Fig. 2 Flowchart of the penalization decision-making task

data processing

Behavioral data:

An analysis of variance (ANOVA) on decision correctness revealed (Fig. 3) that the main effects of refereeing grade, decision type, and degree of foul play were all significant. Except for the interaction between decision type and referee rank, which was not significant, the interaction between degree of foul and referee rank, the interaction between decision type and degree of foul, and the interaction between decision type, degree of foul, and referee rank were all significant.

Figure 3 Results of correct decision-making rate

An ANOVA analysis of response times to decisions revealed (Figure 4) that the main effects of decision type and foul level were both significant, and the main effect of refereeing grade was not significant. The interaction between degree of foul and decision type was significant, and post hoc tests analyzed the response times of decisions for aggression level as faster than tactical influence and final call in the no foul condition.

Figure 4 Results at the time of decision-making response

Note: Error bars in the graphs are standard errors.

Behavioral outcomes:

High level referees have a significant advantage in light/no foul scenarios (e.g., high ACC 15-20% at no foul) due to ambiguous scenarios that require empirical integration;

Tactics influence decision-making with the longest reaction times (requiring integration of global information), but high level referees still maintain a high rate of correctness.

The results of the HbO ANOVA for all brain regions revealed that the main effect of referee rank was significant in the left dorsolateral superior frontal gyrus and the left middle frontal gyrus brain regions. The main effects of decision type were significant in the left dorsolateral superior frontal gyrus, left middle occipital gyrus, right dorsolateral superior frontal gyrus, and right anterior cingulate and paracingulate gyrus brain regions. The main effect of degree of foul play was significant in the left middle frontal gyrus, left inferior occipital gyrus, right inferior orbital frontal gyrus, and right middle occipital gyrus brain regions.

Fig. 5 Upper panel shows the manifestation of HbO oximetry activation in the left dorsolateral superior frontal gyrus (1) and the left middle frontal gyrus (2); the 

The following figure shows the results of two-by-two comparisons of referee rank variables at the decision type level in the frontal cortex

Note: * p

Figure 6 Upper panel shows HbO oxygen activation in the right middle occipital gyrus; lower panel shows the results of two-by-two comparisons of referee rank variables in the occipital cortex at the level of decision type

Note: # p

Figure 7 Results of HbO activation in prefrontal and occipital cortex

Note: The upper panel (1) shows the HbO activation performance of the right superior frontal gyrus and middle occipital gyrus brain regions in the no-foul condition in the different refereeing level conditions; (2) shows the HbO activation performance of the right inferior occipital gyrus brain region in the interaction of refereeing level and degree of foul; and the lower panel shows the results of two-by-two comparisons of the refereeing level variables in the corresponding conditions; *p

Since there was a significant difference in decision-making correctness between soccer referees of different levels in the no-foul and light-foul conditions, the present study further focused on the underlying neural mechanism differences by conducting two-way repeated measures ANOVA with 3 (refereeing level: national level and above, level 1, and level 3) × 3 (decision-making type: infringement level, tactical impact, and final penalty) in no-foul and light-foul, respectively.

Figure 8 Upper panel shows the performance of HbO activation in the left cuneate brain region in response to the interaction between referee rank, decision type, and degree of foul; the lower panel shows the results of the two-by-two comparisons of the referee rank variable performed in the corresponding conditions

Note: #p

Behavior-fNIRS association:

High level group:ACC is positively associated with bilateral prefrontal/occipital activation (e.g., moderate aggression level decision making is associated with the right anterior cingulate gyrus);

Low level group:The ACC is associated with more brain regions but is inefficient (e.g., extensive occipital lobe activation is required to support decision making when a secondary referee re-fouls), suggesting an uneconomical use of neural resources.

Since the correctness of penalty decisions varied significantly across referee levels, this study also performed a correlation analysis between correctness and fNIRS data:

Fig. 9 Heatmap of correctness of penalty decisions in relation to ROI of brain regions for different decision types and levels of fouls

Note: (1) National, (2) Level I and (3) Level III,* p

Mechanistic explanation: The prefrontal-occipital synergistic network supports efficient "perception→integration" processing, and high-level referees optimize this network empirically to reduce cognitive load (e.g., precise activation of the left cuneus during light fouls).