If opinion polls prove correct, on May 7 the Scottish National party will win nearly all of Scotland’s 59 parliamentary seats, making it the third biggest party at Westminster and potentially giving it a big say in how Britain is governed. There has been plenty of talk about the nationalists’ likely demands but much less attention has been paid to SNP’s record in power.

In a speech last month, Sir John Major described the SNP as a “deeply socialist” party. SNP leader Nicola Sturgeon’s rhetoric might give that impression. But a closer analysis of how the SNP has run Scotland — as a minority government between 2007 and 2011 and thereafter with a majority – reveals it to be more centrist than radical.

Alex Bell, the former head of policy for Alex Salmond, Ms Sturgeon’s predecessor, says the SNP has governed “like One Nation Tories, with pragmatic instincts unhindered by ideological baggage”. Determined to move Scotland towards independence, nationalist leaders want to persuade Scots they can act responsibly. Mr Bell adds: “They have hardly come up with an original policy in the time that they have been in government.”

Ms Sturgeon has played up rhetoric about “keeping Labour honest” and toning down austerity. She has tried to position the SNP as the strongest supporter of the National Health Service. But her government’s record suggests it gives health no special treatment.

Estimates from the Institute for Fiscal Studies suggest the budget for devolved public services has been cut by around four percentage points less in Scotland than in England in the past five years, thanks to the generosity of the Barnett formula.

Yet spending on health in England is forecast to have increased 6 per cent in real terms over the same period, compared with 1 per cent in Scotland.

Spending on schools in Scotland fell by 5 per cent in real terms from 2010 to 2013, according to Audit Scotland, a spending watchdog. Meanwhile the IFS says that spending on schools in England rose in real terms between 2010 and 2015. As a share of its budget, Scotland now spends less than England on the NHS and education.

It is hard to compare outcomes in health and education between Scotland and the rest of the UK, given their different systems.

A 2014 study led by Gwyn Bevan of the London School of Economics found that the NHS in Scotland and England performed similarly on waiting times but that preventable early deaths had fallen faster in the north east of England than in Scotland over the past 15 years. Results in Pisa international education tests are nearly identical in England and Scotland. But the attainment gap between poor and rich pupils is narrower in England, according to Sheila Riddell, a professor at the University of Edinburgh.

The biggest percentage increases in Scottish spending have come not in hospitals and schools, but in areas such as culture, transport, economic development, housing, free care for the elderly — and higher education.

The abolition of the graduate endowment fee for Scottish undergraduates in 2008 has become the totemic policy of the SNP but it has not been universally praised.

Prof Riddell says the abolition of tuition fees has had no discernible impact on poor Scots’ access to universities. At the same time, the number of further education colleges has fallen from 37 in 2011-12 to 20 in 2014-15.

Research by Lucy Hunter Blackburn shows the SNP halved spending on student grants in real terms, meaning that many poorer students are worse off under its system. “Scotland is the only part of the UK where borrowing is highest among students from poorer backgrounds”, the former senior civil servant says.

Another characteristic of the Scottish government is a tendency to resist devolving power. “The first thing that comes to mind when thinking about the SNP government is centralisation”, says Alison Payne, research director at Reform Scotland, a think-tank. She notes that, as well as college and fire station closures, council tax has been frozen since 2007, restricting local authorities’ flexibility.

Ms Payne says the clearest example of centralisation is in policing. In an effort to save money, in 2013, Scotland’s eight local police forces were replaced by a single force: Police Scotland.

Police Scotland is led by Chief Constable Sir Stephen House, the former chief constable of Strathclyde police. The “Strathclydisation” of Scotland’s police force has meant the use elsewhere of tactics popular in Glasgow, such as armed police officers.

Dr Kath Murray of the University of Edinburgh has documented how “stop and search” policies pioneered by Strathclyde have been appropriated by the single force. Rates are four times as high in Scotland as in England and Wales and most are “without reasonable suspicion or legal authority”. An independent review has been launched.

Despite the controversy over some aspects of policing, this major reform is also evidence of the SNP government’s keenness to win the consent of interest groups. “Scotland has a more consensual way of making public policy”, Prof Keating explains. This is partly a function of Scotland’s size. SNP advisers say that for most policy areas they can to bring together the key decision makers in one room — and they know each other already.

The mix of centrism, centralisation and corporatism has, in many eyes, gone alongside another defining aspect of the SNP — outward competence. Lindsay Paterson, a professor at Edinburgh university, says that the SNP has come across as “substantial, competent and on message”, in contrast to the previous Labour-led government. But Prof Paterson adds that the party’s discipline and lack of scrutiny means “they have created a sense of competence even when they haven’t been particularly competent”.

The core of the SNP team has known each other for at least two decades. There has been one major reshuffle to replace a failing minister in eight years, Mr Bell says. Backbenchers are loyal and parliamentary committees are less combative than at Westminster.

So “Sturgeon’s challenge is to persuade the party it really is progressive despite evidence to the contrary”, according to Mr Bell. “She needs to dampen expectations”. For if it performs as expected next week, the SNP will find itself “finally being embroiled in areas where it has to make unpopular decisions”.