In various embodiments, the persistent modifiers are persistent multipliers. Generally, in certain such embodiments, the multi-play game has a plurality of separate outcome-generating elements and is associated with a plurality of separate multiplier banks. Each multiplier bank is associated with a persistent multiplier maintained from game play to game play until distributed. When a random multiplier increase event occurs, the gaming system increases the persistent multiplier of at least one of the multiplier banks. When a random multiplier distribution event occurs for one of the multiplier banks, the gaming system distributes the persistent multiplier of that multiplier bank among the plurality of outcome-generating elements. The gaming system does so by determining a plurality of individual multipliers based on that persistent multiplier and assigning each individual multiplier to one of the outcome-generating elements. The gaming system uses the individual multipliers to modify any awards associated with their respective assigned outcome-generating elements.