  Multi-competitor races often feature complicated within-race strategies that
are difficult to capture when training data on race outcome level data.
Further, models which do not account for such strategic effects may suffer from
confounded inferences and predictions. In this work we develop a general
generative model for multi-competitor races which allows analysts to explicitly
model certain strategic effects such as changing lanes or drafting and separate
these impacts from competitor ability. The generative model allows one to
simulate full races from any real or created starting position which opens new
avenues for attributing value to within-race actions and to perform
counter-factual analyses. This methodology is sufficiently general to apply to
any track based multi-competitor races where both tracking data is available
and competitor movement is well described by simultaneous forward and lateral
movements. We apply this methodology to one-mile horse races using data
provided by the New York Racing Association (NYRA) and the New York
Thoroughbred Horsemen's Association (NYTHA) for the Big Data Derby 2022 Kaggle
Competition. This data features granular tracking data for all horses at the
frame-level (occurring at approximately 4hz). We demonstrate how this model can
yield new inferences, such as the estimation of horse-specific speed profiles
which vary over phases of the race, and examples of posterior predictive
counterfactual simulations to answer questions of interest such as starting
lane impacts on race outcomes.
