elo_scores.py

#!/usr/bin/env python2

import numpy as np

#ELO basics
# Expected result given 2 elo scores:
def expected(r1, r2):
    sigma = 400.
    return 1./(1.+pow(10., (r2-r1)/sigma))
    
#(minus) rating difference of r1 (r2) given result
def delta_rating(r1, r2, result):
    k_factor = 32
    return k_factor*(result-expected(r1,r2))

#How to read:
# player i wins against player i 50% due to symmetry
# player 1 wins against player 2 80% (hence player 2 wins against player 1 20%)
# player 1 wins against player 3 90% (hence player 3 wins against player 1 10%)
# etc.
w_example = np.array([[ 0.5,  0.8,  0.9,  0.8],
                      [ 0.2,  0.5,  0.6,  0.5],
                      [ 0.1,  0.4,  0.5,  0.5],
                      [ 0.2,  0.5,  0.5,  0.5]])

w_simple = np.array([[ 0.5, 0.7],
                     [ 0.3, 0.5]])

def eig1(M):
    eigval, eigvect = np.linalg.eig(M) #calculate eigenvectors and eigenvalues
    return eigvect[:,np.isclose(eigval,1.)]  #select eigenvector with eigenvalue 1

def elo_scores(w, avg=1200):
    assert np.all(w.T + w) == 1 and np.all(w>=0) #r<=1 follows from w.T + w == 1
    if np.linalg.det(w) == 0:
      print "Warning: win array with determinant zero supplied. (Identical win rates)."
    v = eig1(w/np.sum(w,axis=1))
    scores = v*avg*len(v)/sum(v)
    return scores

Example:

In [107]: elo_scores(w_example)
Out[107]: array([ 1800.+0.j,  1080.+0.j,   900.+0.j,  1020.+0.j])