Time-rank duality in a simple model for Formula 1 racing

Two natural ways of modelling Formula 1 race outcomes are a probabilistic approach, based on the exponential distribution, and statistical regression modelling of the ranks. Both approaches lead to exactly soluble race-winning probabilities. Equating race-winning probabilities leads to a set of equivalent parametrisations. This time-rank duality is attractive theoretically and leads to new ways of dis-entangling driver and car level effects as well and a simplified Monte Carlo simulation algorithm. Results are illustrated by applications to the 2022 and 2023 Formula 1 seasons.