Donald Trump attends a “Celebrity Apprentice” red carpet event at Trump Tower on Feb. 3, 2015, in New York. (Andrew H. Walker/Getty Images)

There is a feud underway between the president of the United States and the former governor of California. In some contexts, we would expect that sentence to refer to, say, policy differences on land use or perhaps an early battle in an upcoming presidential election. In the universe of 2017, though, we are, of course, talking about television ratings.

We should predicate discussion of this feud by noting that there is a decent chance that the whole thing is contrived. The former governor — Arnold Schwarzenegger — is in charge of getting good ratings for NBC’s “The New Celebrity Apprentice.” The president — Donald Trump — mentioning the show in any context probably helps to that end. Trump, of course, is still an executive producer of the show, so he has competing interests: He’d like it to do well, but he’s also probably happy to have it be doing worse with someone else as the host.

“We had tremendous success on ‘The Apprentice,’ ” Trump said on Thursday at … the National Prayer Breakfast. “And when I ran for president, I had to leave the show. That’s when I knew for sure that I was doing it. And they hired a big, big movie star, Arnold Schwarzenegger, to take my place. And we know how that turned out. The ratings went down the tubes. It’s been a total disaster.” He then jokingly asked the audience to pray for better ratings.

Trump often fosters the impression that “The Apprentice” and its variation, “The Celebrity Apprentice,” were runaway successes from start to finish, Season 1 to Season 14. In reality, the show’s trajectory was more like M. Night Shyamalan’s: one surprise smash hit and, then, not so much.

We went back and pulled viewership for the first seven seasons — six of “The Apprentice” and the first of the celebrity version — to illustrate the point. We used only ratings from when Trump’s show was in the top 20 most-watched for the week it aired. You can see two things: The number of viewers slipped quickly and continuously, and appearances in the top tier of network programming became more and more rare.

Only during one week was “The Apprentice” the top-rated show in America, according to Nielsen ratings reported at the time: The first season finale. The introduction of the celebrity iteration offered a small boost, but nothing too substantial.

It is true that, relative to the most recent season hosted by Trump, Schwarzenegger is underperforming. That was in 2015, shortly before Trump began flirting publicly with the idea of running for president. But the season before that, Trump’s show did worse, only slightly better than where Arnold is now — at least through five shows.

Incidentally, the finale of that 2015 season got lower ratings than the premiere. Within two weeks, Trump began discussing the idea of a presidential bid.

Again: The ratings for the Schwarzenegger-hosted show aren’t good. But it’s not at all clear that they would be much better if Trump were still hosting. “The Apprentice” had its moment, and the moment has now passed. Schwarzenegger has done Trump one favor, at least. Trump managed to sell Arnold his fluky old car after rolling back the odometer and giving it a fresh paint job. Now, when it finally stalls out for the last time, Trump can say it wasn’t his fault.