Quantifying the probability of a shot in women’s collegiate soccer through absorbing Markov chains

A Bayesian model is used to evaluate the probability that a given skill performed in a specified area of the field will lead to a predetermined outcome by using discrete absorbing Markov chains. The transient states of the Markov process are defined by unique skill-area combinations. The absorbing states of the Markov process are defined by a shot, turnover, or bad turnover. Defining the states in this manner allows the probability of a transient state leading to an absorbing state to be derived. A non-informative prior specification of transition counts is used to permit the data to define the posterior distribution. A web application was created to collect play-by-play data from 34 Division 1 NCAA Women’s soccer matches for the 2013–2014 seasons. A prudent construction of updated transition probabilities facilitates a transformation through Monte Carlo simulation to obtain marginal probability estimates of each unique skill-area combination leading to an absorbing state. For each season, marginal probability estimates for given skills are compared both across and within areas to determine which skills and areas of the field are most advantageous.