President Trump has decided that it is important that he keep tweeting from his personal Twitter account because it allows him to speak directly to the American people outside of the filter of the mainstream media, by which he means the media’s pesky insistence on fact-checking his comments and including unflattering news in analysis of his presidency. Over the weekend, Trump took this defense of his social-media use to a new place: Not only is his tweeting perfectly fine for a president, but it is defining what it means to be presidential.

In a sense, this is probably true, for better or worse.

But Trump’s defense of his tweeting depends largely on the idea that he’s unusually skilled at social media, playing the strings of Twitter like the first-chair violinist at the New York Philharmonic.

What if, instead, Trump’s not that great at Twitter? What if … Barack Obama is better?

Allow us to present that case.

Overall, Trump’s two accounts — his personal account, @realDonaldTrump, and his presidential one, @POTUS — get more retweets in a month than Obama’s (@BarackObama and @POTUS44, respectively). (We’re using retweets as a metric here for two reasons. First, it’s accessible data. Second, it captures one aspect of the point of social media: social interaction.) Trump has used @POTUS only since January, since that was when he was inaugurated. Obama has used only @BarackObama since then, retaking the account from the advocacy organization Organizing for Action, which had been renting the account during his two terms in office. (The @POTUS44 account is an archive of Obama’s official White House tweets while in office.)

The exception came in January, when Obama’s farewell tweets got a ton of attention.

That’s simply a raw count of retweets, the total for each tweet added to the others for that month. So we have to note: Trump also tweets far more than does Obama.

If we look at the number of retweets per tweet — how much engagement each tweet gets on average — we see that Obama actually fares much better than does Trump.

Trump’s totals are actually hurt by how much he tweets. The more he tweets in a week, the lower his number of retweets per tweet (over the past month).

The dichotomy in where each president is successful poses an interesting question. Which of these demonstrates a more effective use of Twitter: tweeting a lot to rack up retweets, or getting more retweets on each tweet? I posed this question on Twitter, in an unscientific poll, without mentioning the point I was investigating.

More than two-thirds of respondents figured that more retweets per tweet was the preferable metric. Meaning that Obama is using Twitter more effectively.

There’s a case to be made that more total retweets in a month means that more people are seeing each tweet. That may be true. But it may also mean that the user who tweets more is getting the same, smaller group of people to retweet his tweets over and over — meaning that the overall audience for each tweet is smaller.

If we look at the most-retweeted tweets from each account (extending back a year or for the period that each president controlled the account), the top 10 tweets from Obama’s presidential account racked up far more retweets than any from Trump. That, objectively, is a bigger audience on a per-tweet basis.

That includes this tweet, which is the most retweeted from Obama’s time in office.

Obama’s top seven tweets from his time as president all earned more retweets than the top 10 tweets from either of Trump’s two accounts.

Some may argue that Trump, unlike Obama, actually tweets his own tweets, with Obama’s being crafted by committee. It’s not clear whether that’s still true for Obama, but, even assuming that it is, this ignores the role that Trump’s social-media director, Dan Scavino, plays in his use of Twitter. The early morning TV-watching tweets are probably Trump, but many aren’t.

Obama’s most-retweeted tweet overall came during the 2012 campaign. Until Ellen DeGeneres tweeted a selfie at the Oscars in 2014, it held the title for most-retweeted in history. The person who formulated that tweet, Obama’s 2012 social-media director, Laura Olin, told The Washington Post over Twitter (of course) that she would have preferred more cumulative retweets than a higher per-tweet average.

“It’s always nice when a given post pops because of a certain moment,” she said, “but ongoing high levels of engagement indicate that people care about the meat-and-potatoes governing stuff, too, not just the cute ‘Happy birthday Michelle’ messages — which are wonderful but don’t necessarily serve to convey shared values or further an agenda to make people’s lives better.”

In that sense, Trump is outperforming his predecessor.

What’s more, the numbers above exclude the awareness brought to Trump’s tweets when they are provocative enough to earn him attention from the mainstream media.

That’s the sort of coverage that Trump never complains about.

President Trump drew condemnation for tweeting a violent, doctored video of him punching CNN on July 2, but the real punches were thrown at a WWE match in 2007. (Jenny Starrs/The Washington Post)