Whole-History Rating

Whole-History Rating (WHR) is a time-aware Bradley-Terry model. It estimates one rating for each day on which a competitor played and links consecutive ratings with a Wiener-process prior. Later results can therefore revise earlier ratings while the curve remains smoother when games are close together.

from datetime import datetime
from elote import WholeHistoryRatingCompetitor

alice = WholeHistoryRatingCompetitor(w2=300.0)
bob = WholeHistoryRatingCompetitor(w2=300.0)
alice.beat(bob, match_time=datetime(2025, 1, 10))
print(alice.rating)
print(alice.rating_at(datetime(2025, 1, 10)))
print(alice.rating_history())

Fitting is lazy: results mark the connected component dirty, while rating, rating_at, rating_history and expected_score trigger at most max_iterations Newton sweeps. precision controls the Elo-point convergence tolerance. Lower values cost more but give a tighter fit.

w2 is the per-day variance in Elo points squared. A larger value permits faster rating movement between playing days; a smaller value makes the curve smoother.

Reference

Coulom, R. (2008). Whole-History Rating: A Bayesian Rating System for Players of Time-Varying Strength.