Among Donald Trump’s unorthodoxies is his campaign’s refusal to use big data. “I’ve always felt it was overrated,” Mr. Trump said in May. “Obama got the votes much more so than his data-processing machine. And I think the same is true with me.”

David Plouffe, who ran Barack Obama’s campaign in 2008, tweeted: “Trump now wants to ban data and modeling from his campaign. Agree with him that Obama got the votes not data. But flying blind is nuts.” Democratic operative Ron Klain quipped in response: “Plouffe: Ix-nay on the elping-hay of rump-tray.”

They have reason to laugh. Campaign professionals in both parties agree the Democrats have a large lead in information about voters—and that smart use of data can make the difference, at least in close elections. When she officially becomes the party’s nominee this week, Hillary Clinton will inherit the database Mr. Obama’s team built over two campaigns.

In 2008 the Obama campaign gathered so much information that it was “confident it knew the name of every one of the 69,456,897 Americans” who voted for him, according to journalist Sasha Issenberg. The 2012 campaign built a fully merged database Republicans have yet to match.

“We are going to measure every single thing in this campaign,” Obama campaign manager Jim Messina said in 2011. His team built a database connecting personal data from traditional sources, such as reports from field workers and pollsters, with voters’ social-media posts and other online behavior, plus commercial consumer data of the sort that online retailers and credit agencies use.