A lot has been made of Bernie Sanders’s appeal with independent voters during the Democratic presidential primary. He has won people who identify as independents in state after state, while Hillary Clinton has won people who identify as Democrats. Some Sanders backers have argued that this will translate to the general election; they point to general election polls that show Sanders doing better against Donald Trump than Clinton is.

The problem with this analysis, however, is that most independents are really closeted partisans, and there is no sign that true independents disproportionately like Sanders.

Most voters who identify as independent consistently vote for one party or the other in presidential elections. In a Gallup poll taken in early April, for instance, 41 percent of independents (who made up 44 percent of all respondents) leaned Democratic, and 36 percent leaned Republican. Just 23 percent of independents had no partisan preference. In the last three presidential elections, the Democratic candidate received the support of no less than 88 percent of self-identified independents who leaned Democratic, according to the American National Elections Studies survey. These are, in effect, Democratic voters with a different name.

Right now, Clinton is struggling with this group. According to a Gallup poll conducted May 15 to May 21, her favorable rating among Democratic-leaning independents was just 51 percent, compared with 73 percent among people who identify as Democrats. That’s a 22-percentage-point difference. Sanders and Trump, on the other hand, had gaps of just 3 and 7 percentage points, respectively, between independents who lean toward their party and their party’s pure partisans.

Sanders did slightly better with Democratic-leaning independents (71 percent favorable) than he did with plain-old Democrats (68 percent favorable), but that appeal does not seem to extend to true independents — those who are most likely to change party allegiances between elections and whose split between the Republican and Democratic candidates nearly matched the split in the nation overall in the last two elections, according to the ANES. In the Gallup poll, Sanders had a 35 percent favorable rating among independents who don’t lean toward either party. Clinton’s favorable rating with that group was 34 percent. Trump’s was a ridiculously low 16 percent.

One could argue that Sanders has greater potential with these true independents than Clinton: Just 63 percent of them had formed an opinion of him, according to the Gallup poll, while 83 percent had done so for Clinton. But it’s also possible that these true independents will turn against him in greater numbers as they learn more about him.

For now, though, Sanders’s big advantage over Clinton in general election matchups is his edge among Democratic-leaning independents, not pure independents. Currently, all the Democratic groups that like Clinton also like Sanders, but the reverse is not true. As my colleague Nate Silver and NBC News’s Mark Murray have both pointed out over the past week: Clinton has yet to win over a number of Sanders supporters, but Sanders does very well among most Clinton supporters.

But that we’re talking about Clinton’s need to win over Democratic-leaning independents rather than true independents is a hopeful sign for her campaign — these voters have tended to stick with the Democratic Party. If Clinton can lure these Sanders voters back into her tent, she’ll probably lead Trump by somewhere around 5 percentage points nationally, instead of the 2 percentage points she leads him by now. My guess is that she’ll probably win many of them over, considering that a large portion are normally reliable Democratic voters. This year is so crazy, though — who can really say?