An alternative rating system to ELO

[mapkoc]

Hola,

here's a function to update ratings based on the Glicko system and using scythe's same signature.

Since inactive time and rating deviation are not stored, I used the games played to compute the deviation.

http://www.glicko.net/glicko/glicko.pdf

http://www.glicko.net/glicko/glicko2.pdf

import math

# Rating deviation extrema
RDmax = 350        
RDmin = 30

# Linear mapping
GPthr = 160.0    # games played threshold
m = GPthr / (RDmin - RDmax)        # slope

# Simple Glicko without rating deviation aging
def get_rating_adjustment(rating, opponent_rating, games_played, opponent_games_played, result):
    r = rating
    rj = opponent_rating
    sj = (result + 1) / 2    # outcome
    

    # Linear mapping of games played to rating deviation
    # instead of RD = min(math.sqrt(RD_{old}^2 + c^2), 350)
    RD = RDmin if games_played > GPthr else m * games_played + RDmax
    RDj = RDmin if opponent_games_played > GPthr else m * opponent_games_played + RDmax
    
    # Rating delta
    q = math.log(10) / 400
    gj = 1 / math.sqrt(1 + 3 * math.pow(q * RDj / math.pi, 2))
    Ej = 1 / (1 + math.pow(10, gj * (rj - r) / 400))
    d2 = 1 / (math.pow(q * gj, 2) * Ej * (1 - Ej))
    value = 1 / RD / RD + 1 / d2
    # RDnew = math.sqrt(1 / value)    # not used for now
    return round(q * gj * (sj - Ej) / value)

Edited December 29, 2017 by mapkoc
code fix

[Dunedan]

> here's a function to update ratings based on the Glicko system and using scythe's same signature.

I guess the motivation is to have a better algorithm than ELO? Is there any previous discussion on this topic?

> Since inactive time and rating deviation are not stored, I used the games played to compute the deviation.

Aren't you neglecting the major advantages of Glicko compared to ELO by doing that?

[mapkoc]

Sorry for hijacking your thread.
I've always been interested in how were lobby ratings implemented and from your discussion I finally found how.
I tested both functions and mine definitely is wrong, ratings jump too much with each result.

scythe's                                                                                   mine

Either I made a mistake or RD is really important.
Test code:

from random import choice, seed
r1start = 2101
r2start = 1200
r1 = r1start
r2 = r2start
seed()
for x in range(100):
  res = choice([-1, 1])
  r1gain = get_rating_adjustment(r1, r2, 200+x, 20+x, res)
  r2gain = get_rating_adjustment(r2, r1, 20+x, 200+x, -res)
  r1 += r1gain
  r2 += r2gain
  print(str(r1) + " " + str(r2))