elo.py

import math, datetime

REF_DATE = datetime.date(2015, 4, 1)

KP = 260. # The higher this is, the higher the spread of the ratings between users.

# Chosen so that .025 eq_diff implies a .5 outcome and 0 eq_diff implies a 1 outcome:
a = - math.log(.5) / .025

def mplier_for_experience(submissions):
    """
    This decays fast towards 1.
    """
    return math.exp(-submissions / 3. + 2.8) + 1.

def decay(x):
    """
    This decays slowly towards .8.
    """
    return math.exp(-x/60. + 1.2) + .8

def K(submissions):
# The higher K is, the more effective is a single position to a user's rating.
    days = (datetime.date.today() - REF_DATE).days
    return decay(days) * mplier_for_experience(submissions)

def phi(x):
    'Cumulative distribution function for the standard normal distribution'
    return (1.0 + math.erf(x / math.sqrt(2.0))) / 2.0

def equity_diff_to_p(equity_diff):
    return math.exp(a * equity_diff)

def p_to_equity_diff(p):
    return math.log(p) / a

def rdiff_to_equity_diff(rdiff):
    return p_to_equity_diff(phi(rdiff / KP))

def rdiff_to_p(rdiff):
    return equity_diff_to_p(rdiff_to_equity_diff(rdiff))
    
def match_increment(player_rating, position_rating, eq_diff, 
                        player_submissions, position_submissions):
    """ Winner's rating comes first. """
    rdiff = player_rating - position_rating
    p_from_rating = phi(rdiff / KP)
    p_from_selection = equity_diff_to_p(eq_diff)
    surplus = p_from_selection - p_from_rating
    player_result = K(player_submissions) * surplus
    position_result = - K(position_submissions) * surplus
    return player_result, position_result
    
if __name__ == '__main__':
    import scipy
    import pylab
    x = scipy.linspace(-.15, 0, 200)
    y = [equity_diff_to_p(xi) for xi in x]
    pylab.plot(x, y)
    pylab.show()