Recent studies of plant-animal mutualistic networks have assumed that interaction frequency between mutualists predicts species impacts (population-level effects), and that field estimates of interaction strength (per-interaction effects) are unnecessary. Although existing evidence supports this assumption for the effect of animals on plants, no studies have evaluated it for the reciprocal effect of plants on animals. We evaluate this assumption using data on the reproductive effects of pollinators on plants and the reciprocal reproductive effects of plants on pollinators. The magnitude of species impacts of plants on pollinators, the reciprocal impacts of pollinators on plants, and their asymmetry were well predicted by interaction frequency. However, interaction strength was a key determinant of the sign of species impacts. These results underscore the importance of quantifying interaction strength in studies of mutualistic networks. We also show that the distributions of interaction strengths and species impacts are highly skewed, with few strong and many weak interactions. This skewed distribution matches the pattern observed in food webs, suggesting that the community-wide organization of species interactions is fundamentally similar between mutualistic and antagonistic interactions. Our results have profound ecological implications, given the key role of interaction strength for community stability.