import math

def K_factor(rating, board_weight=1.0):
    '''maximum change possible at a given rating; lower for higher ratings.
       called "con" in EGF rating system.
       board_weight is 1 for 19x19, .5 for 13x13, .25 for 9x9.
    '''
    r100 = rating / 100
    return board_weight * (122 - (r100 * 6) + (r100 * r100 / 15))

def A_factor(rating):
    '''rating difference normalizer in the logistic curve: see http://senseis.xmp.net/?GoR'''
    return 205 - (rating / 20)

def compute_change(winner_rating, loser_rating):
    ''' return the change in ratings for as a tuple: (change_winner, change_loser)'''
    stronger_rating = max(winner_rating, loser_rating)
    weaker_rating = min(winner_rating, loser_rating)
    rating_diff = stronger_rating - weaker_rating
    # expected probability of winning for each player
    # S_E_xxx naming taken from EGF description at http://senseis.xmp.net/?GoR
    S_E_weaker = 1 / (math.exp(rating_diff / A_factor(weaker_rating)) + 1)
    S_E_stronger = 1 - S_E_weaker
    if winner_rating == stronger_rating:
        return (K_factor(winner_rating) * (1 - S_E_stronger),
                K_factor(loser_rating) * (0 - S_E_weaker))
    else:
        return (K_factor(winner_rating) * (1 - S_E_weaker),
                K_factor(loser_rating) * (0 - S_E_stronger))

if __name__ == '__main__':
    changes = compute_change(1047, 1422)  # http://online-go.com/game/485007
    assert round(1047 + changes[0]) == 1107
    assert round(1422 + changes[1]) == 1377