Not many politicians choose to have a blooper tape at their launch. But Gladys Berejiklian is battling an interesting problem: she comes across as too diligent, too hard working, too serious.

So in her introductory video screened before she took the stage at the Liberals’ state campaign launch at Penrith on Sunday, it was the glimpses of a spontaneous, laughing, mistake-making Gladys that got star billing. Her ministers got asked to point out her faults: stubborn, said health minister, Brad Hazzard. Too punctual, said the treasurer, Dominic Perrottet.

In a state with record low unemployment, the strongest growth of all the states and coffers overflowing with funds, Berejiklian should be looking at a solid win.

She also has a great personal story: a child of migrants, public-school educated, highly successful academically and the state’s second woman premier.

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But instead she is behind in the polls.

With just 13 days until NSW goes to the polls, a ReachTEL poll commissioned by the Sun Herald and published this weekend, had her government trailing Labor 49-51 on two-party preferred terms.

Part of the Berejiklian government’s problem is that despite an impressively long list of projects, many are still not finished. They’re tantalisingly close. The North West metro, Sydney’s first new rail line in decades, is due to open in April. The extensions to major freeways will be ready within six months and the Eastern Suburbs light rail by the end of the year.

During its 16 years in office Labor announced several ambitious transport plans but failed to deliver. Transport projects take time, and with little in the infrastructure pipeline, there have been precious few ribbons for the Liberal premier to cut.

Labor’s Michael Daley, who has been anxious to avoid too much scrutiny of his party’s record, has instead adopted a “look over there” approach by grabbing on to the argument that Berejiklian is wasting money on edifices such as redevelopment of Allianz stadium, at the expense of other spending priorities such as health and education.

The difference between knocking down the stadium – $750m versus a refurbishment at $314m is just over $400m, which in the scheme of a $50bn infrastructure spend is not huge.

But Daley has found a sweet spot with this argument that somehow the government is prioritising stadiums over schools and hospitals.

She’s also battling the headwinds created by her federal counterparts. Australia’s third Liberal prime minister in four years, Scott Morrison, attended Sunday’s launch but did not share the stage.

Nonetheless, he was at pains to take a bit of Berejiklian’s glory at a doorstop outside the event, reminding the media, who were more interested in whether he had been sidelined, that it was “always the Liberals” who deliver on the economy.

But perhaps there is another current in Australian society that Berejiklian is battling: her gender.

NSW has never elected a female premier, though the state has had two.

Labor’s Kristina Keneally, was given the job when the party had hit rock bottom, rocked by a series of corruption scandals. It had almost no chance of gaining another term in power.

Berejiklian inherited better circumstances, after the resignation of former premier Mike Baird for personal reasons, but still must overcome a narrative that she is somehow too serious, too scolding, and if Labor prevails, too chaotic and too arrogant.

Questions have been asked if there is an element of sexism operating in the electorate that rewards men for toughness and hard work but marks women down for the same.

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Labor’s Michael Daley, who is still struggling to be sufficiently known, was certainly not hiding his federal leader. Bill Shorten was centre stage at Labor’s launch in Revesby, driving home the narrative of an arrogant government that’s not listening.

Though which one was deliberately blurred.

Daley was hammering away at his theme, that the Berejiklain government is out of touch.

The only way to fix things was to change government he said.

“Before our hospitals are sold. Before they privatise the rest of our electricity network and hike prices even higher. Before the Liberals and Nationals build more air-conditioned corporate boxes than air-conditioned classrooms.”

Berejiklian’s message is in direct contrast: “NSW can have it all,” she says, adding that it’s not a matter of choosing between hospitals and schools.

In fact, her government has spent up big on hospitals in particular.

She will now seek to ramp up a big sales pitch in the last two weeks of the campaign.