If one person wins the lottery, it is a huge event for them, but for all players combined it is almost imperceptible, because the average winnings per ticket remain a pittance. The same goes for climate: the El Niño phase does not happen often, but when it does, temperatures in the Pacific Northwest shift dramatically. Standard measures of causal effect average the influence over all phases, and the powerful El Niño effect drowns in the average, like one lucky winner's jackpot lost among a sea of losing tickets.
To measure the effect of a specific value, you compare two probability distributions. The first is the temperature distribution after you forcibly set the El Niño phase. The second is the usual distribution, averaged over all phases. The difference between them shows how strongly a particular event changes the picture. It turns out that El Niño's effect on temperature is about three times larger than the average effect across all phases. Moreover, the influence comes directly through the atmosphere, not through ocean memory. This approach helps not only in climate science, but also in neuroscience, where it is important to assess the impact of a specific stimulus on neural activity.
The mutual information between winning the lottery and spending is nearly zero, because the probability of winning is minuscule, although for a specific winner the effect is huge. Specific measures capture this contrast.