merge

cpp/glicko2.cpp

@@ -33,7 +33,7 @@
 
 class Glicko2_impl
 {
-public:
+	public:
 
 		// constructors
 		Glicko2_impl();
@@ -116,7 +116,7 @@ Glicko2_impl::~Glicko2_impl()
 
 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));
 }
 

cpp/glicko2.h

@@ -47,7 +47,7 @@ class Glicko2_impl;
  */
 class Glicko2
 {
-public:
+	public:
 
 
 
@@ -230,7 +230,7 @@ public:
 
 
 
-private:
+	private:
 
 		/**
 		 * Private Implementation.

rb/glicko2.rb

@@ -41,7 +41,7 @@ class Glicko2
   protected
 
   # Glicko2 reprensentation (Glicko2 uses different scales from Glicko)
-    attr_accessor :g2rating, :g2deviation, :g2volatility
+  attr_reader :g2rating, :g2deviation, :g2volatility
 
   # a nested Class to hold a single result
   Result = Struct.new(:opponent, :result)
@@ -52,11 +52,13 @@ class Glicko2
   LOSS = 0.0
   DRAW = 0.5
 
+  # system constant, determines delta volatility over time; should be [0.3,1.2]
+  DVOL = 0.3
+
   # 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
@@ -67,7 +69,12 @@ class Glicko2
 
   # Comparison operator
   def <=>(other)
-      self.rating <=> other.rating
+    p_win(other) <=> 0.5
+  end
+
+  # get the probability of beating opponent
+  def p_win(opponent)
+    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))))))
   end
 
   # Get the current rating.  This rating is a Glicko rating, not a Glicko2 rating.
@@ -108,14 +115,14 @@ class Glicko2
   # and/or add_draw().  This method is called automatically whenever update()
   # is called.
   def clear_results
-      @opponents = []
+    @opponents = Array.new
-      @results = []
+    @results   = Array.new
   end
 
   # Add a result to this rating.  Note that no calculation is performed until
   # update() is called.
   def add_result(opponent,result)
-      @results.push( Result.new(opponent.clone, result) )
+    @results << Result.new(opponent.clone, result)
   end
 
   # Add a win result to this rating.  Note that no calculation is performed until
@@ -136,83 +143,86 @@ class Glicko2
     add_result(opponent,Glicko2::DRAW)
   end
 
-    # util func
+  # util func 'g'
   def Glicko2.g(deviation)
     1.0 / (Math.sqrt(1.0 + 3.0 * deviation ** 2.0 / (Math::PI ** 2.0)))
   end
 
-    # util func
+  # 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
-      # util func
+    # Note that if a player does not compete during the rating period, then
-
+    # only Step 6 applies. 
-      # bail if no opponents set
     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
 
-      # compute variance
+    # 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)
 
-      #variance = 0.0
+    # Step 2. For each player, convert the ratings and RD's onto the Glicko-2
-      #@results.inject(0.0) do |variance,r|
+    # scale.
-      # g_i = Glicko2.g(r.opponent.g2deviation)
+    # ... (ratings already stored in G2 format)
-      # e_i = Glicko2.E(@g2rating,r.opponent.g2rating,r.opponent.g2deviation)
-      # g_i ** 2.0 * e_i * (1.0 - e_i)
-      #end
 
-      variance = 0.0
+    # Step 3.  Compute the quantity v. This is the estimated variance of the
-      @results.each do |r|
+    # 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)
+      e_i = Glicko2.E(@g2rating, r.opponent.g2rating, r.opponent.g2deviation)
-        variance += g_i ** 2.0 * e_i * (1.0 - e_i)
+      sum + g_i**2.0 * e_i * (1.0 - e_i)
     end
-      variance = 1.0 / variance
 
-      # compute delta
+    # Step 4. Compute the quantity 'delta', the estimated improvement in rating
-      delta = 0.0
+    # by comparing the pre-period rating to the performance rating based only
-      @results.each do |r|
+    # on game outcomes.
-        delta += Glicko2.g(r.opponent.g2deviation) * (r.result - Glicko2.E(@g2rating, r.opponent.g2rating, r.opponent.g2deviation))
+    delta = variance * @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 * (r.result - e_i)
     end
-      delta *= variance
 
-      # determine new volatility
+    # Step 5. Determine the new value of the volatility.
-      new_volatility = 0.0
+    a      = Math.log(@g2volatility**2.0)
-      a              = Math.log( @g2volatility**2.0 )
+    x0, x1 = 0.0, a
-      x              = 0.0
+    while ((x0 - x1).abs > 0.0000001)
-      x_new          = a
+      x0 = x1
-      while ( (x - x_new).abs > 0.0000001 )
+      d  = @g2deviation**2.0 + variance + Math.exp(x0)
-        x     = x_new
+      h1 = -(x0 - a)/(DVOL**2.0) - 0.5*Math.exp(x0)/d + 0.5*Math.exp(x0)*(delta/d)*(delta/d)
-        d     = @g2deviation**2.0 + variance + Math.exp(x)
+      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)
-        h1    = -(x - a)/(@dvolatility**2.0) - 0.5*Math.exp(x)/d + 0.5*Math.exp(x)*(delta/d)*(delta/d)
+      x1 = x0 - h1/h2
-        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)
+    new_volatility = Math.exp(x1 / 2.0)
 
-      # update the rating deviation to the new pre-rating period value
+    # Step 6. Update the rating deviation to the new pre-rating period value.
-      pre_deviation = Math.sqrt( @g2deviation**2.0 + new_volatility**2.0 )
+    pre_deviation = Math.sqrt(@g2deviation**2.0 + new_volatility**2.0)
 
-      # update the rating and deviation
+    # 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_deviation = 1.0 / (Math.sqrt(1.0/(pre_deviation**2.0) + 1.0 / variance))
-      new_rating    = 0.0
+    new_rating    = @g2rating + new_deviation**2.0 * @results.inject(0.0) do |sum,r|
-      @results.each do |r|
+      g_i = Glicko2.g(r.opponent.g2deviation)
-          new_rating += Glicko2.g(r.opponent.g2deviation) * (r.result - Glicko2.E(@g2rating, r.opponent.g2rating, r.opponent.g2deviation))
+      e_i = Glicko2.E(@g2rating, r.opponent.g2rating, r.opponent.g2deviation)
+      sum + g_i * (r.result - e_i)
     end
-      new_rating  = new_rating * new_deviation**2.0
-      new_rating += @g2rating
 
-      # wipe our result lists
+    # Step 8. Convert ratings and RD's back to original scale.
-      clear_results
-
-      # copy new values
     @g2deviation  = new_deviation
     @g2volatility = new_volatility
     @g2rating     = new_rating
+
+    # wipe our result lists
+    clear_results
   end
+
 end