The gaming system and method disclosed herein provides a plurality of players with an opportunity to win a plurality of progressive awards maintained by the gaming system. The gaming system accumulates a quantity of progressive event points for each player playing at one of the gaming machines in the gaming system. In one embodiment, the gaming system uses an accumulated quantity of progressive event points for a designated player to determine which one or more of the progressive awards the designated player wins. In another embodiment, the gaming system uses an accumulated quantity of progressive event points to determine the designated player's probability of winning one or more of the progressive awards. Accordingly, the gaming system provides a point-based system in which either a progressive award to win or a probability of winning a progressive award is determined based on the quantities of progressive event points accumulated by the players.