Political prognosticator Nate Silver said Sunday that he gives Republican Donald Trump a 25 percent chance of winning the 2016 presidential election, while noting that he has been wrong before.

Mr. Silver admitted that he initially gave Mr. Trump only a 5 percent chance of capturing the Republican nomination, saying he would peak early and “flame out” like 2012 presidential contender Herman Cain.

“This is one of the crazier things we’ve seen in politics for a long time. I think it was fair for us to be skeptical early on about the odds this could occur,” Mr. Silver told CNN’s “Reliable Sources.”

Mr. Silver, who heads the statistical-analysis website FiveThirtyEight, included a few caveats in his latest prediction on the contest between presumptive nominees Mr. Trump and Democrat Hillary Clinton.

“If you held the election today — there’s enough polling to know that today, Clinton would very probably win, but you can have recessions, you can have terror attacks, Clinton is not a very popular candidate herself, maybe Trump is a black swan,” Mr. Silver said. “So I don’t know. I put Trump’s chances of becoming president at 25 percent, much higher today than a year ago.”

Mr. Silver has a strong track record — in the 2012 race, his website correctly predicted the winner in all 50 states — but he also described the 2016 primary as “the most amazing election I have ever seen.”

“I think Trump’s rise to power is inherently kind of amazing and remarkable, also scary in some other respects,” he said.

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