This is written for By Night, but is applicable to regular OSR games as well.
Fisticuffs are commonplace in pulp stories, and many modern day characters may find themselves in a situation where they are not armed, but having to defend themselves.
Rather than hit point damage, unarmed attacks primarily inflict "shock". Base shock is 1D4, modified by strength bonus. Each point of shock gives a 10% chance of the target being stunned, dazed or otherwise incapacitated.
While still active, a character may spend a round inactive. This permits them to roll a Constitution check. On a success, 1 point of shock is shaken off.
Incapacitated characters generally come to in 2D6 rounds.
Creatures that are larger and tougher than humans, such as a bear or shark, cannot be incapacitated under normal circumstances by un-armed attacks. Instead, each point shock gives a 5% chance of driving the creature away for 1D6 rounds.