The day before House Democrats began their impeachment inquiry against President Trump, he was defiant.

Earlier in 2019, Trump had claimed that his approval rating among Republicans was 93 percent. Suddenly, in July, it jumped to 94 percent, which is what he consistently claimed during the rest of the summer.

The next time he tweeted about his approval among Republicans, though, he added another point.

The intended implication was that the impeachment inquiry was strengthening his support with his base. Never mind that poll numbers don’t sit steadily at the same number; the nature of measuring approval means that there will be some variability. And never mind that, from a statistical standpoint, 93 percent and 95 percent approvals in polling are functionally equivalent. Trump had a point to make, and he was going to make it.

Notice that there’s no sourcing for these polls. As Trump kept hyping these numbers, we looked for any public source, without luck. It’s likely that Trump either was told that he had a 95 percent approval in some poll somewhere and simply kept hyping it, which he has a habit of doing, or that he just decided himself that he was at 95 percent approval. This is a guy who once said that his net worth depended on how he felt about it. Why shouldn’t his political worth be similarly malleable?

On Monday morning, Trump again touted that 95 percent approval — combining it with what he claimed was a 53 percent approval rating overall.

If you’re curious about that “plus add 9 points,” it has a simple provenance. Trump has decided that one way to amplify his popularity is to insist that “some people say” that you should throw 5 to 10 points on top of his recorded approval ratings because polls don’t capture the real number. There’s reason to think that the contrary is true, that Trump’s approval ratings in public polls are actually overestimating his support. But, of course, Trump is not in the reality game. Historically, the polls he touts — including the real ones — are themselves about 10 points higher than what polling averages show.

What’s interesting about Trump’s tweet Monday is that it’s unusually accurate. It’s not actually accurate, mind you — just more accurate than the past numbers he has cited.

Last week, Gallup reported that Trump’s approval in January was at 49 percent, the highest value the pollster has recorded. (Gallup stopped publishing daily poll results in 2018.)

Among Republicans, his approval was at 94 percent — or what he claimed it was in September.

It’s possible that what Trump is doing is adding in the margin of error in the Gallup poll, which is four percentage points. To speak colloquially, that margin of error suggests that Trump’s approval might be somewhere between 45 and 53 percent, and Trump is simply picking the highest value. Of course, that’s a bit like saying that because it’s possible that you could roll a pair of sixes three times in a row, that’s how you’ll place your bet at the craps table.

The Gallup figure is higher than FiveThirtyEight’s average, but the average, which considers a range of polls, also shows a recent upswing for Trump.

Notice, though, that no poll is near 53 percent.

The most recent poll to show Trump with 53 percent approval was conducted by Rasmussen Reports in the days before the impeachment inquiry began. Rasmussen is a favorite of Trump’s, because its focus on “likely voters” almost always has Trump’s approval higher than the polling average or Gallup’s numbers.

Notice how the Gallup dots are both above and below the average line on the graph above, while Rasmussen’s are almost uniformly above it. FiveThirtyEight gives Gallup a B grade on its polling. Rasmussen gets a C+.

Gallup’s poll may be a blip. It may not be. But particularly because of that poll, Trump’s claims about his strength in polling are less wrong than usual.