## Bayesian Analysis

### A Comparison of Truncated and Time-Weighted Plackett–Luce Models for Probabilistic Forecasting of Formula One Results

#### Abstract

We compare several variants of the Plackett–Luce model, a commonly-used model for permutations, in terms of their ability to accurately forecast Formula One motor racing results. A Bayesian approach to forecasting is adopted and a Gibbs sampler for sampling from the posterior distributions of the model parameters is described. Prediction of the results from the 2010 to 2013 Formula One seasons highlights clear strengths and weaknesses of the various models. We demonstrate by example that down weighting past results can improve forecasts, and that some of the models we consider are competitive with the forecasts implied by bookmakers odds.

#### Article information

Source
Bayesian Anal., Volume 13, Number 2 (2018), 335-358.

Dates
First available in Project Euclid: 28 February 2017

Permanent link to this document
https://projecteuclid.org/euclid.ba/1488250819

Digital Object Identifier
doi:10.1214/17-BA1048

Mathematical Reviews number (MathSciNet)
MR3780426

Zentralblatt MATH identifier
06989951

#### Citation

Henderson, Daniel A.; Kirrane, Liam J. A Comparison of Truncated and Time-Weighted Plackett–Luce Models for Probabilistic Forecasting of Formula One Results. Bayesian Anal. 13 (2018), no. 2, 335--358. doi:10.1214/17-BA1048. https://projecteuclid.org/euclid.ba/1488250819

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#### Supplemental materials

• Supplementary material: Supplementary Material for “A comparison of truncated and time-weighted Plackett–Luce models for probabilistic forecasting of Formula One results”. The Supplementary material contains further details on the Gibbs sampling algorithm of Section 3, details of predictive simulations, an analysis of sensitivity of predictions to prior assumptions and an investigation into optimal choices of the time weighting parameter.