Ex-intelligence chief James Clapper says Russia won the election for Trump. This study backs him up.

President Trump and his allies have been attacking former Director of National Intelligence James Clapper over the past few days, part of his attempt to make "Spygate" happen. Clapper is on a media tour to promote his new book, Facts and Fears, and along with explaining how Trump is distorting his words and the FBI's attempt to investigate Russia, Clapper has been explaining his contention in the book that the Russians, to their surprise, "swung the election to a Trump win."

"Since I left the government," Clapper told PBS NewsHour on Wednesday, "it's what I call my informed opinion that given the massive effort the Russians made, the number of citizens that they touched, and the variety and the multidimensional aspects of what they did to influence opinion and affect the election, and given the fact that it turned on less than 80,000 votes in three states, to me it just exceeds logic and credulity that they didn't affect the election, and it's my belief they actually turned it."

On CNN Thursday night, Clapper swatted down more Trump team attacks and reiterated his "informed opinion" about Russia handing the election to Trump, though, he told Jake Tapper, "I don't have the empirical evidence to go with it."

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But there is some empirical evidence, if not conclusive, in a new working paper at the National Bureau of Economic Research. Automated Twitter bots — a key tool that Russians used in the election — may have added 3.23 percentage points to Trump's vote in 2016, as well as 1.76 percentage points to the "leave" vote in Britain's Brexit campaign, the researchers found. "Our results suggest that, given narrow margins of victories in each vote, bots' effect was likely marginal but possibly large enough to affect the outcomes," write authors Yuriy Gorodnichenko from U.C. Berkeley and Tho Pham and Oleksandr Talavera from Britain's Swansea University. You can read more about the study at Bloomberg News.