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The arithmetic also misbehaves exactly where the events are most interesting. As the counterfactual probability falls toward zero, $\lim_{p_0 \to 0} \mathrm{PR} = \infty, \qquad \lim_{p_0 \to 0} \mathrm{FAR} = 1$. AR6 records that several studies of events from 2016 onward reported an infinite risk ratio, corresponding to a fraction of attributable risk of one, because the event’s occurrence probability was close to zero in simulations without anthropogenic influence — while noting in the same passage that the lower bound of the uncertainty range is difficult to estimate accurately in these cases [ 1 ] . Paciorek, Stone and Wehner develop a frequentist framework for exactly this sampling problem and argue that the bootstrap widely used in the literature performs poorly for small estimated probabilities, recommending methods with better behaviour in repeated samples [ 11 ] .