bradley-terry-algo.py

import pandas as pd
import numpy as np

dat = pd.DataFrame({
    "player1" : ["A", "A", "A", "A","A","B","B", "B", "C", "C", "C", "C", "C"],
    "player2" :[ "B", "C", "B", "B", "C", "A", "C", "C", "A", "B", "A", "B", "B"],
    "player1_won" : [ 1, 0, 1, 1, 1, 0, 1, 0 , 1, 0 , 0, 0, 0]
})

names = sorted(set(dat["player1"]))
n_players = len(names)

def get_wij(i,j):
    ni = names[i]
    nj = names[j]
    dat1 = dat.query("player1 == '{i}' & player2 == '{j}'".format(i=ni,j=nj))
    dat2 = dat.query("player1 == '{j}' & player2 == '{i}'".format(i=ni,j=nj))
    n = sum(dat1["player1_won"]) +  sum(1- dat2["player1_won"])
    return n


wij = np.matrix(
    [ [ get_wij(j, i) for i in range(n_players)] for j in range(n_players)]
)

W = np.array(wij.sum(axis = 1)).flatten()

def get_p_next(i, W, wij, p):
    sum_hold = 0
    for j in range(3):
        if i == j:
            continue
        numerator = wij[i,j]  + wij[j,i]
        denominator = p[i] + p[j]
        sum_hold += (numerator / denominator)
    return W[i] / sum_hold

p = [0.5] * n_players

for it in range(50):
    pnext = [ get_p_next(i , W , wij, p) for i in range(n_players)]
    p = pnext / sum(pnext) 

p[0] / (p[0] + p[1])

bradley-terry.py

import pandas as pd
import patsy
from sklearn.linear_model import LogisticRegression


# Setup test data
dat = pd.DataFrame({
    "player1" : ["A", "A", "A", "A","A","B","B", "B", "C", "C", "C", "C", "C"],
    "player2" :[ "B", "C", "B", "B", "C", "A", "C", "C", "A", "B", "A", "B", "B"],
    "player1_won" : [ 1, 0, 1, 1, 1, 0, 1, 0 , 1, 0 , 0, 0, 0]
})

# Generate the design matrix 
# Left side of formula is unused but has to be specified to satisfy
# the dmatricies function. Use "-1" to supress the intercept term
design_matrix_1 = patsy.dmatrices( "player1_won ~ player1 - 1", dat)[1]
design_matrix_2 = patsy.dmatrices( "player1_won ~ player2 - 1", dat)[1]
difference_matrix = design_matrix_1 - design_matrix_2

ddf = pd.DataFrame(difference_matrix)

# Remove first column to make the problem tractable
# This essentially fixes the parameter for team A to 0
ddf.drop(ddf.columns[0], axis=1, inplace=True)

# Configure logistic regression removing regularisation and
# supressing the intercept term
model = LogisticRegression(
    penalty = "none",
    fit_intercept = False
)

fit = model.fit(ddf, dat["player1_won"])

fit.coef_