winning: Contest Win Probabilities and Ability Calibration
Solves the horse race problem in both directions. Infers
relative ability from win probabilities (or betting dividends) for
contests whose entrants share a common performance distribution,
with dead heats handled exactly, by the lattice fixed-point
algorithm of Cotton (2021) <doi:10.1137/19M1276261>. Also computes
all N win probabilities of a factor-structured Gaussian race
(multinomial probit with low-rank-plus-diagonal covariance) in one
shared-lattice pass of O(Q*N*L) operations, and inverts observed
shares to abilities by a damped Newton method with analytic slopes.
A dependency-free base-R port of the reference python package
'winning'. Performances are times: lowest wins.
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