# Example¶

The elora package comes pre-bundled with a text file containing the final score of all regular season NFL games 2009–2018. Let’s load this dataset and use the model to predict the point spread and point total of “future” games using the historical game data.

## Training data¶

First, let’s import Elora and load the nfl.dat package data. Let’s also load numpy for convenience.

import pkgutil
import numpy as np

from elora import Elora

# the package comes pre-bundled with an example NFL dataset
pkgdata = pkgutil.get_data('elora', 'nfl.dat').splitlines()


The nfl.dat package data looks like this:

# date, home, score, away, score
2009-09-10 PIT 13 TEN 10
2009-09-13 ATL 19 MIA  7
2009-09-13 BAL 38 KC  24
2009-09-13 CAR 10 PHI 38
2009-09-13 CIN  7 DEN 12
2009-09-13 CLE 20 MIN 34
2009-09-13 HOU  7 NYJ 24
2009-09-13 IND 14 JAC 12
2009-09-13 NO  45 DET 27
2009-09-13 TB  21 DAL 34
2009-09-13 ARI 16 SF  20
2009-09-13 NYG 23 WAS 17
...


After we’ve loaded the package data, we’ll need to split the game data into separate columns.

dates, teams_home, scores_home, teams_away, scores_away = zip(
*[l.split() for l in pkgdata[1:]])


Let’s start by analyzing the home team point spreads.

spreads = [int(h) - int(a) for h, a in zip(scores_home, scores_away)]


Note, if I swap the order of scores_home and scores_away, my definition of the point spread picks up a minus sign. This means the point spread binary comparison anti-commutes under label interchange. Let’s define a new constant to pass this information to the Elora class constructor.

commutes = False


Much like traditional Elo ratings, the elora model includes a hyperparameter k that controls how fast the ratings update. Prior experience indicates that

k = 0.245


is a good choice for NFL games. Generally speaking, this hyperparameter must be tuned for each use case.

We’ll also select an Elora regressor scale parameter to set the standard deviation of our comparison predictions. A larger scale parameter indicates greater uncertainty.

scale = 13.5


These parameters will be passsed to the elora class constructor momentarily. First, we’ll want to subclass the elora.Elora regressor in order to further customize some of its class methods. Namely, we’ll redefine the regression_coeff class method so that it regresses our ratings to their median value by a fixed fraction each offseason.

class EloraNFL(Elora):
def regression_coeff(self, elapsed_time):
elapsed_days = elapsed_time / np.timedelta64(1, 'D')
return .6 if elapsed_days > 90 else 1


Using the previous components, the model estimator is initialized as follows:

# instantiate the estimator class object


Note that at this point we’ve not yet trained the model on any data; we’ve simply specified various hyperparameters and auxillary options. The model is trained by calling its fit function on the training data:

nfl_spreads.fit(dates, teams_home, teams_away, spreads)


Once the model is conditioned to the data, we can easily generate predictions by calling its various instance methods:

# time one day after the last model update
time = nfl_spreads.last_update_time + np.timedelta64(1, 'D')

# predict the mean outcome at 'time'

# predict the interquartile range at 'time'
nfl_spreads.quantile([.25, .5, .75], time, 'CLE', 'KC')

# predict the win probability at 'time'

# generate prediction samples at 'time'


Furthermore, the model can rank teams by their expected performance against a league average opponent on a neutral field. Let’s evaluate this ranking at the end of the 2018–2019 season.

# end of the 2018–2019 season
time = nfl_spreads.last_update_time + np.timedelta64(1, 'D')

# rank teams by expected mean spread against average team


## Point total predictions¶

Everything demonstrated so far can also be applied to point total comparisons with a few small changes. First, let’s create the array of point total comparisons.

totals = [int(h) + int(a) for h, a in zip(scores_home, scores_away)]


Next, we’ll need to set

commutes = True


since the point total comparisons are invariant under label interchange. Finally, we’ll need to provide somewhat different inputs for the k and scale hyperparameters, and the regression_coeff class method:

k = .03
scale = 13.5

class EloraNFL(Elora):
def regression_coeff(self, elapsed_time):
elapsed_days = elapsed_time / np.timedelta64(1, 'D')
return .6 if elapsed_days > 90 else 1


Putting all the pieces together,

nfl_totals = EloraNFL(k, scale=scale, commutes=False)

nfl_totals.fit(dates, teams_home, teams_away, totals)


And voila! We can easily predict the outcome of a future point total comparison.

# time one day after the last model update
time = nfl_totals.last_update_time + np.timedelta64(1, 'D')

# predict the mean outcome at 'time'
nfl_totals.mean(time, 'CLE', 'KC')