Hillary Clinton did not win the Iowa caucuses with a coin toss. She didn’t “win” at all. Not really. Delegates in Iowa are allotted proportionally. She won half. Bernie Sanders won half.

Yes, some of those delegates were decided by an obscure rule requiring the toss of a coin, and Clinton’s winning of the coin toss was something of a mathematical improbability. But she did not “win” and Sanders did not “lose” in Iowa, because “winning” and “losing” are meaningless terms in a situation in which the candidates split the delegate count right down the middle.

“Winning” and “losing” are meaningful terms in two ways. One, if Clinton won a runaway majority of delegates. For instance, if she won 70 percent and Sanders won 30. Two, if delegates are allotted according to the winner-takes-all rule. In that case, the candidate winning more than 49.5 percent wins all the delegates.

Only in the latter situation would it matter that Hillary Clinton mathematically improbably won a handful of Iowa delegates with a coin toss. But that is not the situation, and so all the controversy over the Iowa coin toss amounts to a lot of noise.

That doesn’t explain the cause of the noise, however. One cause is naturally our national media, which tends to treat every state contest as if it were winner-takes-all. I’m guessing that tendency comes mostly from the professional need for a kind of shorthand. “Win” and “lose” aren’t the only misused electoral terms. Even The New York Times this week conflated “primaries” and “caucuses.”

Another cause of noise is ignorance. Many Americans unfortunately don’t know how their federalist system works. This is amplified by international news outlets covering the campaigns.

Nominating elections are won and lost state by state. Some have primaries. Some have caucuses. Some primaries are closed, for party members only. Some are open. Democrats can vote for Republicans, and vice versa. Some states choose not to legally bind their delegates to candidates. They can change candidates at the convention. Both parties have what are called “super-delegates,” who can pledge themselves to whomever they wish regardless of winners. Such party officials serve as a bulwark against an “excess of democracy.”

Even as candidates fight from state to state, the real objective in their minds is the total number of delegates needed to secure the nomination. Achieving that number means ginning up enthusiasm, especially among base voters in early states like Iowa, New Hampshire, South Carolina and Nevada, because the more energy generated, the more likely they are to win the Big One.

But part of me suspects the social-media hysteria over Clinton’s “coin toss victory” stems from the deep distrust of Hillary Clinton and her husband among left-liberals on the margins of the Democratic Party. They already believe the Clintons are crooks. A coin toss deciding who gets some Iowa delegates only confirms that perception. A barrage of media reports saying that Clinton beat Sanders by a hair only arouses a sense of rage that’s always already there.

I have been unconvinced that Clinton’s fiercest critics are motivated by sexism, but it’s hard to keep dismissing the claim. And I’m not just talking about what clothes she wears, her awkwardness on camera, or her clearly staged spontaneity.

Clinton, like the rest of the Democratic Party, has progressed enormously over the course of eight years under the leadership of Barack Obama. But Clinton’s detractors believe she’s stuck in the 1990s, a decade whose politics are unrecognizable in today’s Democratic Party. The Democrats are more progressive, more diverse, and more unified on issues than they have been in decades.

Yes, politicians can and do pander. They say things today. They’ll say the opposite tomorrow. But in Clinton’s case, that’s not flip-flopping. It’s the inevitable result of having a long public career. As Harry Enten noted last year at FiveThirtyEight, Clinton was liberal by the standards of the 1990s and she remains liberal. I’d go farther to suggest that thanks to the president and now Bernie Sanders, we have a Hillary Clinton who is more liberal than ever.

That probably will not appease her critics. Once a minion of Wall Street, always a minion of Wall Street, even as the Dodd-Frank financial reform law she supported is shrinking too-big-to-fail banks. The law’s capital-reserve requirements are preventing those big banks from being as profitable as they were. They are breaking themselves up. As president, Clinton could sit on her hands while the reform law continued to make for a more stable economy.

But there’s something about Clinton that her critics evidently know to be true, something that defies fact and history, something that’s universal and timeless and immune to concrete circumstance — and it’s that implacable belief that I find most troubling.

Photo: Bernie Sanders (left) greets Hillary Clinton after the Democratic presidential debate at Drake University. Mandatory Credit: Rodney White/The Des Moines Register via USA TODAY Sports

John Stoehr is the Koeppel Journalism Fellow at Wesleyan University and a lecturer in political science at Yale.