Date Published: March 23, 2017
Publisher: Public Library of Science
Author(s): Stefanie Hüttermann, Benjamin Noël, Daniel Memmert, Jaime Sampaio.
The ability to simultaneously attend to multiple objects declines with increases in the visual angle separating distant objects. We explored whether these laboratory-measured limits on visual attentional spread generalize to a real life context: offside calls by soccer assistant referees. We coded all offside calls from a full year of first division German soccer matches. By determining the x-y coordinates of the relevant players and assistant referee on the soccer field we were able to calculate how far assistant referees had to spread their visual attention to perform well. Counterintuitively, assistant referees made fewer errors when they were farther away from the action due to an advantageous (smaller) visual angle on the game action. The pattern held even when we accounted for individual differences in a laboratory-based attentional spread measure of ten of the assistant referees. Our finding that errors are linked to smaller visual angles may explain the complaints of fans in some situations: Those seated directly behind the assistant referee, further from the players, might actually have it easier to make the right call because the relevant players would form a smaller visual angle.
Referees often take the blame for mistaken calls, but in some cases they may be at an unfair disadvantage. The perception of spatially disparate but simultaneous events might exceed the limits of their ability to spread attention; in laboratory tasks, the ability to make accurate judgments about spatially disparate objects diminishes as the visual angle between those objects increases .
We examined all offside calls from a complete season (2010/2011) of first German division soccer games (306 games). To be included in our analysis, the two involved offensive players, the defensive player as well as the assistant referee must have been clearly visible in the video. The initial coding yielded 355 flagged offside calls from 211 games. Assistant referees are supposed to position themselves at the offside line so that they can better judge the left/right position of the relevant offensive and defensive players. If the player deviates substantially from that position, their calls might be influenced not just by left/right judgments but also by differences in the relative depth of the players (see [3,6,7]). Oudejans et al.  observed perceptual illusions in which assistant referees were positioned more than 1m from the imaginary offside line. However, considering that there was no case in our data set in which the distance between the assistant referee and the offside line was bigger than 1m we did not have to control for that confound. The mean deviation from the offside line was 0.79m.
Even though our database included all calls from an entire season of a top league, the set of calls in our database cannot be treated as independent. Each assistant referee worked in multiple games, but the data set does not include enough observations per game and per assistant referee to examine the extent of non-independence of the calls. Given that assistant referees may differ in their bias to make calls and that those biases might vary across games (e.g., based on the aggressiveness of the play), treating each call as independent of other calls might not be justified. This issue has largely been ignored in other analyses of decision-making errors in sports, with papers regularly treating each observation as if it was independent of all other observations. Given this potential non-independence, the assumptions underlying null-hypothesis significance testing are possibly violated. If we had sufficient data to construct a full multi-level model incorporating games and assistant referees, we would be better able to account for any possible non-independence. Unfortunately, each game and assistant referee has too few calls to make such an analysis possible. Consequently, we present all of our data graphically and provide complete descriptive statistics rather than conducting null-hypothesis significance tests. All of our analyses should be treated as exploratory.
Although each game has two assistant referees, only one of them can make a call on a given play—each assistant referee is responsible for offside calls on one end of the pitch, and they maintain a position corresponding to the offside line (the defender’s position). Of the 50 assistant referees involved in the games included in our analyses in Study 1, 31 made calls in which all relevant players (passer, receiver, second last defender) and the respective assistant referee were clearly visible. To determine whether the decision performance of assistant referees on the field can be compared to generally existing visual/attentional limitations, we subsequently recruited ten of these 31 assistant referees who were willing and able to come to the lab to determine their maximum visual angle using a laboratory-based attentional spread measure . This measurement task has been used in a number of research studies (for a review see ) and has the potential to precisely quantify participants’ attentional spread or visual angle when two stimuli/events have to be perceived simultaneously. If a relationship between false decisions of assistant referees on the pitch and a limitation of their attentional spread in the lab will be found, consideration should be given to possible training concepts in the lab to improve performances on the soccer field in the long term.
Averaging across meridians, the maximum visual angle was 33.25° (SD = 3.05°). If the separation between both stimuli exceeded this threshold, performance decreased. A repeated measures ANOVA revealed that attentional spread differed as a function of meridian, F(2,18) = 4.492, p = .026, ηp2 = .333, and that it was largest along the horizontal meridian (M = 37.25°, SD = 7.12°; diagonal: M = 33.50°, SD = 5.92°; vertical: M = 29.00°, SD = 4.28°). Although we tested all meridians, for the following analyses, we focused exclusively on the horizontal meridian which is most likely related to the horizontal attentional spread measured in Study 1 (i.e., the separation between the passer and defender). The visual angle of the assistant referees was calculated via the horizontal attentional spread and their distance to the test area (i.e., attentional spread in the depth). (One needs to note here that opposed to Study 1, the attentional spread in the depth always stayed the same and the measured visual angle was only varied by the alteration of the horizontal attentional spread.)
Visual angle is associated with error rates in offside decisions by soccer assistant referees, just as it is for laboratory measures of attentional spread. Assistant referees are more error prone when the visual angle that is required in order to perceive the relevant players increases. Smaller separations in depth between the assistant referee and the players negatively affect the assistant referee’s decision-making, possibly due to an associated greater visual angle.