Eventually, Trump’s chief of staff, Reince Priebus, dismissed that latter notion. Priebus said the tweet stemmed from the fact that Trump “loves Judge Jeanine and he wanted to do Judge Jeanine a favor.” There you go. Mystery solved.

Except that our familiarity with Trump’s tweets about what he’s watching on television tends to blind us from the subtext to that explanation. On this occasion, politics weren’t underlying Trump’s tweet, Priebus said. Instead, it’s simply the president of the United States … trying to promote a commercial program as a favor to a friend.

Uh, okay.

As it turns out, there’s an established valuation to such tweets. As you’re probably aware, there’s a robust economy built on getting celebrities to tweet positive things about products. You see Kim Kardashian posting a photo of some new lipstick on Instagram and you can be pretty confident that the lipstick company paid some go-between to get her to do that.

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One such go-between is a company called Captiv8, which both tracks and builds brand-celebrity advertising deals. The company has even developed estimates of the value to a brand for getting a sponsored social-media item on various platforms for celebrities (or “influencers,” which is the term for platform-specific celebrities) with various audience sizes. Someone with follower counts the size of Trump’s for example, could expect the following payments for sponsored posts, according to Captiv8’s Krishna Subramanian.

• Twitter: $60,000 per tweet

• Instagram: $150,000 per post

• Facebook: $187,000 per post

In other words, that tweet from Trump promoting Pirro’s show was more than a favor to Pirro and her employer, Fox News. It was, essentially, a gift worth $60,000.

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With these metrics in mind, we went back through Trump’s social-media posts since he announced his candidacy to see how often he actively encouraged people to watch or buy particular programs or products. Although the list of those posts that appears at the bottom of this article is probably incomplete, it gives a sense of the value that Trump has provided to news networks.

By our estimates, Trump has provided Fox and its affiliated networks (Fox News, Fox Business) with more than $5 million in free advertising. In second place is NBC and its affiliate MSNBC, at $2 million — thanks mostly to a big push for his 2015 “Saturday Night Live” appearance.

Unsurprisingly, Trump’s promotion of his media appearances — by far his most common sort of promotion — was stacked before and through the Republican primaries. As the general-election campaign kicked into gear, that promotion was largely focused on his Fox News appearances.

Captiv8’s Subramanian notes that Trump may not have demanded the full $5 million from Fox News — or anyone else. Celebrities can adjust their rates up or down. “You can get someone who will take a lower rate to work for a brand that they like more,” he said, adding that “those price points are a pretty good range for where people fall, including the Kardashians.”

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Although no social-media company connects brands to celebrities to have the celebrities disparage them, Subramanian figured that the hit to a company’s value from a negative post would be damaging, perhaps to the extent that a positive tweet or Facebook post was helpful. In other words, Trump’s 52 tweets about the “failing @nytimes” could be thought of as the equivalent of $3.1 million in bad publicity.

All of this should be considered in light of the mutually beneficial relationship Trump enjoys with the media. Last March, the New York Times calculated that Trump had been the beneficiary of the equivalent of about $2 billion in advertising by dint of his ability to generate free media attention to what he was doing. Mind you, that was still eight months before the election, so who knows how it grew.

With that in mind, the $11 million in free social-media attention he gave to Fox, NBC, CBS, ABC and CNN is a pretty cheap return on investment. Captiv8 could only hope for that kind of return on investment.

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