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In this work, we study the spatial evolutionary public goods game by introducing payoff aspirations for players, and players update their strategies with a stochastic probability depending on the difference between their collecting payoffs from neighbors and own payoff aspirations. A striking finding is that the cooperation level is a nonmonotonic function of the enhancement factor for a fixed aspiration level, which means a proper enhancement factor leads to the optimal cooperation level, whereas too high or too low enhancement factors will impede the evolution of cooperation for a particular aspiration level. This phenomenon is contradictory to the previous finding that a larger enhancement factor always leads a higher cooperation level. We explain this anomaly with a comprehensive analysis of the probabilities transitions of C players to D players as well as the reverse. The presented results may be not only helpful …