winning

A generalization of factor multinomial probit models that scales to millions of variables

This package prices the winner of many: N competitors whose performances can follow any noise distribution and can be correlated through common factors. One pass over a shared survival field gives all N win probabilities, and the same pass yields removal counterfactuals and photo-finish tie densities. Calibration runs in the other direction, from observed shares back to abilities. Factor probit, Luce's softmax and the finite-temperature softmin are special cases of one parameterized race.

Quick start

from winning import race_probabilities, calibrate_abilities, removal_shares

p = race_probabilities(mu, V=V, D=D)     # all N shares, one field pass
mu_hat = calibrate_abilities(p, V=V, D=D)  # abilities back from shares
q = removal_shares(mu, V=V, D=D)         # P(j wins | i removed), all pairs

Max-wins semantics for the probit literature live in winning.probit (shares, calibrate_utilities, supplied-covariance fitting); the density-agnostic engine in winning.thurstone; the paper-faithful kernels in winning.factor.

Papers

• Scalable share calibration for factor multinomial probit models (2026, submitted). All shares of a correlated Gaussian race in one O(QNL) pass, matrix-free graph-Laplacian derivatives, and inversion of observed shares to utilities at ten thousand alternatives in under a minute. The algorithm ships here as winning.factor; every experiment is a committed script under research/experiments/.
• Rating Formula 1: a case for non-Gaussian noise in rating systems (2026). Seventy-five seasons of grands prix, a retirement-slab noise density, a qualifying control, and a stratified test against historical bookmaker odds.
• Inferring relative ability from winning probability (SIAM, 2021). The lattice algorithm this package grew from: recovering ability densities from a vector of win probabilities, as in pari-mutuel markets.
• Who ya gonna call? and How to respond to an RFQ: the same order statistic in trading, where the best response to a request for quote is a horse race entry.

Demos

• Fit a correlated race — the inverse problem, live: drag observed shares and a correlation, and the engine calibrates standalone abilities in the browser, against the naive independent fit.
• The photo-finish circuit — interactive: the race as a resistor network, computed live in your browser by the shipped algorithm. Click a runner to delete it and watch the share flow to factor-similar survivors, against the IIA prediction.
• race_field_demo.py — one shared survival field prices every competitor by division; the naive O(N²) route against the O(N) field.
• cavity_downdate_demo.py — the rank-one cavity twin: one inverse contains every leave-one-out inverse.
• js/factor — the calibration core in the browser: dependency-free JavaScript at machine-precision parity with the Python; it powers the circuit demo above.

Heritage

winning began as the reference implementation of the SIAM paper above and owns the core outright: the lattice machinery once split into the thurstone package is vendored back as winning.thurstone, and thurstone is maintained as a compatibility shim whose imports resolve here. Legacy 1.x imports still work. By Peter Cotton, with sibling packages at microprediction.

Get the source

github.com/microprediction/winning · pip install winning · Research scripts