Last week, halfway through the Republican convention in Cleveland, I wrote that the GOP gathering was so shambolic that it might not give Donald Trump the “bounce” he needed.

I was right about the convention, but wrong about the bounce.

Trump undeniably got one. In the average of national polls compiled by RealClearPolitics, Trump was three points behind Hillary Clinton before Cleveland; now he’s one point ahead.

The USC Dornsife/Los Angeles Times poll showed a similar swing with a more striking result: Trump seven points ahead.

What does that mean for Hillary Clinton, whose convention in Philadelphia was smoother and snazzier? It means she’s virtually certain to get a bounce, too.

The main functions of modern conventions are to unify the party, give voters a reason to tune in to its message and give the nominee free television time for an acceptance speech — the only such opportunity of the campaign.

By those measures, the Democratic convention clearly did better than the Republicans. Despite lingering anger among his supporters, Bernie Sanders endorsed Clinton; Ted Cruz and other GOP rivals refused to endorse Trump.

The Democrats’ stage paraded stars from President Obama and Bill Clinton to Meryl Streep and Katy Perry; the Republicans offered Newt Gingrich and Scott Baio.

Trump likes to brag about his television ratings, but the Democrats won the ratings race. It was “a surprisingly good convention,” GOP pollster Frank Luntz wrote.

Why does that matter? Because it means more voters, including skeptical independents and wavering Democrats, tuned in to get their dose of Clinton’s message. She and her surrogates got the shot they wanted — over and over and over.

By the middle of next week, if the normal rules of politics apply, we’ll see the effect: a clear bounce.

And if that doesn’t happen? Then we’ll know she’s in serious trouble.

Doyle McManus is a columnist for the Los Angeles Times.