Getting Your Eye In: A Bayesian Analysis of Early Dismissals in Cricket

A Bayesian Survival Analysis method is motivated and developed for analysing sequences of scores made by a batsman in test or first class cricket. In particular, we expect the presence of an effect whereby the distribution of scores has more probability near zero than a geometric distribution, due to the fact that batting is more difficult when the batsman is new at the crease. A Metropolis-Hastings algorithm is found to be efficient at estimating the proposed parameters, allowing us to quantify exactly how large this early-innings effect is, and how long a batsman needs to be at the crease in order to ``get their eye in''. Applying this model to several modern players shows that a batsman is typically only playing at about half of their potential ability when they first arrive at the crease, and gets their eye in surprisingly quickly. Additionally, some players are more ``robust'' (have a smaller early-innings effect) than others, which may have implications for selection policy.