In foul decision-making by football referees, visual search is important for gathering task-specific information to determine whether a foul has occurred. Yet, little is known about the visual search behaviours underpinning excellent on-field decisions. The aim of this study was to examine the on-field visual search behaviour of elite and sub-elite football referees when calling a foul during a match. In doing so, we have also compared the accuracy and gaze behaviour for correct and incorrect calls. Elite and sub-elite referees (elite: N = 5, Mage ± SD = 29.8 ± 4.7yrs, Mexperience ± SD = 14.8 ± 3.7yrs; sub-elite: N = 9, Mage ± SD = 23.1 ± 1.6yrs, Mexperience ± SD = 8.4 ± 1.8yrs) officiated an actual football game while wearing a mobile eye-tracker, with on-field visual search behaviour compared between skill levels when calling a foul (Nelite = 66; Nsub−elite = 92). Results revealed that elite referees relied on a higher search rate (more fixations of shorter duration) compared to sub-elites, but with no differences in where they allocated their gaze, indicating that elites searched faster but did not necessarily direct gaze towards different locations. Correct decisions were associated with higher gaze entropy (i.e. less structure). In relying on more structured gaze patterns when making incorrect decisions, referees may fail to pick-up information specific to the foul situation. Referee development programmes might benefit by challenging the speed of information pickup but by avoiding pre-determined gaze patterns to improve the interpretation of fouls and increase the decision-making performance of referees.
Although causal inference has shown great value in estimating effect sizes in, for instance, physics, medical studies, and economics, it is rarely used in sports science. Targeted Maximum Likelihood Estimation (TMLE) is a modern method for performing causal inference. TMLE is forgiving in the misspecification of the causal model and improves the estimation of effect sizes using machine-learning methods. We demonstrate the advantage of TMLE in sports science by comparing the calculated effect size with a Generalized Linear Model (GLM). In this study, we introduce TMLE and provide a roadmap for making causal inference and apply the roadmap along with the methods mentioned above in a simulation study and case study investigating the influence of substitutions on the physical performance of the entire soccer team (i.e., the effect size of substitutions on the total physical performance). We construct a causal model, a misspecified causal model, a simulation dataset, and an observed tracking dataset of individual players from 302 elite soccer matches. The simulation dataset results show that TMLE outperforms GLM in estimating the effect size of the substitutions on the total physical performance. Furthermore, TMLE is most robust against model misspecification in both the simulation and the tracking dataset. However, independent of the method used in the tracking dataset, it was found that substitutes increase the physical performance of the entire soccer team.