That is the question by a recent paper in by Baugh et al. (2020) in JAMA Open. The authors surveyed nearly 300 current college football players from 4 teams in the 5 most competitive NCAA football conferences. They found that:
Of the 265 participants for whom all relevant data were available, 111 (42%) underestimated their risk of concussion (χ2 = 98.6; P = .003). A similar proportion of athletes (113 [43%]) underestimated their risk of injury, although this was not statistically significant (χ2 = 34.0; P = .09). An alternative analytic strategy suggested that 241 athletes (91%) underestimated their risk of injury (Wilcoxon statistic, 7865; P < .001) and 167 (63%) underestimated their risk of concussion (Wilcoxon statistic, 26 768; P < .001).
Overall, the answer seems like that answer is ‘yes’, athletes are underestimating their risk of concussion, but not at widely low rates. This study does not, however, get at whether individuals perceive the severity of a concussion accurately. In expected value terms, football’s risk involves likely probability of injury times the expected injury levels conditional on the event occurring. The Baugh et al. study only deals with the first issue. A follow-on study should examine whether football players are accurately understanding concussion severity.
An important topic to insure that football players and their families internalize risks and benefits of playing this game.