sim-elo.py

import math
import random

def alt_win_probability(p1, p2):
    diff = p1 - p2
    p = 1 - 1 / (1 + math.exp(0.00583 * diff - 0.0505))
    return p

def win_probability(p1, p2):
    diff = p1 - p2
    p = 1 - 1 / (1 + 10 ** (diff / 400.0))
    return p

def rate_1vs1(p1, p2, k=20, drawn=False):
    rp1 = 10 ** (p1/400)
    rp2 = 10 ** (p2/400)
    exp_p1 = rp1 / float(rp1 + rp2)
    exp_p2 = rp2 / float(rp1 + rp2)
    if drawn == True:
        s1 = 0.5
        s2 = 0.5
    else:
        s1 = 1
        s2 = 0
    new_p1 = p1 + k * (s1 - exp_p1)
    new_p2 = p2 + k * (s2 - exp_p2)
    return new_p1, new_p2

def run_sim(starta, startb):
    ayes, bees = [], []
    for i in range(1, 1000):
        a, b = starta, startb
        for j in range(0, 1000):
            if random.random() <= win_probability(starta, startb):
                a, b = rate_1vs1(a, b)
            else:
                b, a = rate_1vs1(b, a)
        ayes.append(a)
        bees.append(b)

    print sum(ayes) / len(ayes), sum(bees) / len(bees)
    return sum(ayes) / len(ayes)


x = []
for i in range(0, 10):
    x.append(run_sim(1550,1450))
print sum(x) / len(x)