For most of the 2016 presidential election cycle, the conventional wisdom about the Republican Party Convention has been that Donald Trump could never win the party’s nomination. He was too brash, too crude, too rude, too divisive, too inexperienced, too liberal, too strangely coiffed to win a major party nomination for the presidency.

But as we settle into the early caucus and primary voting, all those earlier bets are off. In actual overseas betting (in countries like Great Britain, where wagers on American presidential nominations are legal), Trump is currently the odds-on favorite to be the Republican nominee.

Just how odd are those odds?

More than one commentator has observed that we have never had a president in American history who lacked service in a prior elected office or a high-level appointment. No one has ever won the presidency without previously having contested a local, state or federal election, secured a senior appointment or won a battlefield victory.

Success in business does not disqualify a person for the presidency — but, by itself, it has never been enough to win that office. Just ask Ross Perot or Wendell Willkie. In the list of presidential elections that have taken place since the beginning of the 20th century, only Perot and Willkie (a third-party candidate in the 1990s, and the 1940 Republican nominee, respectively) have made a serious run for the presidency without significant prior public service.

Since 1900, 62 of the names that appeared on national presidential ballots were individuals who went on to win more than 10 percent of the popular vote. This includes all the Republican and Democratic nominees from William McKinley to Mitt Romney and from William Jennings Bryan to Barack Obama, plus Teddy Roosevelt in his Bull Moose days and the Progressive Party’s Robert La Follette, as well as George Wallace and Perot.

Of the 62 serious presidential candidates in the last two centuries:

• 31 were sitting or former governors;
• 38 had previously won a state or local election;
• 38 had won a federal election; and
• 58 held at least one elected public position before running for the presidency.

Serious candidates for the highest office in the land almost always run and win some other political office first.

What about the exceptions? There are four people who made a credible run for the presidency since the beginning of the 20th century without winning prior elected office.

That group includes Dwight Eisenhower, who served as NATO commander and as the allied general in charge of the European theater during World War II. He was a world leader long before he was president and, like George Washington, actually put his national and international reputation at risk when he ran for the presidency. He was no Donald Trump.

Herbert Hoover — like Trump, Perot and Willkie — had great success in the private sector. When the world went to war in 1914, he became involved in relief work, first in Belgium and later across the European continent. He led the U.S. Food Administration and international organizations that saved civilian lives during the war and in the years that followed. His was public service of an extraordinary kind. At the end of the war, The New York Times called Hoover one of the “ten most important living Americans.” He had never sought elected office, but both the Democrats and the Republicans thought of him as a potential presidential candidate. When Harding won in 1920, Hoover served as secretary of commerce. He was no Donald Trump.

Perot and Willkie were more like Trump than any other serious presidential contenders since 1900; and only Willkie won a major party nomination. That is one name out of 62 consequential presidential candidates, or something less than 2 percent.

If history provides any lessons for today’s politics, the odds of a Trump nomination are very small. But as Adlai Stevenson, an unsuccessful presidential candidate in the 1950s, once observed: “In America, anyone can become president. That’s one of the risks you take.”

Indeed it is.