A gaming system includes a gaming machine for redeeming an accrued attribute in subsequent plays of a wagering game. A wagering game instance may include a randomly triggered bonus game. One or more occurrences, events, or conditions are accrued in a tally during the bonus game. The tally grants an attribute for redemption in one or more subsequent randomly generated outcomes (e.g., subsequent plays of the wagering game, spins of the bonus game, etc.). The occurrences, events, or conditions may include any quantifiable measurement, including a number of winning, losing, or performed spins of the bonus game, appearance of specific symbols, wins over a threshold amount, etc. The resulting attribute(s) diminish over time and may include a win amount multiplier, a number of added symbols to one or more reels, a modified math model for a predetermined number of spins, additional game features or eligibility, etc.