Having just lost an election, many Republicans are anxious to remake our party in the image of Democrats. The theory seems to be that whatever we’re doing isn’t working, so we better change everything.

But in fact, whatever Republicans did in 2012 — other than an overly long primary fight — worked amazingly well, given the circumstances.

In a detailed analysis of the 2012 election, William A. Galston, a fellow with the liberal Brookings Institution, makes a number of fascinating observations that Republicans would do well to consider before embracing amnesty, abortion, gay marriage and Beyoncé.

In my analysis of his analysis, the single most important factor in the election was simply that Obama was an incumbent. As Galston notes, beating an incumbent president is a feat that has happened only five times since the turn of the last century. Republicans have done it only once.

On closer examination, in all these cases the incumbent president faced a primary challenge. In three of the five, the incumbent also had a third-party challenger in the general election.

● In 1912, Theodore Roosevelt ran against incumbent William Howard Taft and, failing to win the Republican nomination, ran on a third-party “Bull Moose” ticket against him.

● In 1932, President Herbert Hoover faced a number of primary opponents, including Calvin Coolidge and John Blaine (and it was also a few years into the Great Depression).

● In 1976, Ronald Reagan nearly beat a never-elected incumbent, Gerald Ford, in the primary, losing narrowly on the convention floor, 1,070 to 1,187. (And Ford still almost pulled it out!)

● In 1980, Teddy Kennedy ran a primary campaign against President Jimmy Carter all the way to the convention, and John Anderson ran as a liberal third-party candidate in the general election.

● In 1992, Pat Buchanan ran against incumbent George H.W. Bush, winning an astounding 37 percent of the vote in the New Hampshire primary, and then Ross Perot ran a shockingly popular third-party campaign, winning 19 percent of the general election vote — mostly, polls showed, from Bush.

The one time Republicans beat an incumbent was in 1980 when Reagan beat Carter. Not only was the economy in shambles, not only had Iranian savages been holding 52 American hostages for more than a year, but Carter was badly battered by these extra opponents. (And that’s to say nothing of an amphibious rabbit assault!)

Running as the “true liberal,” Kennedy won 11 of 24 primaries against Carter, including the not-insignificant states of New York, Pennsylvania, California and New Jersey. (He impressed voters during the campaign by not drowning any more campaign aides.)

Kennedy battled Carter right up to the national convention in August, even seeking a rule change in an attempt to snatch the nomination from Carter.

A month after the convention, Kennedy’s supporters were still so bitter, one-third of them said they’d prefer Reagan to Carter. Another third said they were either undecided or supporting the liberal third-party candidate, John Anderson. (The rest had unaccountably drowned after being driven off a bridge.)

Independent candidate Anderson directed all his campaign fire at Carter, vowing to stay in the race even if it meant a Reagan victory. On Election Day, if Anderson’s votes had gone to Carter, Reagan would have squeaked into office with less than a 2 million-vote margin and Jimmy Carter would still be whining about it.

By contrast, Obama faced zero opposition from his party, the media, the education establishment or Hollywood, all of which were madly in love with him.

And yet, Obama may be the only president ever to win re-election with fewer votes than his initial election, down nearly 4 million votes compared to 2008.

Galston identifies the game-changing elections in the past century, leading to a period of one-party dominance, as 1900, 1936 and 1984. In each of these elections, the turnout rose and the winner received both a higher vote total and a higher share of the popular vote compared to his prior election.

As Galston says, “None of these things happened in 2012.” Turnout was down by 3.5 percentage points, Obama received 3.9 million fewer votes than in 2008, and even his percentage of the vote declined by about 2 points.

In 2008, a majority of voters said they thought the government should do more, not less. In 2012, a majority thought government was doing too much.

After Republican Gerald Ford — a technical incumbent — lost his re-election in 1976, Republicans didn’t engineer a comeback by adopting the idiotic policies of the Democrats. They certainly shouldn’t after the 2012 election.

Last year, Republicans had to run against an incumbent with a unified party and a unified media, 100 percent behind him, and they had to do it after waging their own bitter, endless primary fight, providing a wealth of sound bites for Obama TV ads.

Still, Obama did worse than nearly any other incumbent who has won re-election. Indeed, had the election been held a week earlier, Obama probably would have lost.

Stop running scared, Republicans. It makes you look like Democrats.

Ann Coulter is an author and political commentator.