Modelling a Simulation Environment to analyse Race Strategy in Formula E

Abstract

In this report, I investigate strategic decision making in the Formula E racing series for Porsche. Formula E is an electric car circuit racing series, where the main tasks of race strategy are allocating energy consumption across the race and timing mandatory "attack mode" activations (similar to small-scale pitstops). I work on a flawed existing tool that simulates Formula E races with the goal of identifying optimal strategies. By learning from Porsche's experience and comparing the tool against related literature, I investigate how to model a Formula E race.

To do this, I outline a method to measure the realism of our simulated races. By defining a race as a set of stochastic processes approximated with empirical data, I find a dissimilarity metric for the underlying probability distributions of two collections of races. My dissimilarity metric is based on Kantorovich's formulation of the optimal transport problem as applied to probability measures. The cost function used within this dissimilarity metric is based on how differently two drivers' individual races evolve from start to end, using gaps between times of arrival.

I introduce various alterations to the race model, based on experience and related literature. Through applying my metric to different versions of my race model, I evaluate these alterations and find improvements. Doing so shows measurable gains in the race model were achieved; this is also checked by measuring the prediction error of simulations versus the true observed race.

My approach yields a scalar metric that allows fast and straightforward tuning of any race model. It uses a high degree of aggregation to successfully compare otherwise not trivially comparable data. While already delivering a significantly improved model, my dissimilarity metric in conjunction with the prediction error-based metrics can help to find further improvements in the future. This is also independent of the used simulation method or format, since my metric only requires realisations of true and simulated races as input.