The gaming system and method disclosed herein provides that the probability that a group bonus event will be triggered for a plurality of gaming devices in the gaming system is independent of the number of players that are currently playing such gaming devices. The gaming system and method disclosed herein further provides that different players that are wagering different amounts at different rates are provided different quantities of evaluation points such that if a group bonus event is triggered, different players are provided different group bonus event awards proportional to each individual player's wagering activity.