To hear President Trump tell it, his approval rating should be far higher than it is based on the economy alone. He has taken to referring to the economy as the best in history, slowly sliding that self-assigned praise into his regular rhetorical rotation. (We’ve fact-checked it.)

And to hear Trump tell it, one of the central metrics that should be considered when looking at the strength of the economy is the unemployment rate. In September, the unemployment rate dropped to 3.7 percent, the lowest it has been since 1969. Trump regularly touts that figure and specific demographic numbers, citing historic or near-historic lows in the unemployment rates of women, African Americans and Hispanics. You can sense the undercurrent of frustration in each tweet: With numbers like these, how can you not think he’s doing a great job?

The answer is that presidential job approval is often linked generally to the economy, but often disconnected from employment numbers.

It would be natural to expect a link between employment and presidential job approval. If you were to compare those numbers to one another, you might expect a line looking something like the one below: As the unemployment rate goes up, approval goes down.

Instead, plotting monthly approval ratings against the unemployment rate each month for presidents stretching back to Harry Truman looks like this.

Each color on that chart represents a different presidency, but which doesn’t matter for the moment. What matters is that the result is an amorphous blob. If we round the unemployment rates to the nearest integer, the average of approval ratings for months at that rate similarly doesn’t follow a smooth downward trajectory, as we might expect.

(If you’re curious, the relationship between the rate of change in the unemployment rate and approval ratings is also all over the place.)

There are some presidencies in which the expected pattern loosely holds. Take Bill Clinton, for example. His approval was higher when the unemployment rate was lower. It’s messy, but there’s clearly a correlation.

Dwight Eisenhower’s chart is similar. His approval ratings, always strong, were better when more people were working.

Also in this category: Ronald Reagan. The lowest approval ratings Reagan saw were when a tenth of the country was out of work.

That’s where the pattern ends. Consider the two Bushes, both of whom went to war in the Middle East during their presidencies — and both of whom enjoyed approval ratings spikes as a result.

Most of the variation on the chart below is in the elder Bush’s approval rating.

His son’s chart is even more dramatic.

In each case, George H.W. Bush and George W. Bush saw approval ratings driven more by external factors than the health of the economy. In the case of the younger Bush, his approval ratings were driven downward by the extended conflict in Iraq as he transitioned into his second term.

That’s why Lyndon Johnson’s chart doesn’t show a correlation between approval and the unemployment rate. Many Americans were working during his presidency, but as the Vietnam War accelerated, his approval plunged.

These days, something else has shifted that affects the possible relationship between jobs and approval: partisanship.

Barack Obama’s approval rating was remarkably static from about 2010 on, with Democrats generally approving of his job performance and Republicans opposing it. The result is that, almost no matter what he did, his approval rating didn’t move much.

The densest part of the dots below, flowing around the 50 percent mark in the shape of a W, is his presidency written in reverse. The left-most dot is the latest rating for Obama, when his approval was bolstered by the 2016 election and as the unemployment rate continued to drop. That middle spike in the W shape is the 2012 election, when his approval rose before quickly falling again.

Trump picked up at the left end of that W. Like Obama, his approval ratings haven’t moved much. The result is a clot of low unemployment and low approval.

Trump is being judged on things beyond employment, as were the Bushes and Johnson, and Trump’s approval is largely cemented thanks to partisan divergence in views of his performance.

The president who most resembles Trump, in fact, is Truman. Data for Truman begin in 1948, after which his approval quickly fell (and stayed) under 50 percent. Just a little clot a bit lower and to the left of Trump’s — lower unemployment and lower approval.

It’s not clear the extent to which Trump is making an argument for his success vs. expressing confusion at the state of his polling. Trump clearly believes he should be seeing higher approval ratings; earlier this week, he told a reporter that anyone who doesn’t offer an opinion in a poll is someone who supports him. But is he raising the point about the unemployment rate because he wants to persuade people to like him or because those low figures, in his estimation, must mean that he’s viewed more positively than polls suggest?

If it’s the latter, the graphs above show the flaw in that thinking. No matter how good or bad the employment picture in the United States, something else can quickly have an outsize effect on how your presidency is viewed.