Josh Kraft is running in the wrong race.

He should be challenging a vulnerable Gov. Maura Healey in the Democratic primary next year.

Kraft, son of Patriots owner Robert Kraft, right now is fighting an admirable but likely futile battle to beat a powerful incumbent, Boston Mayor Michelle Wu.

The polls have Kraft, a first-time politician, trailing by double digits and the general election is in November, enough time to close the gap. But barring an unlikely sudden collapse by the popular Wu, he’s going to fall short.

Incumbent mayors in Boston are traditionally almost impossible to beat, a fact which Kraft certainly knew when he took on the race.

Wu has built a strong profile as a nationally known progressive leader and easily won her first race against a more moderate opponent.

But what if Kraft, a Democrat who until a few years ago was an independent, announced right after the election that he’s not done in politics?

He will be an even better candidate the next time around, more polished and learning from his rookie mistakes. So he should not be deterred or discouraged by losing to Wu.

It’s certainly not unusual for a politician on his maiden campaign to lose the first time around. Just ask Charlie Baker, who failed in his first gubernatorial campaign but came back to win the second go around.

A Kraft candidacy is too good to waste on a losing mayoral race. He’s got plenty of potential and money and the name recognition to build a statewide campaign right away after the November election.

He’s progressive enough so he can appeal to Democrats. But he would also appeal to voters in the middle, like Baker. And he won’t have to face the carpet-bagging charge, because he’s a Massachusetts guy.

Kraft has taken strong positions on Wu’s financial mismanagement and failure to listen to the public. Those issues are transferable to a statewide election and Healey.

Just look at Kraft’s new TV ads, which use testimonials from people to soften his image and begin to attack Wu.

“Josh will be a great mayor, a different kind of mayor, because he listens,” one ad says.

Substitute “governor” for “mayor” in the ad and it’s a great message to run against Healey, who also is known for pushing her agenda without listening to voters.

“Josh could have gone into the family business,” another ad says, referring to the Kraft family’s sports and business empire. “Instead, he chose service.”

That could also be an effective ad for a statewide campaign against Healey, who before becoming governor was attorney general for eight years.

It won’t be easy to dispatch Healey, a tough campaigner, but the race now looks more winnable than the mayoral campaign.

Running as a Democrat would give Kraft the ability to tap into disaffected party members as well as undeclared voters. Right now two Republicans are running against Healey, but they face the difficult job of separating themselves from President Trump and appealing to non-Republicans, which make up about 90% of the electorate in Massachusetts.

While Healey looks vulnerable, no prominent Democrats right now have enough guts to take her on in the primary.

Healey has completely mismanaged the migrant crisis, spending $1 billion a year because of the surge of immigrants under her watch.

She only recently has tried to contain it, and is now trying to rewrite history to make it seem like she’s the one who is fixing the problem.

Voters know better. And Kraft could exploit that, arguing that Healey should have known early on that the migrant crisis would bankrupt the state.

The business community would likely rally around Kraft in a statewide campaign, and he could take strong positions on taxes and Massachusetts’ out of control spending that would appeal to moderates.

So why not give it a try? And if he succeeds, he can lord it over the mayor and exact some revenge. Maybe he could even get his father’s soccer stadium built.