A new Boston Globe poll has Martha Coakley locked in a statistical dead heat with Charlie Baker, the presumptive Republican nominee for governor. Coakley’s lead in a matchup against Baker was once as high as 15 points. She enjoyed a double-digit edge over Baker as recently as last month.

But as big as the evaporation of Coakley’s lead over Baker looks, it’s just the beginning of the Democratic attorney general’s troubles. A closer look at polling in the governor’s race reveals far deeper worries for the Democrats’ likely nominee.

Polling data show that Coakley has been treading water since the beginning of the year. A January WBUR/MassINC Polling Group survey found Coakley getting 39 percent of the vote in a hypothetical November matchup against Baker. Seven months later, the Globe has Coakley polling at 39 percent against Baker. For much of the year, Coakley has been polling in the low 40’s; the gubernatorial race has narrowed because all the movement in the polls has been behind Baker.

Baker trailed Coakley by as much as 15 percentage points in a March WBUR poll. He was consistently down by double digits as recently as last month. The Globe’s most recent poll has him down by just three points.

Baker has closed the gap against Coakley by erasing her hold on independents, and eroding her edge among women voters.

A February Boston Herald/Suffolk University poll had Coakley down by four points against Baker among independent voters — a comfortable place to be, because unenrolled Massachusetts voters normally break against Democratic candidates. The March WBUR poll had Coakley up by four points with independents. As recently as mid-June, the Globe’s poll had Coakley and Baker dead even with independents. But Baker has made enormous gains with independent voters since then, and the poll the Globe released Friday has Baker with a 13-point lead over Coakley among independents.

Polls have consistently given Coakley enormous 30-point-plus leads over Steve Grossman and Don Berwick in September’s Democratic gubernatorial primary. Coakley is also the only of the three Democratic gubernatorial hopefuls to have consistently outpolled Baker in a November matchup. She’s been outpolling Baker largely because of strong support among women voters.

Women have been a key constituency for Democratic candidates in recent Massachusetts elections. When Elizabeth Warren topped Scott Brown two years ago, she led Brown by 18 points among women. A MassINC Polling Group survey taken after the 2010 gubernatorial contest found Baker had lost women voters to Gov. Deval Patrick by 24 points. By contrast, a Washington Post poll taken after Coakley’s 2010 Senate loss to Brown put her edge with women voters at just three points.

Women voters have paced Coakley’s head-to-head leads over Baker all year. Baker has been gaining on Coakley in recent weeks because he’s been eroding this edge. A mid-June Globe poll had Coakley over Baker by 28 points among women voters; over the past month, that margin has dropped to 19 points. Both sides of the prospective November matchup appear to be keenly aware of the importance of women voters. Baker has been on a big push recently with his wife, Lauren, and his running mate, Karyn Polito. And the state Democratic Party seized on Baker’s comments last week on a recent Supreme Court decision to paint him as a candidate indifferent to women’s health issues.

Meanwhile, Baker’s lead among men has grown from a six-point margin last month, to 14 points today.

Democrats make up 36 percent of the state’s electorate, so it would be difficult for Coakley to fall far below the roughly 40-percent mark she’s been polling at since January. Still, with Baker looking stronger every week, the longer Coakley stays stuck at 40 percent, the more her electoral floor also looks like her ceiling. Coakley doesn’t have to make enormous gains to come out on top in November.

Democrats have broken the 50 percent mark in a gubernatorial contest just once since Michael Dukakis left office, and the presence of two well-funded independent candidates makes it unlikely that November’s gubernatorial will have to clear 50 percent. Still, Coakley is going to have to do better than running in place.