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swaits e639ee28c7 create 1.1 branch 2005-05-12 18:25:57 +00:00
5 changed files with 353 additions and 361 deletions

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+21 -21
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@@ -33,33 +33,33 @@
class Glicko2_impl class Glicko2_impl
{ {
public: public:
// constructors // constructors
Glicko2_impl(); Glicko2_impl();
Glicko2_impl(const Glicko2_impl& rhs); Glicko2_impl(const Glicko2_impl& rhs);
// copy assignment // copy assignment
Glicko2_impl& operator=(const Glicko2_impl& rhs); Glicko2_impl& operator=(const Glicko2_impl& rhs);
// destructor // destructor
virtual ~Glicko2_impl(); virtual ~Glicko2_impl();
// system constants // system constants
static const double dvolatility; static const double dvolatility;
// rating data // rating data
double rating; double rating;
double deviation; double deviation;
double volatility; double volatility;
// result data (copy of each opponent and results, 0.0, 0.5, or 1.0) // result data (copy of each opponent and results, 0.0, 0.5, or 1.0)
std::vector<Glicko2> opponents; std::vector<Glicko2> opponents;
std::vector<double> results; std::vector<double> results;
// utility functions // utility functions
double g(const double& deviation); double g(const double& deviation);
double E(const double& rating, const double& rating_opponent, const double& deviation_opponent); double E(const double& rating, const double& rating_opponent, const double& deviation_opponent);
}; };
@@ -116,7 +116,7 @@ Glicko2_impl::~Glicko2_impl()
double Glicko2_impl::g(const double& deviation) double Glicko2_impl::g(const double& deviation)
{ {
#define PI_SQUARED (9.86960440108935861883) #define PI_SQUARED (9.86960440108935861883)
return 1.0 / (sqrt(1.0 + 3.0 * deviation * deviation / PI_SQUARED)); return 1.0 / (sqrt(1.0 + 3.0 * deviation * deviation / PI_SQUARED));
} }
+148 -148
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@@ -47,195 +47,195 @@ class Glicko2_impl;
*/ */
class Glicko2 class Glicko2
{ {
public: public:
/**
* Enumeration of possible results.
*/
enum RESULT
{
/**
* A win result, internally 1.0.
*/
WIN,
/** /**
* Enumeration of possible results. * A loss result, internally 0.0.
*/ */
enum RESULT LOSS,
{
/**
* A win result, internally 1.0.
*/
WIN,
/**
* A loss result, internally 0.0.
*/
LOSS,
/**
* A draw result, internally 0.5.
*/
DRAW
};
/** /**
* Default constructor. Initializes to a rating of 1500, a rating deviation * A draw result, internally 0.5.
* of 350, and a volatility of 0.06.
*/ */
Glicko2(); DRAW
};
/**
* Copy constructor.
*
* @param rhs Object to copy.
*/
Glicko2(const Glicko2& rhs);
/**
* Constructor with rating, rating deviation, and volatility specified.
*
* @param rating Initial rating.
* @param deviation Initial rating deviation.
* @param volatility Initial volatility.
*/
Glicko2(double rating, double deviation, double volatility);
/** /**
* Copy assignment operator. * Default constructor. Initializes to a rating of 1500, a rating deviation
* * of 350, and a volatility of 0.06.
* @param rhs Object to copy. */
* Glicko2();
* @return Reference to self after copy assignment.
*/ /**
Glicko2& operator=(const Glicko2& rhs); * Copy constructor.
*
* @param rhs Object to copy.
*/
Glicko2(const Glicko2& rhs);
/**
* Constructor with rating, rating deviation, and volatility specified.
*
* @param rating Initial rating.
* @param deviation Initial rating deviation.
* @param volatility Initial volatility.
*/
Glicko2(double rating, double deviation, double volatility);
/** /**
* Destructor. * Copy assignment operator.
*/ *
virtual ~Glicko2(); * @param rhs Object to copy.
*
* @return Reference to self after copy assignment.
*/
Glicko2& operator=(const Glicko2& rhs);
/** /**
* Less than comparison operator. * Destructor.
* */
* @param rhs Object to compare against. virtual ~Glicko2();
*
* @return true if this object's rating is less than rhs's rating; false otherwise.
*/
bool operator< (const Glicko2& rhs);
/** /**
* Get the current rating. This rating is a Glicko rating, not a Glicko2 rating. * Less than comparison operator.
* For details, please see http://www.glicko.com/ *
* * @param rhs Object to compare against.
* @return *
*/ * @return true if this object's rating is less than rhs's rating; false otherwise.
double GetRating() const; */
bool operator< (const Glicko2& rhs);
/**
* Get the current rating deviation. This is a Glicko rating deviation, not a
* Glicko-2 RD. For details, please see http://www.glicko.com/
*
* @return
*/
double GetDeviation() const;
/**
* Get the current rating volatility.
*
* @return
*/
double GetVolatility() const;
/** /**
* Set Glicko rating. Internally this is converted to a Glicko2 rating. * Get the current rating. This rating is a Glicko rating, not a Glicko2 rating.
* For details, please see http://www.glicko.com/ * For details, please see http://www.glicko.com/
* *
* @param rating Rating. * @return
*/ */
void SetRating(double rating); double GetRating() const;
/** /**
* Set Glicko rating deviation. Internally this is converted to a Glicko-2 RD. * Get the current rating deviation. This is a Glicko rating deviation, not a
* For details, please see http://www.glicko.com/ * Glicko-2 RD. For details, please see http://www.glicko.com/
* *
* @param deviation Rating deviation. * @return
*/ */
void SetDeviation(double deviation); double GetDeviation() const;
/** /**
* Set rating volatility. * Get the current rating volatility.
* *
* @param volatility Rating volatility. * @return
*/ */
void SetVolatility(double volatility); double GetVolatility() const;
/** /**
* Clear all results previously added via AddResult(), AddWin(), AddLoss(), * Set Glicko rating. Internally this is converted to a Glicko2 rating.
* and/or AddDraw(). This method is called automatically whenever Update() * For details, please see http://www.glicko.com/
* is called. *
*/ * @param rating Rating.
void ClearResults(); */
void SetRating(double rating);
/**
* Set Glicko rating deviation. Internally this is converted to a Glicko-2 RD.
* For details, please see http://www.glicko.com/
*
* @param deviation Rating deviation.
*/
void SetDeviation(double deviation);
/**
* Set rating volatility.
*
* @param volatility Rating volatility.
*/
void SetVolatility(double volatility);
/** /**
* Add a result to this rating. Note that no calculation is performed until * Clear all results previously added via AddResult(), AddWin(), AddLoss(),
* Update() is called. * and/or AddDraw(). This method is called automatically whenever Update()
* * is called.
* @param opponent Other player in contest. */
* @param result WIN, LOSS, or DRAW; from the point of view of this player. void ClearResults();
*/
void AddResult(const Glicko2& opponent, RESULT result);
/** /**
* Add a win result to this rating. Note that no calculation is performed until * Add a result to this rating. Note that no calculation is performed until
* Update() is called. * Update() is called.
* *
* @param opponent Other (losing) player in contest. * @param opponent Other player in contest.
*/ * @param result WIN, LOSS, or DRAW; from the point of view of this player.
void AddWin(const Glicko2& opponent); */
void AddResult(const Glicko2& opponent, RESULT result);
/**
* Add a loss result to this rating. Note that no calculation is performed until
* Update() is called.
*
* @param opponent Other (winning) player in contest.
*/
void AddLoss(const Glicko2& opponent);
/**
* Add a draw result to this rating. Note that no calculation is performed until
* Update() is called.
*
* @param opponent Other (drawing) player in contest.
*/
void AddDraw(const Glicko2& opponent);
/** /**
* Update rating based on current results list, and clear results. * Add a win result to this rating. Note that no calculation is performed until
*/ * Update() is called.
void Update(); *
* @param opponent Other (losing) player in contest.
*/
void AddWin(const Glicko2& opponent);
/**
* Add a loss result to this rating. Note that no calculation is performed until
* Update() is called.
*
* @param opponent Other (winning) player in contest.
*/
void AddLoss(const Glicko2& opponent);
/**
* Add a draw result to this rating. Note that no calculation is performed until
* Update() is called.
*
* @param opponent Other (drawing) player in contest.
*/
void AddDraw(const Glicko2& opponent);
private: /**
* Update rating based on current results list, and clear results.
*/
void Update();
/**
* Private Implementation.
*/ private:
Glicko2_impl* pimpl;
/**
* Private Implementation.
*/
Glicko2_impl* pimpl;
}; };
+6 -6
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@@ -30,14 +30,14 @@ import copy
class Glicko2: class Glicko2:
""" """
Glicko-2 Rating calculator class. Glicko-2 Rating calculator class.
This class implements the Glicko-2 rating system algorithm written by This class implements the Glicko-2 rating system algorithm written by
Professor Mark E. Glickman. All rating inputs and outputs are Glicko ratings, Professor Mark E. Glickman. All rating inputs and outputs are Glicko ratings,
but internally everything is converted to and considered Glicko-2 ratings. but internally everything is converted to and considered Glicko-2 ratings.
Glicko-2 is an improvement on the original Glicko, which was, in turn, an Glicko-2 is an improvement on the original Glicko, which was, in turn, an
improvement on the ELO system. improvement on the ELO system.
The Glicko-2 system is specified on http://www.glicko.com/ The Glicko-2 system is specified on http://www.glicko.com/
""" """
@@ -229,12 +229,12 @@ if __name__ == "__main__":
B = Glicko2(1400.0, 30.0, 0.06) B = Glicko2(1400.0, 30.0, 0.06)
C = Glicko2(1550.0, 100.0, 0.06) C = Glicko2(1550.0, 100.0, 0.06)
D = Glicko2(1700.0, 300.0, 0.06) D = Glicko2(1700.0, 300.0, 0.06)
A.AddWin(B) A.AddWin(B)
A.AddLoss(C) A.AddLoss(C)
A.AddResult(D,Glicko2.LOSS) A.AddResult(D,Glicko2.LOSS)
A.Update(); A.Update();
print "rating",A.GetRating(), "deviation",A.GetDeviation() print "rating",A.GetRating(), "deviation",A.GetDeviation()
+153 -161
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@@ -1,4 +1,4 @@
#!/usr/bin/env ruby -w #!/usr/bin/env ruby
# #
# #
@@ -38,187 +38,179 @@
# #
class Glicko2 class Glicko2
protected protected
# Glicko2 reprensentation (Glicko2 uses different scales from Glicko) # Glicko2 reprensentation (Glicko2 uses different scales from Glicko)
attr_reader :g2rating, :g2deviation, :g2volatility attr_accessor :g2rating, :g2deviation, :g2volatility
# a nested Class to hold a single result
Result = Struct.new(:opponent, :result)
# a nested Class to hold a single result public
Result = Struct.new(:opponent, :result)
public WIN = 1.0
LOSS = 0.0
DRAW = 0.5
# Constructor with rating, rating deviation, and volatility optionally
# specified. If nothing specified, nitializes to a rating of 1500, a
# rating deviation of 350, and a volatility of 0.06.
def initialize(rating = 1500.0, deviation = 350.0, volatility = 0.06)
@dvolatility = 0.3
self.rating = rating
self.deviation = deviation
self.volatility = volatility
clear_results
end
WIN = 1.0 include Comparable
LOSS = 0.0
DRAW = 0.5
# system constant, determines delta volatility over time; should be [0.3,1.2] # Comparison operator
DVOL = 0.3 def <=>(other)
self.rating <=> other.rating
end
# Constructor with rating, rating deviation, and volatility optionally # Get the current rating. This rating is a Glicko rating, not a Glicko2 rating.
# specified. If nothing specified, nitializes to a rating of 1500, a # For details, please see http://www.glicko.com/
# rating deviation of 350, and a volatility of 0.06. def rating
def initialize(rating = 1500.0, deviation = 350.0, volatility = 0.06) (@g2rating * 173.7178) + 1500.0
self.rating = rating end
self.deviation = deviation
self.volatility = volatility
clear_results
end
include Comparable # Set Glicko rating. Internally this is converted to a Glicko2 rating.
# For details, please see http://www.glicko.com/
def rating=(r)
@g2rating = (r - 1500.0) / 173.7178
end
# Comparison operator # Get the current rating deviation. This is a Glicko rating deviation, not a
def <=>(other) # Glicko-2 RD. For details, please see http://www.glicko.com/
p_win(other) <=> 0.5 def deviation
end @g2deviation * 173.7178
end
# get the probability of beating opponent # Set Glicko rating deviation. Internally this is converted to a Glicko-2 RD.
def p_win(opponent) # For details, please see http://www.glicko.com/
1.0 / (1.0 + 10.0**(((opponent.rating - self.rating) / (400.0 * Math.sqrt(1.0 + 0.0000100723986 * (self.deviation**2.0 + opponent.deviation**2.0)))))) def deviation=(d)
end @g2deviation = d / 173.7178
end
# Get the current rating. This rating is a Glicko rating, not a Glicko2 rating. # Get the current rating volatility.
# For details, please see http://www.glicko.com/ def volatility
def rating @g2volatility
(@g2rating * 173.7178) + 1500.0 end
end
# Set Glicko rating. Internally this is converted to a Glicko2 rating. # Set rating volatility.
# For details, please see http://www.glicko.com/ def volatility=(v)
def rating=(r) @g2volatility = v
@g2rating = (r - 1500.0) / 173.7178 end
end
# Get the current rating deviation. This is a Glicko rating deviation, not a # Clear all results previously added via add_result(), add_win(), add_loss(),
# Glicko-2 RD. For details, please see http://www.glicko.com/ # and/or add_draw(). This method is called automatically whenever update()
def deviation # is called.
@g2deviation * 173.7178 def clear_results
end @opponents = []
@results = []
end
# Set Glicko rating deviation. Internally this is converted to a Glicko-2 RD. # Add a result to this rating. Note that no calculation is performed until
# For details, please see http://www.glicko.com/ # update() is called.
def deviation=(d) def add_result(opponent,result)
@g2deviation = d / 173.7178 @results.push( Result.new(opponent.clone, result) )
end end
# Get the current rating volatility. # Add a win result to this rating. Note that no calculation is performed until
def volatility # update() is called.
@g2volatility def add_win(opponent)
end add_result(opponent,Glicko2::WIN)
end
# Set rating volatility. # Add a loss result to this rating. Note that no calculation is performed until
def volatility=(v) # update() is called.
@g2volatility = v def add_loss(opponent)
end add_result(opponent,Glicko2::LOSS)
end
# Clear all results previously added via add_result(), add_win(), add_loss(), # Add a draw result to this rating. Note that no calculation is performed until
# and/or add_draw(). This method is called automatically whenever update() # update() is called.
# is called. def add_draw(opponent)
def clear_results add_result(opponent,Glicko2::DRAW)
@opponents = Array.new end
@results = Array.new
end # Update rating based on current results list, and clear results.
def update
# util func
def Glicko2.g(deviation)
1.0 / (Math.sqrt(1.0 + 3.0 * deviation ** 2.0 / (Math::PI ** 2.0)))
end
# util func
def Glicko2.E(rating, rating_opponent, deviation_opponent)
1.0 / (1.0 + Math.exp(-Glicko2.g(deviation_opponent)*(rating - rating_opponent)));
end
# bail if no opponents set
if @results.empty?
return nil
end
# Add a result to this rating. Note that no calculation is performed until # compute variance
# update() is called.
def add_result(opponent,result)
@results << Result.new(opponent.clone, result)
end
# Add a win result to this rating. Note that no calculation is performed until #variance = 0.0
# update() is called. #@results.inject(0.0) do |variance,r|
def add_win(opponent) # g_i = Glicko2.g(r.opponent.g2deviation)
add_result(opponent,Glicko2::WIN) # e_i = Glicko2.E(@g2rating,r.opponent.g2rating,r.opponent.g2deviation)
end # g_i ** 2.0 * e_i * (1.0 - e_i)
#end
# Add a loss result to this rating. Note that no calculation is performed until variance = 0.0
# update() is called. @results.each do |r|
def add_loss(opponent) g_i = Glicko2.g(r.opponent.g2deviation)
add_result(opponent,Glicko2::LOSS) e_i = Glicko2.E(@g2rating,r.opponent.g2rating,r.opponent.g2deviation)
end variance += g_i ** 2.0 * e_i * (1.0 - e_i)
end
variance = 1.0 / variance
# compute delta
delta = 0.0
@results.each do |r|
delta += Glicko2.g(r.opponent.g2deviation) * (r.result - Glicko2.E(@g2rating, r.opponent.g2rating, r.opponent.g2deviation))
end
delta *= variance
# determine new volatility
new_volatility = 0.0
a = Math.log( @g2volatility**2.0 )
x = 0.0
x_new = a
while ( (x - x_new).abs > 0.0000001 )
x = x_new
d = @g2deviation**2.0 + variance + Math.exp(x)
h1 = -(x - a)/(@dvolatility**2.0) - 0.5*Math.exp(x)/d + 0.5*Math.exp(x)*(delta/d)*(delta/d)
h2 = -1.0/(@dvolatility**2.0) - 0.5*Math.exp(x)*(@g2deviation**2.0+variance)/(d**2.0) + 0.5*(delta**2.0)*Math.exp(x)*((@g2deviation**2.0) + variance - Math.exp(x))/(d**3.0)
x_new = x - h1/h2
end
new_volatility = Math.exp(x_new / 2.0)
# update the rating deviation to the new pre-rating period value
pre_deviation = Math.sqrt( @g2deviation**2.0 + new_volatility**2.0 )
# Add a draw result to this rating. Note that no calculation is performed until # update the rating and deviation
# update() is called. new_deviation = 1.0 / (Math.sqrt( 1.0/(pre_deviation**2.0) + 1.0 / variance))
def add_draw(opponent) new_rating = 0.0
add_result(opponent,Glicko2::DRAW) @results.each do |r|
end new_rating += Glicko2.g(r.opponent.g2deviation) * (r.result - Glicko2.E(@g2rating, r.opponent.g2rating, r.opponent.g2deviation))
end
new_rating = new_rating * new_deviation**2.0
new_rating += @g2rating
# util func 'g' # wipe our result lists
def Glicko2.g(deviation) clear_results
1.0 / (Math.sqrt(1.0 + 3.0 * deviation ** 2.0 / (Math::PI ** 2.0)))
end
# util func 'E'
def Glicko2.E(rating, rating_opponent, deviation_opponent)
1.0 / (1.0 + Math.exp(-Glicko2.g(deviation_opponent)*(rating - rating_opponent)));
end
# Update rating based on current results list, and clear results.
def update
# Note that if a player does not compete during the rating period, then
# only Step 6 applies.
if @results.empty?
# In this case, the player's rating and volatility parameters remain the
# same, but the RD increases according to:
@g2deviation = Math.sqrt(@g2deviation**2.0 + @g2volatility**2.0)
return
end
# Step 1. Determine a rating and RD for each player at the onset of the
# rating period. The system constant which constrains the change in
# volatility over time, needs to be set prior to application of the system.
# Reasonable choices are between 0.3 and 1.2, though the system should be
# tested to decide which value results in greatest predictive accuracy
# ... (ratings already stored in instance)
# Step 2. For each player, convert the ratings and RD's onto the Glicko-2
# scale.
# ... (ratings already stored in G2 format)
# Step 3. Compute the quantity v. This is the estimated variance of the
# team's/player's rating based only on game outcomes.
variance = 1.0 / @results.inject(0.0) do |sum,r|
g_i = Glicko2.g(r.opponent.g2deviation)
e_i = Glicko2.E(@g2rating, r.opponent.g2rating, r.opponent.g2deviation)
sum + g_i**2.0 * e_i * (1.0 - e_i)
end
# Step 4. Compute the quantity delta, the estimated improvement in rating
# by comparing the pre-period rating to the performance rating based only
# on game outcomes.
delta = variance * @results.inject(0.0) do |sum,r|
sum + Glicko2.g(r.opponent.g2deviation) * (r.result - Glicko2.E(@g2rating, r.opponent.g2rating, r.opponent.g2deviation))
end
# Step 5. Determine the new value of the volatility.
a = Math.log(@g2volatility**2.0)
x0, x = 0.0, a
while ((x0 - x).abs > 0.0000001)
x0 = x
d = @g2deviation**2.0 + variance + Math.exp(x0)
h1 = -(x0 - a)/(DVOL**2.0) - 0.5*Math.exp(x0)/d + 0.5*Math.exp(x0)*(delta/d)*(delta/d)
h2 = -1.0/(DVOL**2.0) - 0.5*Math.exp(x0)*(@g2deviation**2.0+variance)/(d**2.0) + 0.5*(delta**2.0)*Math.exp(x0)*((@g2deviation**2.0) + variance - Math.exp(x0))/(d**3.0)
x = x0 - h1/h2
end
new_volatility = Math.exp(x / 2.0)
# Step 6. Update the rating deviation to the new pre-rating period value.
pre_deviation = Math.sqrt(@g2deviation**2.0 + new_volatility**2.0)
# Step 7. Update the rating and RD to the new values.
new_deviation = 1.0 / (Math.sqrt(1.0/(pre_deviation**2.0) + 1.0 / variance))
new_rating = @g2rating + new_deviation**2.0 * @results.inject(0.0) do |sum,r|
sum + Glicko2.g(r.opponent.g2deviation) * (r.result - Glicko2.E(@g2rating, r.opponent.g2rating, r.opponent.g2deviation))
end
# Step 8. Convert ratings and RD's back to original scale.
@g2deviation = new_deviation
@g2volatility = new_volatility
@g2rating = new_rating
# wipe our result lists
clear_results
end
# copy new values
@g2deviation = new_deviation
@g2volatility = new_volatility
@g2rating = new_rating
end
end end
+25 -25
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@@ -1,34 +1,34 @@
#!/usr/bin/env ruby -w #!/usr/bin/env ruby
require_relative 'glicko2' require 'glicko2'
require 'test/unit' require 'test/unit'
class TestGlicko2 < Test::Unit::TestCase class TestGlicko2 < Test::Unit::TestCase
def test_simple def test_simple
a = Glicko2.new(1500.0, 200.0, 0.06) a = Glicko2.new(1500.0, 200.0, 0.06)
b = Glicko2.new(1400.0, 30.0, 0.06) b = Glicko2.new(1400.0, 30.0, 0.06)
c = Glicko2.new(1550.0, 100.0, 0.06) c = Glicko2.new(1550.0, 100.0, 0.06)
d = Glicko2.new(1700.0, 300.0, 0.06) d = Glicko2.new(1700.0, 300.0, 0.06)
a.add_win(b)
a.add_loss(c)
a.add_result(d,0.0)
assert_equal(1500.0, a.rating)
assert_equal(200.0, a.deviation)
a.update()
assert_in_delta(1464.05,a.rating,0.01)
assert_in_delta(151.516,a.deviation,0.01)
a.add_win(b) a.update()
a.add_loss(c)
a.add_result(d,0.0) assert_in_delta(1464.05,a.rating,0.01)
assert_in_delta(151.516,a.deviation,0.01)
assert_equal(1500.0, a.rating)
assert_equal(200.0, a.deviation)
a.update()
assert_in_delta(1464.05,a.rating,0.01)
assert_in_delta(151.516,a.deviation,0.01)
a.update()
assert_in_delta(1464.05,a.rating,0.01)
assert_in_delta(151.875,a.deviation,0.01)
end
end
end end