One enduring myth about the surging candidacy of Donald Trump is that the billionaire is benefiting from a primary calendar in which a large number of states with “open” presidential primaries are clustered at the beginning of the process. In an open primary, voters can elect to participate in either party’s primary, and the thinking is that Trump’s early victories in open primary states have been driven by non-Republican voters piling into the GOP race and upsetting the balance.

But while it is true that Trump has dominated in states with open primaries, the claim that he is doing so only because non-Republicans are able to vote for him doesn’t stand up to examination. For one, he had now won the same number of closed primary states – seven – as his closest rival, Texas Sen. Ted Cruz.

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Trump has won eight out of the nine open primary contests held so far, losing only in Minnesota, where Florida Sen. Marco Rubio won. However, in every single open primary state where Trump won, the billionaire former reality television star earned the votes of a plurality or a majority of registered Republicans.

In other words, even if the rules had been changed in those states to allow only Republicans to vote, Trump still would have won. Sometimes by a large margin. In fact, rather than help Trump, it’s arguable that open primaries in at least two states have hurt him. Senator Marco Rubio earned a larger share of Independents than Trump did in both Virginia and Vermont. In Virginia, where Trump only beat Rubio by 2.8 percentage points, the open primary actually reduced Trump’s margin of victory. Likewise in Vermont, if only registered Republicans’ votes had counted, Trump would have notched a bigger win than he ultimately did.

Kyle Kondik managing editor of Sabato’s Crystal Ball at the University of Virginia’s Center for Politics, said that people may be “overstating” the impact of an open primary on the results.

In some cases, he said, voters are actually allowed to switch their registration at the voting site, allowing them to vote in the other party’s “closed” primary on election. The registration change, he said, is theoretically a minor barrier “to someone who really wants to participate in the other party primary.”

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However, there doesn’t appear to be much evidence for widespread last-minute party switching in the primaries so far.

Kondik also offered a different potential explanation for the persistent idea that closed primaries will be the Trump campaign’s kryptonite.

“More broadly, I think many of us have been getting caught in the technical weeds in trying to find an argument that raises alarm bells for Trump,” he said. “If you take a step back, he’s very clearly leading this race, and he’s won contests across the country. Unless someone defeats him on March 15 – maybe Kasich in Ohio has the best chance – he’s well on the way to the nomination.”