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This paper presents two complementary frameworks to optimize Formula 1 race strategies, jointly accounting for energy allocation, tire wear and pit stop timing. First, the race scenario is modeled using lap time maps and a dynamic tire wear…
There is enduring interest in disentangling the effects of skill and luck in sport. A key issue in Formula 1 is distinguishing between car-level and driver-level effects. Four elite teams currently dominate Formula 1 and have won every…
Successful performance in Formula One is determined by combination of both the driver's skill and race-car constructor advantage. This makes key performance questions in the sport difficult to answer. For example, who is the best Formula…
Inspired by applications in sports where the skill of players or teams competing against each other varies over time, we propose a probabilistic model of pairwise-comparison outcomes that can capture a wide range of time dynamics. We…
Formula 1 performance is a combination of the car's ability and the driver's ability. While a given race or season can tell you how well a car and driver performed jointly, isolating the individual impact of the driver and constructor…
We derive some simple relations that demonstrate how the posterior convergence rate is related to two driving factors: a "penalized divergence" of the prior, which measures the ability of the prior distribution to propose a nonnegligible…
Formula One race weekends are structured around multiple sessions: practices, qualifying, and the Grand Prix itself, each contributing to final race performance. This study analyzes nearly two decades of races, encompassing 7,800…
Computing the probability of a formula given the probabilities or weights associated with other formulas is a natural extension of logical inference to the probabilistic setting. Surprisingly, this problem has received little attention in…
One-directional traffic on two-lanes is modeled in the framework of a spring-block type model. A fraction $q$ of the cars are allowed to change lanes, following simple dynamical rules, while the other cars keep their initial lane. The…
Rankings are central to decision-making in fields ranging from education to online platforms, yet classical deterministic methods such as the Borda count method or Copeland-type pairwise methods ignore uncertainty due to sampling noise or…
Informative path-planning is a well established approach to visual-servoing and active viewpoint selection in robotics, but typically assumes that a suitable cost function or goal state is known. This work considers the inverse problem,…
Scoring rules aggregate individual rankings by assigning some points to each position in each ranking such that the total sum of points provides the overall ranking of the alternatives. They are widely used in sports competitions consisting…
A model is proposed to allocate Formula One World Championship prize money among the constructors. The methodology is based on pairwise comparison matrices, allows for the use of any weighting method, and makes possible to tune the level of…
We present a physically-inspired model and an efficient algorithm to infer hierarchical rankings of nodes in directed networks. It assigns real-valued ranks to nodes rather than simply ordinal ranks, and it formalizes the assumption that…
Naturalistic driving data were applied to study driver acceleration behaviour, and a probability model of the driver was proposed. First, the question of whether the database is large enough is resolved using kernel density estimation and…
In Formula 1, race strategies are adapted according to evolving race conditions and competitors' actions. This paper proposes a reinforcement learning approach for multi-agent race strategy optimization. Agents learn to balance energy…
The effects of real-time provision of travel-time information on the behaviour of drivers are considered. The model of Marecek et al. [arXiv:1406.7639, Int. J. Control 88(10), 2015] is extended to consider uncertainty in the response of a…
Engineering a high-performance race car requires a direct consideration of the human driver using real-world tests or Human-Driver-in-the-Loop simulations. Apart from that, offline simulations with human-like race driver models could make…
We introduce a counting process to model the random occurrence in time of car traffic accidents, taking into account some aspects of the self-excitation typical of this phenomenon. By combining methods from probability and differential…
The task of ranking individuals or teams, based on a set of comparisons between pairs, arises in various contexts, including sporting competitions and the analysis of dominance hierarchies among animals and humans. Given data on which…