The right man in the right place? Substitutions and goal-scoring in soccer

Objectives: We investigate how the goal-scoring probability in international club soccer evolves after player substitutions. Design: To this end, we analyse rich data concerning 2,025 recent soccer games played in the two most prestigious club soccer competitions, i.e. the UEFA Champions League and the UEFA Europa League. Method: As first in the literature, we control for within-game dynamics by applying a minute-by-minute bivariate probit approach. Results/Conclusions: We find that teams experience increased goal-scoring probabilities after their first and second substitution and a decreased probability of scoring after the three substitutions made by their opponent. This association is less distinct during the first 3 mins after the substitution, which is consistent with difficulties to adapt to (i) the game intensity by the substitute player or (ii) tactical changes by the entire team. Furthermore, we find that the change in the goal-scoring probability is substantially bigger if the team is losing at the moment of the substitution.