Social foraging shows unexpected features such as the existence of a group size threshold to accomplish a successful hunt. Above this threshold, additional individuals do not increase the probability of capturing the prey. Recent direct observations of wolves (Canis lupus) in Yellowstone Park show that the group size threshold when hunting its most formidable prey, bison (Bison bison), is nearly three times greater than when hunting elk (Cervus elaphus), a prey that is considerably less challenging to capture than bison. These observations provide empirical support to a computational particle model of group hunting which was previously shown to be effective in explaining why hunting success peaks at apparently small pack sizes when hunting elk. The model is based on considering two critical distances between wolves and prey: the minimal safe distance at which wolves stand from the prey, and the avoidance distance at which wolves move away from each other when they approach the prey. The minimal safe distance is longer when the prey is more dangerous to hunt. We show that the model explains effectively that the group size threshold is greater when the minimal safe distance is longer. Actually, the model reveals that the group size threshold results from the nonlinear combination of the variations of both critical distances. Although both distances are longer when the prey is more dangerous, they contribute oppositely to the value of the group size threshold: the group size threshold is smaller when the avoidance distance is longer. This unexpected mechanism gives rise to a global increase of the group size threshold when considering bison with respect to elk, but other prey more dangerous than elk can lead to specific critical distances that can give rise to the same group size threshold. Our results show that the computational model can guide further research on group size effects, suggesting that more experimental observations should be obtained for other kind of prey as e.g. moose (Alces alces).