RUSSIA attracts conspiracy theories. Just ask the thousands of Poles who marched on April 10th, the eighth anniversary of the plane crash near Smolensk, Russia, that killed Lech Kaczynski, then Poland’s president, and 95 other passengers. As always, the annual commemoration (there are smaller monthly ones) began with mass at Warsaw’s cathedral, and ended with a speech by Mr Kaczynski’s twin brother Jaroslaw, head of the populist Law and Justice (PiS) party and Poland’s de facto leader. He promised that Poles would soon know the truth about how their president died. Mr Kaczynski and his party have long implied that Russia downed the plane on purpose.

There has never been much evidence for this. The plane fell short of the runway in heavy fog. Investigations by Russian and Polish authorities blamed the weather, poor airport maintenance and human error. Yet Mr Kaczynski and his allies hinted that it was an assassination. In recent years PiS has even alleged collusion by Donald Tusk, Mr Kaczynski’s political nemesis, who was prime minister at the time and is now president of the European Council.

Hardly anyone outside Poland’s ruling party believes the Smolensk conspiracy theories. But Russia also faces more credible allegations of skulduggery, notably the attempted murder in Britain on March 6th of Sergei Skripal and his daughter, Yulia. In this case, the most far-fetched theories are those that absolve Russia.

The evidence points to Moscow. Mr Skripal is a former Russian spy who was exposed as a double agent. The nerve toxin that poisoned him, novichok, was developed by the Soviet Union in the 1970s. Russia has a track record: in London in 2006 its agents assassinated Alexander Litvinenko, another ex-spy, by slipping polonium into his tea. Britain’s allies, convinced that Russia is the only plausible suspect, have expelled 160 Russian spies and diplomats.

In response, Russia has thrown up flimsy alternative explanations. Its state-controlled press has suggested that the novichok might have come from Kazakhstan, or that it could have been obtained by the mafia or Ukraine. With breathtaking chutzpah, the Russian embassy in London castigated Britain for failing to protect Russian citizens on its soil—citing Mr Litvinenko’s death. The Kremlin settled on the story that the British poisoned Mr Skripal themselves, to malign Russia ahead of its presidential election last month.

These theories have not convinced many Europeans, but they have sown doubt. Fringe parties sympathetic to Russia warn of a plot to restart the cold war. (“I have a feeling something else is behind this,” said Marine Le Pen, leader of France’s National Front.) After Boris Johnson, Britain’s foreign secretary, got embroiled in a row over where the evidence came from, the misgivings spread. Several officials in Germany’s Social Democratic Party warned that the measures against Russia outpaced the proof. On social media, sceptics wondered why Russia would take the risk—the logic used by Dmitry Kiselev, a Kremlin TV propagandist, who opined last month that since “only Britain stands to benefit”, it must be to blame.

It is a common observation that overuse of the cui bono? (“who benefits?”) style of thinking leads to conspiracy theories. They appeal strongly to people who desire to feel special, according to research by Roland Imhoff, a German social psychologist. Joseph Uscinski, an American political scientist, finds that they are popular among groups that lose political contests, and may disappear when they win.

That could help explain why, in PiS’s third year in power, interest in Smolensk theories remains marginal. Just 17% of Poles believe the crash was caused by an explosion, whereas 55% do not, according to a poll this week. Antoni Macierewicz, the government’s most ardent Smolensk-explosion believer, was sacked as defence minister in January. A report he commissioned has been delayed. Mr Kaczynski has ended the monthly Smolensk rallies. But the annual one will continue, and he vows to find the “real” killer.