The Tsarevich Alexei, born in 1904 and the only son of Nicholas II, had hemophilia B, inherited through his mother from Queen Victoria. In the early twentieth century there was no treatment. A bruise could produce internal bleeding into a joint that swelled, caused agonizing pain and could kill.
The condition was a state secret. Almost nobody outside the immediate family and a few doctors knew the heir to the Russian throne was chronically ill.
Grigori Rasputin was a Siberian peasant of no education and considerable presence who had arrived in St Petersburg as a wandering holy man and had become known in aristocratic religious circles. He was introduced to the imperial family in 1905. From about 1907 he was called in during Alexei's crises, and the boy improved.
There are three plausible explanations and they are not exclusive.
Hemophilic bleeding episodes remit spontaneously. Crises pass, and the timing of a recovery relative to an intervention is what generates the belief.
Rasputin's presence appears to have calmed both the child and the mother. Stress and agitation raise blood pressure and worsen bleeding; a calm room is not nothing.
And he reportedly told the family to stop the doctors' treatments. The pharmacology matters here: aspirin was newly available and widely prescribed for pain, and aspirin inhibits platelet function. If the physicians were giving Alexei aspirin, then instructing them to stop would have produced a genuine improvement by removing an anticoagulant.
None of these are miracles, and Alexandra did not have access to any of them as explanations.
What she had was a sequence: the child is dying, Rasputin comes or sends a telegram, the child recovers. The Chapmans' work on illusory correlation shows how readily people perceive a relationship between co-occurring events, particularly when they expect one. Add the most powerful motivation available — a mother watching her son die — and the perceived relationship becomes unshakeable.
Two structural features made it unshakeable in practice as well as in feeling.
The secrecy eliminated audit. Because the illness could not be discussed, the evidence for Rasputin's power could not be examined by anyone outside the family, and criticism of him at court appeared to be motivated by jealousy or prudery, since the critics could not state the real subject.
And the stakes forbade doubt. If Rasputin was a fraud, Alexei was going to die. Dissonance reduction in that situation runs entirely in one direction.
From that position — no office, no rank, no qualification — he acquired influence over ministerial appointments during the war, which is the political catastrophe usually attributed to him. He was murdered in December 1916 by a conspiracy of aristocrats including Prince Felix Yusupov. The dynasty fell three months later.