President Obama’s standing in the eyes of the American people has recovered after a three-year slump — and that’s good news for Hillary Clinton.

Obama’s job approval rating — the percentage of voters who say he’s doing a decent job — has reached an average of about 50 percent over the last two months.

A 50-50 split may not look like a historic achievement, but it’s a better number than Obama has seen since 2013. And it’s not a mirage; the president’s standing has been on a gradual upswing for the last four months.

That’s been enough to make Obama aides throw their hats in the air, figuratively speaking. “Five points makes a huge difference,” one of them told me last week.

Politicians routinely pretend that they don’t pay attention to the polls, but there’s no question Obama pays attention to his. During his years in the polling wilderness, he often sounded frustrated that he wasn’t getting credit for his accomplishments.

Now, though, Obama sounds more confident that he might be able to end his presidency on a high note. “I feel greatly encouraged,” he told Democrats in Texas last month. “I think when people step back and get some perspective, they’ll say we did good.”

And he sounds eager to campaign for a Democratic successor “who can continue the legacy that we built” — especially if it’s Hillary Clinton, who has embraced his record more fervently than Bernie Sanders.

A popular president, even one on the way out, is naturally a bigger asset to his party than an unpopular one. Alan Abramowitz of Emory University has found that when a two-term president leaves office, his party is likely to win the next election if his job approval is over 50 percent, but lose if the number is below 50 percent.

But there’s a quirk inside Obama’s improved poll numbers.

The president and his aides would like to think his standing has improved mostly because Americans have finally recognized that the economy is on the upswing, and acknowledge the president’s role in making that happen. But most of the available evidence doesn’t support that theory. The Gallup Poll’s economic confidence index, a measure of how Americans feel about the economy, is the same now as it was late last year, when the president was less popular.

“There’s no clear correlation with presidential approval,” Democratic pollster Mark Mellman noted.

Instead, Obama’s numbers appear to have gone up in large part because the Republican campaign — in particular, GOP front-runner Donald Trump — has reminded many voters why they chose Obama in the first place.

The public image of the Republican Party has fallen as the president’s has risen. During the last three months, the CNN-ORC poll found that the share of voters with an unfavorable view of the GOP swelled from 50 percent to 61 percent. In the same period, Trump impressed increasing numbers of American voters — in the wrong direction. In the CNN-ORC poll, 67 percent of adults said they had an unfavorable impression of the real estate magnate, the highest negative rating ever recorded for a major party’s presidential candidate.

The Trump hypothesis is bolstered by other surveys showing that much of Obama’s increased support has come from younger voters and Latinos, two groups that have reacted strongly against the Republican front-runner. Both groups are strongly opposed to more restrictive immigration policies, Trump’s signature issue.

Obama has tried quite bluntly to capitalize on the vulnerabilities of the GOP field as he has tuned up his message for the fall campaign.

“I actually think that Donald Trump and Ted Cruz have done us a favor,” he said at a Democratic fundraising event in San Francisco on April 9.

The favor, he explained in Los Angeles, “is laying bare, unvarnished, some of the nonsense that we’ve been dealing with in Congress on a daily basis. People act as if these folks are outliers. But they’re not. … We should thank Mr. Trump and Mr. Cruz for just being honest.”

That’s a partisan argument, of course, aimed at rallying Democrats around their president and, eventually, their new nominee.

But that’s what a presidential campaign is mostly about: making sure a party’s voters “come home” and vote for their side — or against the other side, which is just as effective. That’s pretty much what Obama did in 2012, when he succeeded in painting Mitt Romney as a heartless plutocrat.

Obama’s standing is still fragile. He and his aides would feel better if he were over the 50 percent mark. They know that an economic reversal (which they consider unlikely) or a terrorist attack (entirely possible) could blow a hole in his job approval.

But for the moment, their prospects for securing the Obama legacy with a third Democratic term have been improved — thanks to the unlikely assistance of Donald Trump.

— Doyle McManus is a columnist for the Los Angeles Times. His email address is doyle.mcmanus@latimes.com.