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@@ -0,0 +1,19 @@
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Copyright 2013 Stephen Waits <steve@waits.net>
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Permission is hereby granted, free of charge, to any person obtaining a copy of
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this software and associated documentation files (the “Software”), to deal in
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the Software without restriction, including without limitation the rights to
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use, copy, modify, merge, publish, distribute, sublicense, and/or sell copies
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of the Software, and to permit persons to whom the Software is furnished to do
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so, subject to the following conditions:
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The above copyright notice and this permission notice shall be included in all
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copies or substantial portions of the Software.
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THE SOFTWARE IS PROVIDED “AS IS”, WITHOUT WARRANTY OF ANY KIND, EXPRESS OR
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IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,
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FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE
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AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER
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LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM,
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OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN THE
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SOFTWARE.
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An implementation of the Glicko2 algorithm in several languages (ruby,
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python, c++).
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//
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//
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// Copyright (c) 2013 Stephen Waits
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//
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// This software is provided 'as-is', without any express or implied warranty. In
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// no event will the authors be held liable for any damages arising from the use
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// of this software.
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//
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// Permission is granted to anyone to use this software for any purpose,
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// including commercial applications, and to alter it and redistribute it freely,
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// subject to the following restrictions:
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//
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// 1. The origin of this software must not be misrepresented; you must not claim
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// that you wrote the original software. If you use this software in a
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// product, an acknowledgment in the product documentation would be
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// appreciated but is not required.
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//
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// 2. Altered source versions must be plainly marked as such, and must not be
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// misrepresented as being the original software.
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//
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// 3. This notice may not be removed or altered from any source distribution.
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//
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//
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//
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// Glicko-2 Rating calculator package.
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//
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// This package implements the Glicko-2 rating system algorithm written by
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// Professor Mark E. Glickman. All rating inputs and outputs are Glicko ratings,
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// but internally everything is converted to and considered Glicko-2 ratings.
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//
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// Glicko-2 is an improvement on the original Glicko, which was, in turn, an
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// improvement on the ELO system.
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//
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// The Glicko-2 system is specified on http://www.glicko.com/
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//
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package glicko2
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import (
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"fmt"
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"math"
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)
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// system constant, determines delta volatility over time; should be [0.3,1.2]
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const kDVOL float64 = 0.3
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// Glicko2 state reprensentation (Glicko2 uses different scales from Glicko)
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type Glicko2 struct {
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rating float64
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deviation float64
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volatility float64
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wins [](*Glicko2)
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losses [](*Glicko2)
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draws [](*Glicko2)
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}
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// Initializer with rating, rating deviation, and volatility specified.
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func NewGlicko2(rating float64, deviation float64, volatility float64) *Glicko2 {
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return newGlicko2(rating, deviation, volatility)
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}
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// Initializer with default rating, rating deviation, and volatility.
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func NewDefaultGlicko2() *Glicko2 {
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return newGlicko2(1500.0, 350.0, 0.06)
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}
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// helper for initialization
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func newGlicko2(rating float64, deviation float64, volatility float64) *Glicko2 {
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g := new(Glicko2)
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g.SetRating(rating)
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g.SetDeviation(deviation)
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g.SetVolatility(volatility)
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return g
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}
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// get the probability of beating opponent
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func (g *Glicko2) ProbWin(opponent *Glicko2) float64 {
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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())))))))
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}
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// Get the current rating. This rating is a Glicko rating, not a Glicko2 rating.
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// For details, please see http://www.glicko.com/
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func (g *Glicko2) Rating() float64 {
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return ((g.rating * 173.7178) + 1500.0)
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}
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// Set Glicko rating. Internally this is converted to a Glicko2 rating.
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// For details, please see http://www.glicko.com/
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func (g *Glicko2) SetRating(rating float64) {
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g.rating = (rating - 1500.0) / 173.7178
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}
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// Get the current rating deviation. This is a Glicko rating deviation, not a
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// Glicko-2 RD. For details, please see http://www.glicko.com/
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func (g *Glicko2) Deviation() float64 {
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return (g.deviation * 173.7178)
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}
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// Set Glicko rating deviation. Internally this is converted to a Glicko-2 RD.
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// For details, please see http://www.glicko.com/
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func (g *Glicko2) SetDeviation(deviation float64) {
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g.deviation = deviation / 173.7178
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}
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// Get the current rating volatility.
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func (g *Glicko2) Volatility() float64 {
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return g.volatility
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}
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// Set rating volatility.
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func (g *Glicko2) SetVolatility(volatility float64) {
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g.volatility = volatility
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}
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// helper to make a copy of a Glicko2 struct
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func (g *Glicko2) duplicate() *Glicko2 {
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c := *g
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return &c
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}
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// Clear all results previously added via add_result(), add_win(), add_loss(),
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// and/or add_draw(). This method is called automatically whenever update()
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// is called.
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func (g *Glicko2) ClearResults() {
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g.wins = nil
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g.losses = nil
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g.draws = nil
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}
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// Add a win result to this rating. Note that no calculation is performed until
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// Update() is called.
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func (g *Glicko2) AddWin(loser *Glicko2) {
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g.wins = append(g.wins, loser.duplicate())
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}
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// Add a loss result to this rating. Note that no calculation is performed until
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// Update() is called.
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func (g *Glicko2) AddLoss(winner *Glicko2) {
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g.losses = append(g.losses, winner.duplicate())
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}
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// Add a draw result to this rating. Note that no calculation is performed until
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// Update() is called.
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func (g *Glicko2) AddDraw(drawer *Glicko2) {
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g.draws = append(g.draws, drawer.duplicate())
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}
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// Print a Glicko2 struct
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func (g *Glicko2) Print() {
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fmt.Printf(" rating: %v\n", g.Rating())
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fmt.Printf(" deviation: %v\n", g.Deviation())
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fmt.Printf("volatility: %v\n", g.Volatility())
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for _, win := range g.wins {
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fmt.Printf(" *beat\n")
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fmt.Printf(" rating: %v\n", win.Rating())
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fmt.Printf(" deviation: %v\n", win.Deviation())
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fmt.Printf(" volatility: %v\n", win.Volatility())
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}
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}
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// util func 'g'
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func calcG(deviation float64) float64 {
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return 1.0 / (math.Sqrt(1.0 + 3.0*(deviation*deviation)/(math.Pi*math.Pi)))
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}
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// util func 'E'
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func calcE(rating float64, rating_opponent float64, deviation_opponent float64) float64 {
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return 1.0 / (1.0 + math.Exp(-calcG(deviation_opponent)*(rating-rating_opponent)))
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|
}
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// Update rating based on current results list, and clear results.
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func (g *Glicko2) Update() {
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// merge wins, losses, draws slices for convenience
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results := append(append(g.wins, g.losses...), g.draws...)
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// Note that if a player does not compete during the rating period, then
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// only Step 6 applies.
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if len(results) == 0 {
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g.deviation = math.Sqrt((g.deviation * g.deviation) + (g.volatility * g.volatility))
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return
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}
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// Step 1. Determine a rating and RD for each player at the onset of the
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// rating period. The system constant which constrains the change in
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// volatility over time, needs to be set prior to application of the system.
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// Reasonable choices are between 0.3 and 1.2, though the system should be
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// tested to decide which value results in greatest predictive accuracy
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// ... (ratings already stored in instance)
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// Step 2. For each player, convert the ratings and RD's onto the Glicko-2
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// scale.
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// ... (ratings already stored in G2 format)
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// Step 3. Compute the quantity v. This is the estimated variance of the
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// team's/player's rating based only on game outcomes.
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variance := 0.0
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for _, r := range results {
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g_i := calcG(r.deviation)
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e_i := calcE(g.rating, r.rating, r.deviation)
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variance += (g_i * g_i) * e_i * (1.0 - e_i)
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}
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variance = 1.0 / variance
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// Step 4. Compute the quantity 'delta', the estimated improvement in rating
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// by comparing the pre-period rating to the performance rating based only
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// on game outcomes.
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delta := 0.0
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for _, r := range g.wins {
|
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delta += calcG(r.deviation) * (1.0 - calcE(g.rating, r.rating, r.deviation))
|
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}
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for _, r := range g.losses {
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delta += calcG(r.deviation) * (0.0 - calcE(g.rating, r.rating, r.deviation))
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}
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for _, r := range g.draws {
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delta += calcG(r.deviation) * (0.5 - calcE(g.rating, r.rating, r.deviation))
|
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}
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delta *= variance
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// Step 5. Determine the new value of the volatility.
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new_volatility := 0.0
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a := math.Log((g.volatility * g.volatility))
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x := 0.0
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x_new := a
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for math.Abs(x-x_new) > 0.0000001 {
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x = x_new
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d := (g.deviation * g.deviation) + variance + math.Exp(x)
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h1 := -(x-a)/(kDVOL*kDVOL) - 0.5*math.Exp(x)/d + 0.5*math.Exp(x)*(delta/d)*(delta/d)
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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)
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x_new = x - h1/h2
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}
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new_volatility = math.Exp(x_new / 2.0)
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|
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// Step 6. Update the rating deviation to the new pre-rating period value.
|
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pre_deviation := math.Sqrt((g.deviation * g.deviation) + (new_volatility * new_volatility))
|
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|
||||||
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// Step 7. Update the rating and RD to the new values.
|
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new_deviation := 1.0 / (math.Sqrt(1.0/(pre_deviation*pre_deviation) + 1.0/variance))
|
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new_rating := 0.0
|
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for _, r := range g.wins {
|
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new_rating += calcG(r.deviation) * (1.0 - calcE(g.rating, r.rating, r.deviation))
|
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|
}
|
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for _, r := range g.losses {
|
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|
new_rating += calcG(r.deviation) * (0.0 - calcE(g.rating, r.rating, r.deviation))
|
||||||
|
}
|
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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.
|
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|
g.deviation = new_deviation
|
||||||
|
g.volatility = new_volatility
|
||||||
|
g.rating = new_rating
|
||||||
|
|
||||||
|
// wipe our result lists
|
||||||
|
g.ClearResults()
|
||||||
|
}
|
||||||
@@ -0,0 +1,47 @@
|
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|
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()
|
||||||
|
}
|
||||||
|
|
||||||
|
}
|
||||||
+14
-10
@@ -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
|
# 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
|
# 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)
|
sum + g_i**2.0 * e_i * (1.0 - e_i)
|
||||||
end
|
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
|
# by comparing the pre-period rating to the performance rating based only
|
||||||
# on game outcomes.
|
# on game outcomes.
|
||||||
delta = variance * @results.inject(0.0) do |sum,r|
|
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
|
end
|
||||||
|
|
||||||
# Step 5. Determine the new value of the volatility.
|
# Step 5. Determine the new value of the volatility.
|
||||||
a = Math.log(@g2volatility**2.0)
|
a = Math.log(@g2volatility**2.0)
|
||||||
x0, x = 0.0, a
|
x0, x1 = 0.0, a
|
||||||
while ((x0 - x).abs > 0.0000001)
|
while ((x0 - x1).abs > 0.0000001)
|
||||||
x0 = x
|
x0 = x1
|
||||||
d = @g2deviation**2.0 + variance + Math.exp(x0)
|
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)
|
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)
|
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
|
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.
|
# 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)
|
||||||
@@ -208,7 +210,9 @@ class Glicko2
|
|||||||
# Step 7. Update the rating and RD to the new values.
|
# 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 = @g2rating + new_deviation**2.0 * @results.inject(0.0) do |sum,r|
|
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
|
end
|
||||||
|
|
||||||
# Step 8. Convert ratings and RD's back to original scale.
|
# Step 8. Convert ratings and RD's back to original scale.
|
||||||
|
|||||||
Regular → Executable
File mode changed.
Reference in new issue
Block a user