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 stupidly 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 Beyonce.

It appears that 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, incumbent William Howard Taft lost his re-election to fellow Republican Theodore Roosevelt after first facing him as a primary opponent, then as a third-party candidate on the “Bull Moose” ticket.

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

— In 1976, incumbent Gerald Ford was primaried by Ronald Reagan, who nearly beat Ford on the convention floor, losing by on 1,070 votes to 1,187. (And Ford still almost won the general election!)

— In 1980, President Jimmy Carter was primaried by Teddy Kennedy all the way to the convention, then faced John Anderson, a liberal third-party candidate, in the general election.

— In 1992, incumbent George H.W. Bush was challenged by Pat Buchanan, who won an astounding 37 percent of the vote in the New Hampshire primary. Then, Ross Perot ran a shockingly popular third-party campaign, winning 19 percent of the general election vote — mostly, polls showed, from Bush voters.

The one time Republicans beat a sitting Democratic president was in 1980 when Reagan beat Carter. Not only had Iranian savages been holding 52 American hostages for more than a year, but Carter was badly battered by both a primary challenge and general election opponent. (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, California, Pennsylvania, 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.

By contrast, Obama faced zero opposition from his party, the media, 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 first 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.

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 an incumbent squeaked back in last year.

In 2012, Republicans had to run against an incumbent with a unified party and a unified media, 100 percent behind him. They had to do it after waging their own bitter, endless primary fight, providing a wealth of sound bites for Obama TV ads and a lot of sour Republican primary voters.

Still, Obama did worse than nearly any other incumbent who has won re-election – which, as we have seen, is almost all of them. Indeed, had the election been held a week earlier, before Hurricane Sandy, Obama probably would have lost.

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