We borrowed a playing card system years back that worked like this:
-A player is hit and calls for a medic.
-The medic rushes over and has the hit player draw blindly from the deck of cards.
-The card drawn by the player dictated how soon & where the player would regen back into the game.
-The medic puts the card back into the deck, telling the player how long they are out for.


Not the best system, but it worked for our group. The dice sounds way better though.