Higher level of Doctor doesn't mean less number of injuries, it means smaller injuries in terms of time.
Prove it.
Doctors help reduce the severity of player injuries. Once a player is injured, a Doctor will also help him heal more quickly, but the effect is much smaller than the initial reduction in severity. Doctors can have the following specialties:
se·ver·i·ty (s-vr-t)n. pl. se·ver·i·ties1. The state or quality of being severe.2. The act or an instance of severe behavior, especially punishment.