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.
