We'll start by noting that Obama's approval rating in our survey is quite a bit higher than in other recent polls. Earlier this month, CNN-ORC had him at 51 percent. At the end of August, Fox had him at 54. But even in Gallup's weekly averages, Obama has been over 50 percent for most of this year.
In the past, we've seen a good correlation between final vote share and Post-ABC approval polling — even when the approval rating was tested in August or September of the same year. The line on the graphs below shows that correlation for years that we have data: As presidential approval improves, so does the vote share of the president's party. At the low end are 1992, when Bill Clinton beat George H.W. Bush, and 1980, when Ronald Reagan beat Jimmy Carter. At the high end are the reelections of Lyndon Johnson, Dwight Eisenhower and Richard Nixon. High approval, high results. Low approval, low results.
There's a cluster in the middle, though, that sometimes dips a bit under that diagonal line — meaning that the party's candidate underperforms against the president's approval. (Notice that the examples above were all approval ratings of the candidates themselves.) But there are other reasons to assume that Clinton will benefit from Obama's popularity.
If we break down that popularity by group, we see some interesting (if unsurprising) things. Considering net approval (those who view Obama's performance positively minus those who view it negatively) we get a wide spread of opinions.
The biggest negative gap for Obama is among those who voted for Donald Trump in the primary or who support him now. Slightly less disapproving are those who voted for someone besides Trump in the primary. How white voters break down by education and gender closely mirrors the overall polling: White men without college degrees are likely to disapprove of Obama by a much wider margin than white women without degrees, who are more likely to disapprove of him than men with degrees. (That group is split between Clinton and Trump in the new poll.) White women with college degrees are the most likely among white voters to approve of Obama, but the biggest fans of Obama's performance are Hispanic and black voters and backers of Clinton in the primary and general elections.
In other words, there's a strong correlation between how people feel about Obama and how they feel about Clinton. Ninety percent of Clinton supporters approve of Obama's job performance, 64 percent of them do so strongly. About the same percentage of Trump backers disapprove of Obama's job performance, more of them feeling that way strongly.
We can flip that. Eighty-six percent of registered voters who strongly approve of Obama's job performance back Clinton; more than half of those who approve of his performance somewhat plan to back the Democrat in November. Among those who strongly disapprove of Obama, 80 percent plan to back Trump. But even 6 percent of that group is leaning toward Clinton. (Only 1 percent of those who strongly approve of Obama plan to back Trump.)
If the link between support for Clinton and approval for Obama doesn't change, an increase in his approval numbers means an increase in her support. It's moving the little blue 2016 dot up the diagonal line on the graphs above. Those dots don't all rest on the line (because approval isn't the only factor at play), and there aren't so many dots that we can say that an increase in Obama's approval necessarily means Clinton's national numbers will be similarly strong.
But if you're running for president to succeed your party's incumbent, history would suggest that such a task is much easier with Obama's 2016 ratings than Obama's 2014 numbers.