add github mirror

* pull more stuff into temps to clarify long equations

.build.yml

@@ -0,0 +1,11 @@
+image: alpine/edge
+secrets:
+  - 88cce185-d2ec-4573-9546-e33f36f79bbf
+sources:
+  - git+ssh://git@git.sr.ht/~swaits/glicko2
+tasks:
+  - mirror-to-github: |
+      cd ~/glicko2
+      ssh-keyscan -t rsa github.com >> ~/.ssh/known_hosts
+      git remote add github git@github.com:swaits/glicko2.git
+      git push --mirror github

LICENSE

@@ -0,0 +1,19 @@
+Copyright 2013 Stephen Waits <steve@waits.net>
+
+Permission is hereby granted, free of charge, to any person obtaining a copy of
+this software and associated documentation files (the “Software”), to deal in
+the Software without restriction, including without limitation the rights to
+use, copy, modify, merge, publish, distribute, sublicense, and/or sell copies
+of the Software, and to permit persons to whom the Software is furnished to do
+so, subject to the following conditions:
+
+The above copyright notice and this permission notice shall be included in all
+copies or substantial portions of the Software.
+
+THE SOFTWARE IS PROVIDED “AS IS”, WITHOUT WARRANTY OF ANY KIND, EXPRESS OR
+IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,
+FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE
+AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER
+LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM,
+OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN THE
+SOFTWARE.

README.md

@@ -0,0 +1,2 @@
+An implementation of the Glicko2 algorithm in several languages (ruby,
+python, c++).

go/glicko2.go

@@ -0,0 +1,258 @@
+//
+//
+// Copyright (c) 2013 Stephen Waits
+// 
+// This software is provided 'as-is', without any express or implied warranty. In
+// no event will the authors be held liable for any damages arising from the use
+// of this software.
+// 
+// Permission is granted to anyone to use this software for any purpose,
+// including commercial applications, and to alter it and redistribute it freely,
+// subject to the following restrictions:
+// 
+// 1. The origin of this software must not be misrepresented; you must not claim
+//    that you wrote the original software. If you use this software in a
+//    product, an acknowledgment in the product documentation would be
+//    appreciated but is not required.
+// 
+// 2. Altered source versions must be plainly marked as such, and must not be
+//    misrepresented as being the original software.
+// 
+// 3. This notice may not be removed or altered from any source distribution.
+//
+//
+//
+// Glicko-2 Rating calculator package.
+//
+// This package implements the Glicko-2 rating system algorithm written by
+// Professor Mark E. Glickman.  All rating inputs and outputs are Glicko 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
+// improvement on the ELO system.
+//
+// The Glicko-2 system is specified on http://www.glicko.com/
+//
+package glicko2
+
+import (
+	"fmt"
+	"math"
+)
+
+// system constant, determines delta volatility over time; should be [0.3,1.2]
+const kDVOL float64 = 0.3
+
+// Glicko2 state reprensentation (Glicko2 uses different scales from Glicko)
+type Glicko2 struct {
+	rating     float64
+	deviation  float64
+	volatility float64
+	wins       [](*Glicko2)
+	losses     [](*Glicko2)
+	draws      [](*Glicko2)
+}
+
+// Initializer with rating, rating deviation, and volatility specified.
+func NewGlicko2(rating float64, deviation float64, volatility float64) *Glicko2 {
+	return newGlicko2(rating, deviation, volatility)
+}
+
+// Initializer with default rating, rating deviation, and volatility.
+func NewDefaultGlicko2() *Glicko2 {
+	return newGlicko2(1500.0, 350.0, 0.06)
+}
+
+// helper for initialization
+func newGlicko2(rating float64, deviation float64, volatility float64) *Glicko2 {
+	g := new(Glicko2)
+	g.SetRating(rating)
+	g.SetDeviation(deviation)
+	g.SetVolatility(volatility)
+	return g
+}
+
+// get the probability of beating opponent
+func (g *Glicko2) ProbWin(opponent *Glicko2) float64 {
+	return 1.0 / (1.0 + math.Pow(10.0, ((opponent.Rating()-g.Rating())/(400.0*math.Sqrt(1.0+0.0000100723986*((g.Deviation()*g.Deviation())+(opponent.Deviation()*opponent.Deviation())))))))
+}
+
+// Get the current rating.  This rating is a Glicko rating, not a Glicko2 rating.
+// For details, please see http://www.glicko.com/
+func (g *Glicko2) Rating() float64 {
+	return ((g.rating * 173.7178) + 1500.0)
+}
+
+// Set Glicko rating.  Internally this is converted to a Glicko2 rating.
+// For details, please see http://www.glicko.com/
+func (g *Glicko2) SetRating(rating float64) {
+	g.rating = (rating - 1500.0) / 173.7178
+}
+
+// Get the current rating deviation.  This is a Glicko rating deviation, not a
+// Glicko-2 RD.  For details, please see http://www.glicko.com/
+func (g *Glicko2) Deviation() float64 {
+	return (g.deviation * 173.7178)
+}
+
+// Set Glicko rating deviation.  Internally this is converted to a Glicko-2 RD.
+// For details, please see http://www.glicko.com/
+func (g *Glicko2) SetDeviation(deviation float64) {
+	g.deviation = deviation / 173.7178
+}
+
+// Get the current rating volatility.
+func (g *Glicko2) Volatility() float64 {
+	return g.volatility
+}
+
+// Set rating volatility.
+func (g *Glicko2) SetVolatility(volatility float64) {
+	g.volatility = volatility
+}
+
+// helper to make a copy of a Glicko2 struct
+func (g *Glicko2) duplicate() *Glicko2 {
+	c := *g
+	return &c
+}
+
+// Clear all results previously added via add_result(), add_win(), add_loss(),
+// and/or add_draw().  This method is called automatically whenever update()
+// is called.
+func (g *Glicko2) ClearResults() {
+	g.wins = nil
+	g.losses = nil
+	g.draws = nil
+}
+
+// Add a win result to this rating.  Note that no calculation is performed until
+// Update() is called.
+func (g *Glicko2) AddWin(loser *Glicko2) {
+	g.wins = append(g.wins, loser.duplicate())
+}
+
+// Add a loss result to this rating.  Note that no calculation is performed until
+// Update() is called.
+func (g *Glicko2) AddLoss(winner *Glicko2) {
+	g.losses = append(g.losses, winner.duplicate())
+}
+
+// Add a draw result to this rating.  Note that no calculation is performed until
+// Update() is called.
+func (g *Glicko2) AddDraw(drawer *Glicko2) {
+	g.draws = append(g.draws, drawer.duplicate())
+}
+
+// Print a Glicko2 struct
+func (g *Glicko2) Print() {
+	fmt.Printf("    rating: %v\n", g.Rating())
+	fmt.Printf(" deviation: %v\n", g.Deviation())
+	fmt.Printf("volatility: %v\n", g.Volatility())
+	for _, win := range g.wins {
+		fmt.Printf(" *beat\n")
+		fmt.Printf("      rating: %v\n", win.Rating())
+		fmt.Printf("   deviation: %v\n", win.Deviation())
+		fmt.Printf("  volatility: %v\n", win.Volatility())
+	}
+}
+
+// util func 'g'
+func calcG(deviation float64) float64 {
+	return 1.0 / (math.Sqrt(1.0 + 3.0*(deviation*deviation)/(math.Pi*math.Pi)))
+}
+
+// util func 'E'
+func calcE(rating float64, rating_opponent float64, deviation_opponent float64) float64 {
+	return 1.0 / (1.0 + math.Exp(-calcG(deviation_opponent)*(rating-rating_opponent)))
+}
+
+// Update rating based on current results list, and clear results.
+func (g *Glicko2) Update() {
+
+	// merge wins, losses, draws slices for convenience
+	results := append(append(g.wins, g.losses...), g.draws...)
+
+	// Note that if a player does not compete during the rating period, then
+	// only Step 6 applies.
+	if len(results) == 0 {
+		g.deviation = math.Sqrt((g.deviation * g.deviation) + (g.volatility * g.volatility))
+		return
+	}
+
+	// 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 := 0.0
+	for _, r := range results {
+		g_i := calcG(r.deviation)
+		e_i := calcE(g.rating, r.rating, r.deviation)
+		variance += (g_i * g_i) * e_i * (1.0 - e_i)
+	}
+	variance = 1.0 / variance
+
+	// 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 := 0.0
+	for _, r := range g.wins {
+		delta += calcG(r.deviation) * (1.0 - calcE(g.rating, r.rating, r.deviation))
+	}
+	for _, r := range g.losses {
+		delta += calcG(r.deviation) * (0.0 - calcE(g.rating, r.rating, r.deviation))
+	}
+	for _, r := range g.draws {
+		delta += calcG(r.deviation) * (0.5 - calcE(g.rating, r.rating, r.deviation))
+	}
+	delta *= variance
+
+	// Step 5. Determine the new value of the volatility.
+	new_volatility := 0.0
+	a := math.Log((g.volatility * g.volatility))
+	x := 0.0
+	x_new := a
+	for math.Abs(x-x_new) > 0.0000001 {
+		x = x_new
+		d := (g.deviation * g.deviation) + variance + math.Exp(x)
+		h1 := -(x-a)/(kDVOL*kDVOL) - 0.5*math.Exp(x)/d + 0.5*math.Exp(x)*(delta/d)*(delta/d)
+		h2 := -1.0/(kDVOL*kDVOL) - 0.5*math.Exp(x)*((g.deviation*g.deviation)+variance)/(d*d) + 0.5*(delta*delta)*math.Exp(x)*((g.deviation*g.deviation)+variance-math.Exp(x))/(d*d*d)
+		x_new = x - h1/h2
+	}
+	new_volatility = math.Exp(x_new / 2.0)
+
+	// Step 6. Update the rating deviation to the new pre-rating period value.
+	pre_deviation := math.Sqrt((g.deviation * g.deviation) + (new_volatility * new_volatility))
+
+	// Step 7. Update the rating and RD to the new values.
+	new_deviation := 1.0 / (math.Sqrt(1.0/(pre_deviation*pre_deviation) + 1.0/variance))
+	new_rating := 0.0
+	for _, r := range g.wins {
+		new_rating += calcG(r.deviation) * (1.0 - calcE(g.rating, r.rating, r.deviation))
+	}
+	for _, r := range g.losses {
+		new_rating += calcG(r.deviation) * (0.0 - calcE(g.rating, r.rating, r.deviation))
+	}
+	for _, r := range g.draws {
+		new_rating += calcG(r.deviation) * (0.5 - calcE(g.rating, r.rating, r.deviation))
+	}
+	new_rating = new_rating * (new_deviation * new_deviation)
+	new_rating += g.rating
+
+	// Step 8. Convert ratings and RD's back to original scale.
+	g.deviation = new_deviation
+	g.volatility = new_volatility
+	g.rating = new_rating
+
+	// wipe our result lists
+	g.ClearResults()
+}

go/glicko2_test.go

@@ -0,0 +1,47 @@
+package glicko2
+
+import (
+	"testing"
+	"math"
+)
+
+func inRange(want float64, have float64, delta float64) bool {
+	return math.Abs(want-have) <= delta
+}
+
+func TestGlicko2(t *testing.T) {
+	a := NewGlicko2(1500.0, 200.0, 0.06)
+	b := NewGlicko2(1400.0,  30.0, 0.06)
+	c := NewGlicko2(1550.0, 100.0, 0.06)
+	d := NewGlicko2(1700.0, 300.0, 0.06)
+
+	a.AddWin(b)
+	a.AddLoss(c)
+	a.AddLoss(d)
+
+	if a.Rating() != 1500.0 {
+		t.Error()
+	}
+	if a.Deviation() != 200.0 {
+		t.Error()
+	}
+
+	a.Update()
+
+	if !inRange(a.Rating(),1464.05,0.01) {
+		t.Error()
+	}
+	if !inRange(a.Deviation(),151.516,0.01) {
+		t.Error()
+	}
+
+	a.Update()
+
+	if !inRange(a.Rating(),1464.05,0.01) {
+		t.Error()
+	}
+	if !inRange(a.Deviation(),151.875,0.01) {
+		t.Error()
+	}
+
+}

rb/glicko2.rb

@@ -2,7 +2,7 @@
 
 #
 #
-# Copyright (c) 2004 Stephen Waits
+# Copyright (c) 2013 Stephen Waits
 # 
 # This software is provided 'as-is', without any express or implied warranty. In
 # no event will the authors be held liable for any damages arising from the use
@@ -183,24 +183,26 @@ class Glicko2
       sum + g_i**2.0 * e_i * (1.0 - e_i)
     end
 
-    # Step 4. Compute the quantity delta, the estimated improvement in rating
+    # 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))
+      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
 
     # 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
+    a      = Math.log(@g2volatility**2.0)
+    x0, x1 = 0.0, a
+    while ((x0 - x1).abs > 0.0000001)
+      x0 = x1
       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
+      x1 = x0 - h1/h2
     end
-    new_volatility = Math.exp(x / 2.0)
+    new_volatility = Math.exp(x1 / 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)
@@ -208,7 +210,9 @@ class Glicko2
     # 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))
+      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
 
     # Step 8. Convert ratings and RD's back to original scale.