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In recent years, the climate change research community has become highly interested in describing the anthropogenic influence on extreme weather events, commonly termed "event attribution." Limitations in the observational record and in computational resources motivate the use of uncoupled, atmosphere/land-only climate models with prescribed ocean conditions run over a short period, leading up to and including an event of interest. In this approach, large ensembles of high-resolution simulations can be generated under factual observed conditions and counterfactual conditions that might have been observed in the absence of human interference; these can be used to estimate the change in probability of the given event due to anthropogenic influence. However, using a prescribed ocean state ignores the possibility that estimates of attributable risk might be a function of the ocean state. Thus, the uncertainty in attributable risk is likely underestimated, implying an over-confidence in anthropogenic influence. In this work, we estimate the year-to-year variability in calculations of the anthropogenic contribution to extreme weather based on large ensembles of atmospheric model simulations. Our results both quantify the magnitude of year-to-year variability and categorize the degree to which conclusions of attributable risk are qualitatively affected. The methodology is illustrated by exploring extreme temperature and precipitation events for the northwest coast of South America and northern-central Siberia; we also provides results for regions around the globe. While it remains preferable to perform a full multi-year analysis, the results presented here can serve as an indication of where and when attribution researchers should be concerned about the use of atmosphere-only simulations.