Producing better estimates with less information is impossible, so subsampling is not recommended when the cost of saving and using samples is negligible. Samples which are not fully correlated each contain new information (albeit less than uncorrelated samples), and discarding them adds noise to the variance and mean estimates. Subsampling may substantially increase the variance of the mean estimate and the variance estimate. Concretely, we show in Section S9 that when a sufficiently long stationary time series has a purely exponential correlation function with a half-life much greater than the sampling interval, subsampling at the interval of the statistical inefficiency increases the variance of the mean by 31%.