
end
test "create v2" do
assert @valid_v2_base == Player.new_v2(rating: 1.0, rating_deviation: 2.0, volatility: 3.0)
end
test "convert player v1 -> v2" do
assert {Player.scale_rating_to(1.0, :v2), Player.scale_rating_deviation_to(2.0, :v2), 3.0} == Player.to_v2(@valid_v1_base, 3.0)
end
test "convert player v1 -> v2" do
assert {Player.scale_rating_to(1.0, :v2), Player.scale_rating_deviation_to(2.0, :v2), 3.0} ==
Player.to_v2(@valid_v1_base, 3.0)
end
test "convert player v2 -> v1" do
assert {Player.scale_rating_to(1.0, :v1), Player.scale_rating_deviation_to(2.0, :v1)} == Player.to_v1(@valid_v2_base)
end
test "convert player v2 -> v1" do
assert {Player.scale_rating_to(1.0, :v1), Player.scale_rating_deviation_to(2.0, :v1)} ==
Player.to_v1(@valid_v2_base)
end
test "convert player v1 -> v1" do
assert @valid_v1_base == Player.to_v1(@valid_v1_base)
end
test "convert player v1 -> v1" do
assert @valid_v1_base == Player.to_v1(@valid_v1_base)
end
test "convert player v2 -> v2" do
assert @valid_v2_base == Player.to_v2(@valid_v2_base)
end
test "convert player v2 -> v2" do
assert @valid_v2_base == Player.to_v2(@valid_v2_base)
end
test "scale rating v1 -> v2" do
assert_in_delta Player.scale_rating_to(1673.7178, :v2), 1.0, 0.1
end
test "scale rating v1 -> v2" do
assert_in_delta Player.scale_rating_to(1673.7178, :v2), 1.0, 0.1
end
test "scale rating v2 -> v1" do
assert_in_delta Player.scale_rating_to(1.0, :v1), 1673.7178, 0.1
end
test "scale rating v2 -> v1" do
assert_in_delta Player.scale_rating_to(1.0, :v1), 1673.7178, 0.1
end
test "scale rating deviation v1 -> v2" do
assert_in_delta Player.scale_rating_deviation_to(173.7178, :v2), 1.0, 0.1
end
test "scale rating deviation v1 -> v2" do
assert_in_delta Player.scale_rating_deviation_to(173.7178, :v2), 1.0, 0.1
end
test "scale rating deviation v2 -> v1" do
assert_in_delta Player.scale_rating_deviation_to(1.0, :v1), 173.7178, 0.1
end
test "scale rating deviation v2 -> v1" do
assert_in_delta Player.scale_rating_deviation_to(1.0, :v1), 173.7178, 0.1
end
test "rating interval" do
assert {rating_low, rating_high} =
[rating: 1850, rating_deviation: 50]
|> Player.new_v2
|> Player.rating_interval
test "rating interval" do
assert {rating_low, rating_high} =
[rating: 1850, rating_deviation: 50]
|> Player.new_v2()
|> Player.rating_interval()
assert_in_delta rating_low, 1750, 0.1
assert_in_delta rating_high, 1950, 0.1
end
assert_in_delta rating_low, 1750, 0.1
assert_in_delta rating_high, 1950, 0.1
end
end

28
test/result_test.exs
View File

@ -1,22 +1,22 @@
defmodule Glicko.ResultTest do
use ExUnit.Case
use ExUnit.Case
alias Glicko.{
Player,
Result,
}
alias Glicko.{
Player,
Result
}
doctest Result
doctest Result
@opponent Player.new_v2
@opponent Player.new_v2()
@valid_game_result Result.new(@opponent, 0.0)
@valid_game_result Result.new(@opponent, 0.0)
test "create game result" do
assert @valid_game_result == Result.new(@opponent, 0.0)
end
test "create game result" do
assert @valid_game_result == Result.new(@opponent, 0.0)
end
test "create game result with shortcut" do
assert @valid_game_result == Result.new(@opponent, :loss)
end
test "create game result with shortcut" do
assert @valid_game_result == Result.new(@opponent, :loss)
end
end