Mattia Stival and Lorenzo Schiavon’s contribution to the Discussion of ‘Flexible marked spatio-temporal point processes with applications to event sequences from association football’ by Narayanan, Kosmidis and Dellaportas

In association football there exist two types of in-game data: event-sequence data provide qualitative information on the succession of ball-related events in time and space; tracking data report with fine temporal granularity the positions of the ball and every player, in which the ball is just one of many interacting objects. Using event-sequence data, the authors place themselves within a local perspective, with the possible undesirable consequence of missing part of relevant information. To mitigate the impact of this shortcoming, multiple solutions can be accounted for. One option consists in enriching the event-sequence data with additional qualitative knowledge regarding the game situation. If also player tracking data are available, an alternative solution would be merging any observed event in the event-sequence data. When this extra information is missing, a careful model specification is required. The process defined by the authors represents a brilliant answer to this challenge. Since any sequence of ball-related events is partially determined by the player’s locations on the pitch, the observation of a certain sequence carries with it additional implicit information about team positioning. With this model, predictive probability density functions of the occurrence of any marked event can be derived. Hence, one could reconstruct via simulation the distribu- tion of the number of any event combination observable in a limited amount of time. This is allowed by joint modelling the event sequence and the time between subsequent events, with temporal modelling standing as a crucial feature to formulate in-game forecasts, and representing a key difference with respect to other frameworks based on a discrete-time game-states representation. A final remark concerns how model complexity is addressed. It would be interesting to compare the association rule learning method with alternative strategies in which the modelling assumptions or prior distributions directly account for sparsity.