Winning the lottery changes the winner's life, but for the statistics of all players it means almost nothing: the probability of winning is negligible, and the average winnings per ticket remain tiny. The climate has similar events: the El Niño phase does not occur every year, but when it does, the temperature of the Pacific Northwest changes noticeably. Classical causal effect measures average the influence over all possible phases, so the rare but powerful El Niño effect drowns in the average. The authors of the study proposed a way to measure the influence of a specific cause value, as if a statistician looked not at the average winnings of all tickets, but at the winnings of this particular ticket drawn from the lottery drum.

To separate the effect of a specific value from the average, the authors compare two probability distributions of the outcome. The first is the temperature distribution after we forcibly set the cause, for example the El Niño phase. The second is the "natural" distribution, averaged over all possible phases. The difference between these distributions is measured by the Kullback-Leibler divergence, that is, a measure of how much one distribution differs from another. If the temperature shifts strongly after the intervention, the divergence is large, and the effect of the specific value turns out to be large.

Using data from the CESM2 climate model for 1850–2015, the effect of El Niño on Pacific Northwest temperature turned out to be about three times larger than the average effect over all phases. The direct effect, transmitted through atmospheric circulation, exceeds the indirect effect mediated by temperature persistence. This is consistent with the physical mechanism: El Niño affects the region directly, not through ocean memory.

This approach brings together two worlds: statistical causal inference, which can estimate the effects of interventions, and information theory, which captures nonlinear interactions. Previously, information measures did not distinguish the contribution of specific cause values; now they answer the question "what is the effect of this particular value?". The method can be applied not only to climate, but also to neuroscience, where it is important to assess the effect of a specific stimulus on neuronal activity, or to economics, where the effect of a particular policy decision is of interest. The winning ticket can finally be measured separately from all the others.