Butterfly eyespots are known to function in predator deflection and predator intimidation, but it is still unclear what factors cause eyespots to serve one function over the other. Both functions have been demonstrated in different species that varied in eyespot size, eyespot number and wing size, leaving the contribution of each of these factors to butterfly survival unclear. Here, we study how each of these factors contributes to eyespot function by using paper butterfly models, where each factor is varied in turn, and exposing these models to predation in the field. We find that the presence of multiple, small eyespots results in high predation, whereas single large eyespots (larger than 6 mm in diameter) results in low predation. These data indicate that single large eyespots intimidate predators, whereas multiple small eyespots produce a conspicuous, but non-intimidating signal to predators. We propose that eyespots may gain an intimidation function by increasing in size. Our measurements of eyespot size in 255 nymphalid butterfly species show that large eyespots are relatively rare and occur predominantly on ventral wing surfaces. By mapping eyespot size on the phylogeny of the family Nymphalidae, we show that these large eyespots, with a potential intimidation function, are dispersed throughout multiple nymphalid lineages, indicating that phylogeny is not a strong predictor of eyespot size.