first version in go

2013-07-30 01:42:45 -07:00
1 parent cbe79afd1f
commit a8d34856b2
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+// 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"
+)
+
+const dvolatility 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 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
+func calcG(deviation float64) float64 {
+	return 1.0 / (math.Sqrt(1.0 + 3.0*(deviation*deviation)/(math.Pi*math.Pi)))
+}
+
+// util func
+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...)
+
+	// bail if no opponents set
+	if len(results) == 0 {
+		g.deviation = math.Sqrt((g.deviation * g.deviation) + (g.volatility * g.volatility))
+		return
+	}
+
+	// compute variance
+	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
+
+	// compute delta
+	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
+
+	// determine new 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)/(dvolatility*dvolatility) - 0.5*math.Exp(x)/d + 0.5*math.Exp(x)*(delta/d)*(delta/d)
+		h2 := -1.0/(dvolatility*dvolatility) - 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)
+
+	// update the rating deviation to the new pre-rating period value
+	pre_deviation := math.Sqrt((g.deviation * g.deviation) + (new_volatility * new_volatility))
+
+	// update the rating and deviation
+	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
+
+	// wipe our result lists
+	g.ClearResults()
+
+	// copy new values
+	g.deviation = new_deviation
+	g.volatility = new_volatility
+	g.rating = new_rating
+}
@@ -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()
+	}
+
+}