A new poll from the Los Angeles Times/USC Dornsife suggests that the pivotal state of California might be a tighter contest between Hillary Clinton and Bernie Sanders than previously thought. A survey of 1,500 registered voters found that 44% of Democrats said they would support Sanders and 43% said they would back Clinton in the state’s primary which will be held next Tuesday.

At first glance, the results seem to be hugely significant.

With 546 Democratic delegates available, California is the single most influential state this primary season. And, since Sanders needs 837 extra delegates to become the Democratic nominee, he is going to need to count on Democratic Californians’ support. However, (and this will come as no surprise to anyone who has been observing voting processes in primaries so far) things are far more complicated than they first seem.

First of all, Sanders doesn’t just need to win a large number of delegates – he needs to prevent Clinton from winning the small number of delegates that she needs to cross the finish line and become the Democratic nominee. Including superdelegates, Clinton is now only 70 delegates away from that victory. What that means in practice is that Sanders can’t just win by one percentage point, as the Los Angeles Times poll suggests he might – the Vermont senator needs to pick up around 90% of the vote in California and leave Clinton with just 10%. Since Democrats (unlike Republicans) distribute delegates more proportionally to vote share, that 10% would translate to around 55 delegates for Clinton.

Hillary Clinton. Photograph: Mary Altaffer/AP

But that’s not all. Sanders would need similarly spectacular wins on Tuesday in Montana, New Jersey, New Mexico, North Dakota and South Dakota to keep Clinton from winning the nomination.

If that weren’t bad enough, there is good reason to think that the poll from the Los Angeles Times might be overstating Sanders’ share of the vote. Of the 1,500 registered voters they spoke to, 1,184 said that they were likely to vote. Since the poll was conducted so close to the primary (respondents were contacted from 16 to 31 May) it is those likely voters that are the ones to watch, and among them Sanders’ narrow lead vanishes; he commands just 39% compared with Clinton’s 49%.

Finally, the election analyst’s mantra “it’s only one poll” is important here. Looking at the average of the 14 polls that have been conducted in California so far this year, Clinton consistently has a solid lead of between five and 11 percentage points.

Next Tuesday’s primaries probably won’t change the names on the ballot in November – they’re still highly likely to be Clinton and Republican Donald Trump. But that doesn’t mean next week’s primaries are insignificant – understanding the demographics of those candidates’ support will be crucial to figuring out who is likely to become the president of the country.