Simulating the progression of a professional snooker frame

Keywords OR in sports; Snooker; Monte Carlo simulation Highlights * A Monte-Carlo simulation of the progression of a snooker frame is developed. * The development of dynamic measures of player performance is advocated. * Analysis of how a frame's progression and outcome depend on player ability. * Assessment of the influence of the break-off shot on the progression of a frame. * Indictive strategies are conceived when snookered or faced with a risky pot. Abstract This paper is the first to develop a Monte Carlo simulation model of a snooker frame, using post-match video analysis of over 30,000 shots to inform the probability that a top professional will pot a ball on each shot depending on the number of balls remaining on the table and the status of their current visit to the table. We demonstrate that this accurately reflects the progression of a frame at this level, advocating new approaches in viewing a frame as a succession of scoring visits and in using dynamic measures to evaluate player performance. The simulation model also produces a realistic expectation of the probability that the frame will be won from any given position. The model is then used to analyse the effectiveness of the break-off shot and the influence that this has on the outcome of the frame. We also use simulated outcomes to evaluate the choice between taking on a risky pot or playing safe and the merits of alternative approaches to escaping from a snooker. Author Affiliation: Management Science, Lancaster University Management School, LA1 4YX, UK * Corresponding author. Article History: Received 5 February 2021; Accepted 9 November 2022 Byline: James A.P. Collingwood [jacollingwood@yahoo.com] (*), Michael Wright, Roger J. Brooks