  We propose a bottom-up approach to the study of possession and its outcomes
for association football, based on probabilistic finite state automata with
transition probabilities described by a Markov process. We show how even a very
simple model yields faithful approximations to the distribution of passing
sequences and chances of taking shots for English Premier League teams, which
we fit using a whole season of granular game data (380 games). We compare the
resulting model with classical top-down distributions traditionally used to
describe possessions, showing that the Markov models yield a more accurate
asymptotic behaviour.
