Additional time error in association football is associated with interruption type and goal difference

This study explores whether referees are biased when awarding additional time in Association Football. We collected data on Awarded Additional Time (AAT) granted by the referees and Calculated Additional Time (CAT), representing the interruption time meant to be considered for additional time according to the rulebook. Analysis of Additional Time Error (ATE), given as the difference between CAT and AAT, in the second half of German football Bundesliga season 2022/2023, revealed that referees award less AAT than warranted by interruptions (ATE = 2:10 ± 2:24 min). Multiple Linear Regression between either AAT or ATE and the duration of interruption types suggests that referees do not consider Goal Celebrations (for AAT: β = 0.09, p = 0.09, for ATE: β = 0.52, p < 0.01) as important as Substitutions (for AAT: β = 0.25, p < 0.01, for ATE: β = 0.03, p = 0.68), Injuries (for AAT: β = 0.35, p < 0.01, for ATE: β = 0.28, p < 0.01) and VAR (for AAT: β = 0.38, p < 0.01, for ATE: β = 0.10, p = 0.10). Mann-Whitney U-tests indicate a referee's bias towards allocating insufficient AAT in matches with a goal difference greater than one compared (ATE = 3:16 ± 2:26 min) to the other matches (ATE = 1:18 ± 2:00 min) (p < 0.01, ES = 0.17). The Kruskal-Wallis H tests also show slight home bias from the referees, indicating that ATE is higher when the home team is leading more than one goal (ATE = 3:36 ± 2:36 min) (p < 0.01, ES = 0.15). In conclusion, although German Bundesliga referees adhere to the Laws of the Game, they show inconsistencies in handling different interruption types and matches with decisive outcomes. The findings suggest potential enhancement in referee training and decision-making processes and should be considered when advancing the game.