Margin-dependent Elo ratings and predictions model

melo generalizes the Bradley-Terry paired comparison model beyond binary outcomes to include margin-of-victory information. It does this by “redefining what it means to win” using a variable handicap to shift the threshold of paired comparison. The framework is general and has numerous applications in ranking, estimation, and time series prediction.

Quick start

Requirements: Python 2.7 or 3.3+ with numpy and scipy.

Install the latest release with pip:

pip install melo

Example usage:

import pkgutil
import numpy as np
from melo import Melo

# the package comes pre-bundled with an example dataset
pkgdata = pkgutil.get_data('melo', 'nfl.dat').splitlines()
dates, teams_home, scores_home, teams_away, scores_away = zip(
    *[l.split() for l in pkgdata[1:]])

# define a binary comparison statistic
spreads = [int(h) - int(a) for h, a
    in zip(scores_home, scores_away)]

# hyperparameters and options
k = 0.245
lines = np.arange(-59.5, 60.5)
regress = lambda months: .413 if months > 3 else 0
regress_unit = 'month'
commutes = False

# initialize the estimator
nfl_spreads = Melo(k, lines=lines, commutes=commutes,
                   regress=regress, regress_unit=regress_unit)

# fit the estimator to the training data, teams_home, teams_away, spreads)

# specify a comparison time
time = nfl_spreads.last_update

# predict the mean outcome at that time
mean = nfl_spreads.mean(time, 'CLE', 'KC')
print('CLE VS KC: {}'.format(mean))

# rank nfl teams at end of 2018 regular season
rankings = nfl_spreads.rank(time, statistic='mean')
for team, rank in rankings:
    print('{}: {}'.format(team, rank))