elo-grad 0.4.0

Extended Elo rating system implementation exploiting the equivalence with logistic regression.

:chess_pawn: EloGrad

Extended Elo rating system implementation exploiting 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 models are scikit-learn compatible.

:sparkles: Features

• Standard Elo rating system for binary outcomes.
  • pandas and scikit-learn compatible.
  • See examples/nba.ipynb for an example using NBA data.
• Elo rating system for binary outcomes with additional regressors, e.g. home advantage.
  • See Additional Regressors for the theory and examples/nba.ipynb for an example using NBA data.
• Elo rating system for count data based on Poisson regression.
  • pandas and scikit-learn compatible.
  • See Poisson Elo for the theory and examples/football.ipynb for an example using Premier League football data.

:book: Installation

You can install elo-grad with:

pip install elo-grad

:zap: 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]

:clipboard: Minimal Example

from elo_grad import EloEstimator, Regressor

# Input DataFrame with sorted index of Unix timestamps
# and columns entity_1 | entity_2 | score | home
# where 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",
    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

:compass: Roadmap

In rough order, things we want to add are:

• Regularization (L1 & L2)
• Support for Polars
• Head-to-head ratings
• Skellam model support
• Interaction terms
• Other optimizers, e.g. momentum
• Extend plotting support, e.g. plotly
• Support for handling correlation in scores
• Explore any ways we can approximate standard errors for the ratings

:blue_book: 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