It was not on any ballot, but one of the biggest election contests this week pitted pundits against pollsters. It was a pitched battle between two self-assured rivals: those who relied on an unscientific mixture of experience, anecdotal details and “Spidey sense,” and those who stuck to cold, hard numbers.

When the results were tabulated, it became clear that data had bested divination.

The election results that delivered a second term to President Barack Obama on Tuesday left some well-known pundits, many of whom have a partisan bent, eating crow Wednesday morning. They included analysts like Karl Rove, Dick Morris and Michael Barone, all of whom had confidently predicted a victory by Mitt Romney.

The results were much kinder to pollsters and the data devotees who aggregate and average polls or who use mathematical models to make projections.

“While the election’s biggest winner was President Barack Obama, the other victory on Tuesday night went to the careful application of reason, data and, yes, to the science of modern survey research,” Mark Blumenthal, the senior polling editor of The Huffington Post and the founding editor of Pollster.com, wrote Wednesday.

Quite a few of the numbers-crunchers could claim bragging rights on the morning after.

The models used by Sam Wang at the Princeton Election Consortium, Drew Linzer at Votamatic and Nate Silver, who writes the FiveThirtyEight blog for The New York Times, all came remarkably close to forecasting the final result, depending on which candidate ultimately wins Florida.

The average of polls published by Real Clear Politics had Obama ahead on Election Day but understated his margin. And Moody’s Analytics, which models presidential elections based on economic projections, predicted that Obama would get 303 electoral votes, which is what he has now, pending the Florida outcome.

If the data geeks were left arguing about who had come closest to predicting the popular vote down to the decimal point, many commentators were left struggling to explain why they had favored the wrong man.

Morris, a former strategist for Bill Clinton who is now an analyst for Fox News, acknowledged Wednesday that he had “egg on his face” for having predicted a Romney landslide.

Rove, a former strategist for President George W. Bush, wrote in The Wall Street Journal last week: “My prediction: Sometime after the cock crows on the morning of Nov. 7, Mitt Romney will be declared America’s 45th president.”

In an interview on “Fox & Friends” on Wednesday morning, he summed up the election this way: “Well, if you look at the exit polls, basically Obama kept the coalition that he had in 2008.”

Silver, the computer expert who gave Obama a 90 percent chance of winning re-election, predicted on his blog that the president would receive 51 percent of the popular vote as he called each of the 50 states, including all nine battlegrounds.

A website called UnSkewedPolls.com, which aimed to “debunk the media bias and shatter the false illusion being created by the mainstream media,” created a sensation on Twitter with its contention that pollsters for media companies were questioning too many Democrats and too few Republicans. The site tried to adjust the polls’ findings to reflect what the results would look like if more Republicans had been questioned.

But the site’s author, Dean Chambers, acknowledged that his assumption that more voters would identify themselves as Republicans proved to be wrong.

“The polls that were assuming that the turnout was going to be plus 5, or plus 6, in favor of the Democrats, those folks weren’t deliberately skewing — they turned out to be correct,” he said in an interview. “A lot of people on the right, politically, they didn’t want to believe the polls, for whatever reasons. A lot of people told me, ‘I read your site, I really hoped it was true, and now my hopes were dashed.’ ”

Nationally, exit poll results that have not yet been finalized showed Democratic voters outnumbering Republicans, 38 to 32 percent — similar to the difference four years ago, when it was 39 to 32 percent. When Bush won re-election in 2004, in contrast, Democrats and Republicans made up equal shares of the electorate.

Bloomberg News contributed