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A number of papers have recently appeared claiming to show that in the United States executions deter serious crime. There are many statistical problems with the data analyses reported. This article addresses the problem of “influence,” which occurs when a very small and atypical fraction of the data dominate the statistical results. The number of executions by state and year is the key explanatory variable, and most states in most years execute no one. A very few states in particular years execute more than five individuals. Such values represent about 1 percent of the available observations. Reanalyses of the existing data are presented showing that claims of deterrence are a statistical artifact of this anomalous 1 percent.