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Abstract Ensemble forecasts have been shown to better predict observed Atlantic climate variability than that of their own ensemble members. This phenomenon—termed the signal‐to‐noise paradox—is found to be widespread across models, timescales, and climate variables, and has wide implications. The signal‐to‐noise paradox can be interpreted as forecasts underestimating the amplitude of predictable signals on seasonal‐to‐decadal timescales. The cause of this remains unknown. Here, we examine sea level pressure variability from a very large multi‐model ensemble of uninitialized atmosphere‐only simulations, focusing on boreal winter. To assess signal‐to‐noise errors, the ratio of predictable components (RPC) is examined globally, as well as for regional climate indices: the North Atlantic Oscillation, Arctic Oscillation, Southern Annular Mode, and an Arctic index. Our analyses reveal significant correlations between the multi‐model ensemble‐mean and observations over large portions of the globe, particularly the tropics, North Atlantic, and North Pacific. However, RPC values greater than one are apparent over many extratropical regions and in all four climate indices. Higher‐resolution models produce greater observation‐model correlations and greater RPC values than lower‐resolution models in all four climate indices. We find that signal‐to‐noise errors emerge more clearly at higher resolution, but the amplitudes of predictable signals do not increase with resolution, at least across the range of resolutions considered here. Our results suggest that free‐running atmospheric models underestimate predictable signals in the absence of sea surface temperature biases, implying that signal‐to‐noise errors originate in the atmosphere or in ocean–atmosphere coupling.