For decades, researchers have categorized species as “edge-loving” or “edge-avoiding”, but recent studies that show inconsistencies in responses have called these labels into question and led to a sense that edge effects are idiosyncratic and difficult to understand. We suggest that species would be better categorized according to their sensitivity to edges, not the direction of observed responses because no species should be expected to show the same response to all edge types. Measures of edge sensitivity will apply widely across taxa and landscapes and allow metrics that are broadly comparable, making generalities easier to discern. Finally, while the direction of observed edge responses remains a critical (but largely understood) dynamic, most reported edge responses are neutral, so discovering when species are least likely to respond to edges will increase our understanding of edge ecology and associated fragmentation effects. We offer a case study that measures edge sensitivity of 15 butterfly species at 12 edge types. We found that sensitivity is weakly related to vulnerability to predation, but more importantly we show how our results generate new predictions about edge sensitivity that can be explored in future studies.