EloGrad

Extended Elo rating system implementation based on the equivalence with logistic regression.

EloGrad (Elo as Gradient descent) leverages the framing of the Elo rating system as logistic regression with stochastic gradient descent (see Elo as Logistic Regression for a walkthrough) to offer a collection of extensions to the rating system. All rating systems are narwhals compatible for dataframe libraries with full API support.

Features

• Standard Elo rating system for binary outcomes.
  • narwhals compatible.
  • A scikit-learn compatible implementation is available in the sklearn submodule.
  • See examples/nba.ipynb for an example using NBA data and polars.
• Elo rating system for binary outcomes with additional regressors, e.g. home advantage.
  • L1 and L2 regularisation supported for additional regressors (see Regularisation).
  • See Additional Regressors for the theory and examples/nba.ipynb for an example using NBA data and polars.
• Elo rating system for count data based on Poisson regression.
  • narwhals compatible.
  • A scikit-learn compatible implementation is available in the sklearn submodule.
  • See Poisson Elo for the theory and examples/football.ipynb for an example using Premier League football data and pandas.

Installation

You can install elo-grad with:

pip install elo-grad

For the scikit-learn compatible rating systems, the sklearn optional dependencies must be installed as:

pip install elo-grad[sklearn]

Quick Start

Detailed example notebooks are provided in the examples/ directory. To install any extra dependencies required to run the notebooks install with:

pip install elo-grad[examples]

Minimal Example

from elo_grad import EloEstimator, Regressor

# Input dataframe with columns 
# t | entity_1 | entity_2 | score | home
# sorted (in ascending order) on t
# where t is the Unix timestamp (in seconds) of
# the game and score = 1 if player_1 won and score = 0 
# if player_2 won and home is a boolean flag indicating 
# if entity_1 has home advantage.
df = ...
estimator = EloEstimator(
    k_factor=20, 
    default_init_rating=1200,
    entity_cols=("player_1", "player_2"),
    score_col="result",
    date_col="t",
    init_ratings=dict(home=(None, 0)),
    additional_regressors=[Regressor(name='home', k_factor=0.1)],
)
# Get expected scores
expected_scores = estimator.predict_proba(df)
# Get final ratings (of form (Unix timestamp, rating))
ratings = estimator.model.ratings

Roadmap

In rough order, things we want to add are:

• Head-to-head ratings
• Bivariate Poisson
• Interaction terms
• Other optimizers, e.g. momentum
• Extend plotting support, e.g. plotly
• Support hierarchical matches, e.g. tennis matches with sets and games

References

1. Elo rating system: https://en.wikipedia.org/wiki/Elo_rating_system
2. Elo rating system as logistic regression with stochastic gradient descent: https://stmorse.github.io/journal/Elo.html
3. Elo rating system for NFL predictions: https://fivethirtyeight.com/methodology/how-our-nfl-predictions-work/
4. Elo rating system based on Poisson regression: https://github.com/octonion/puzzles/blob/master/elo/poisson.py