GOV. CHARLIE BAKER is not running for reelection, but he is likely to cast a long shadow over the race to replace him. 

A new poll released Monday by the MassINC Polling Group found that the popular Republican governor is likely to play a role even in the Democratic primary.  

The poll finds that Baker remains more popular than any of the Democrats or Republicans running to replace him. Sixty percent of voters have a favorable view of Baker, and 23 percent view him unfavorably. That compares to a rating of 44 percent favorable and 19 percent unfavorable for Attorney General Maura Healey, who is the frontrunner in the Democratic primary. 

Asked about ideology, the biggest group of likely voters – 45 percent – want their next governor to be similar ideologically to Baker, while the remaining voters were split between wanting a governor who was more liberal (26 percent) and more conservative (23 percent). Among likely Democratic primary voters, half wanted their next governor to be ideologically similar to Baker, while 38 percent wanted the person to be more liberal.  

The poll found that 42 percent of voters, including half of Democratic primary voters, were more likely to support a candidate who had Baker’s endorsement.  

His base has long been more in the Democratic Party than it is in the Republican Party,” Steve Koczela, president of the MassINC Polling Group, said of Baker. 

Baker’s popularity may be why Healey has so far hesitated to be too critical of him. According to the MassINC poll, Healey entered the Democratic primary for governor as the immediate frontrunner, but many voters are still deciding. 

The poll found that today, Healey would trounce her opponents with 48 percent of the vote, compared to 12 percent for state Sen. Sonia Chang-Diaz of Jamaica Plain and 3 percent for Harvard professor Danielle Allen. Of the three Democrats running for governor, Chang-Diaz has been the most critical of Baker. Thirty percent of likely Democratic primary voters still have not made up their minds. 

You still have a considerable number who are undecided at this point,” Koczela said. Particularly in party primaries, Koczela said, voters often do not make up their minds until close to an election. 

Part of Healey’s lead may be that she has far higher name recognition than the other candidates. But Koczela said there is no guarantee that other candidates will see a boost in name recognition before the election, so there is an advantage to having strong name recognition early on. 

The poll did not ask about a matchup in the Republican primary, where Geoff Diehl, a Republican former state representative and a supporter of former President Donald Trump, is running against businessman Chris Doughty. Of all the candidates for governor from both parties, it found that only Diehl has a rating that was more unfavorable (16 percent) than favorable (14 percent favorable). Doughty is largely unknown. 

All the candidates will face the challenge of getting voters to turn out.  

With just over seven months before the primaries, 38 percent of voters plan to vote in the Democratic primary, 21 percent in the Republican primary, and 32 percent do not know. Unenrolled voters, who comprise more than half the electorate, can vote in either party primary.  

The poll found that the other statewide races on the ballot without an incumbent running – for lieutenant governor, auditor, and attorney general – are wide open, and voters barely know who the candidates are.  

Former Boston city councilor Andrea Campbell would enter the race for attorney general as the favorite, with 31 percent support compared to 2 percent for Quentin Palfrey and just 3 percent for the only declared candidate in the race, Shannon Liss-Riordan. Her support is highest in the greater Boston region, within Route 128. But the poll found that 63 percent of voters do not know who they would vote for or would not support any of them. 

In the race for auditor, state Sen. Diana DiZoglio and former assistant secretary of transportation Chris Dempsey are effectively tied, with 13 percent and 12 percent, respectively, but 74 percent of voters do not know who they will support, would not vote, or would choose another unnamed candidate. 

In the lieutenant governor’s race, Salem Mayor Kim Driscoll leads with 10 percent of the vote, while state Sen. Adam Hinds, state Sen. Eric Lesser, and state Rep. Tami Gouveia are all tied at 5 percent.  In that race, 74 percent of voters have not made up their minds, would not vote, or would choose another candidate. 

The poll did not ask about the Secretary of the Commonwealth race, where incumbent Bill Galvin is facing Boston NAACP president Tanisha Sullivan in the Democratic primary. 

The poll was paid for by Policy for Progress, a progressive Massachusetts policy organization that is a project of Education Reform Now Advocacy and run by Democratic activist Liam Kerr. The poll of 504 registered voters was conducted January 18-20 and has a margin of error of 4.4 percentage points. The MassINC Polling Group has the same parent company as CommonWealth.