Why Praying for Rain Statistically Appears to Work
A Statistical Trick Hiding in Ancient Customs
For centuries, communities in China turned to dragons when drought struck In Murcia, Spain, the Catholic Church has held special prayers for rain over the past seven hundred years. Both traditions seem to work — rain tends to follow the ritual. Economist Jose-Antonio Espin-Sanchez at Yale University says this is no coincidence. The effectiveness of these rain-making rituals depends on a specific weather pattern.
In places like Murcia, the chance of rain increases with every dry day that passes. The longer a dry spell lasts, the more likely it is to end. When a religious leader performs a ritual during a long drought, the weather often turns soon after. If the first ritual fails, a follow-up mass or procession days or weeks later has an even better chance of appearing to succeed. In China, a deity whose temple failed to bring rain could face desecration. In Murcia, special masses are followed by processions.
Espin-Sanchez and his colleagues compared reports on the customs of 1,290 ethnic groups, as documented in the study published in the Quarterly Journal of Economics They matched these reports with detailed climate data from where the groups lived or still live. Among groups where the chance of rain does not increase with dry days, 30 percent had a rain-making ritual. Among groups where the chance does increase, 44 percent had such a ritual. The difference is not small — it is 14 percentage points.
Simon Papalexiou at the Hamburg University of Technology in Germany, who was not involved in the study, calls the central idea plausible from a statistical perspective. He identifies two distinct mechanisms that make rain-making appear successful. One is true duration dependence: the longer the dry spell lasts, the more likely it is to end. The other is seasonal anticipation: rituals are performed near the end of the dry season, when rainfall would soon become more likely anyway. Both can make the ritual look effective.
How Priests and Rituals Survive Through Timing
Espin-Sanchez built a mathematical model that describes how people adjust their trust in rituals and religious leaders based on what happens. The model allows for two scenarios. In one, savvy priests strategically time their rituals. In the other, pure luck plays the main role. In both cases, priests who choose the moment shortly before the rains return are more likely to keep their jobs.
The model also shows why certain rituals and religions survive over time. “And that religion, or that ritual, is more likely to survive,” Espin-Sanchez says. The study addresses a key gap in the study of religion — the origin of beliefs. “For belief in rituals to make rain, we have a credible mechanism of why this type of belief exists in some places and not in others,” he explains.
Kevin Hong at the University of Macau recently published a study on rain-making in China. His work emphasized confirmation bias — people are more likely to recall and share stories of rain-making successes. He now says that if Espin-Sanchez’s results are real, he might have underestimated the possibility that these rituals are, in a sense, objectively effective. The two perspectives — statistical likelihood and human bias — may both be correct.
The Next Measurement: From Rain to Epidemics
Espin-Sanchez thinks his model could be applied to rituals for other hardships. He mentions certain epidemics or diseases that have a similar pattern. The pattern is sufficiently complex that you cannot really see that it will go away on its own. It is also sufficiently simple that doing something looks like you are curing the illness. The same statistical mechanism could explain why some healing rituals persist.
The study was published in the Quarterly Journal of Economics under DOI 10.1093/qje/qjag026. The next step would be to test whether the model holds for other types of rituals in different parts of the world. Researchers would need to collect data on rituals for epidemics and compare them with the natural course of those diseases. If the pattern matches, it would confirm that the same statistical principle drives belief in many types of supernatural intervention.