If an organisation is playing at the highest level," says Amanda Goodall, "it needs to be led by someone who understands the business at the highest level."

Top architectural, legal and consultancy firms are invariably - and rightly - run by people with a first-class professional record, and not by outsiders claiming generic management or leadership skills. We can see a similar phenomenon in sport. Goodall, a Leverhulme fellow at Warwick Business School, offers striking evidence that it is the star basketball players who, 20 years down the line, prove to be the best coaches in America's top league.

Goodall's new book, Socrates in the Boardroom: Why Research Universities Should Be Led by Top Scholars, draws out this argument in relation to leading universities.

"The better the scholar," she observes, "the better the university does." Whether we look at the world's top 100 universities as a whole, only the American institutions among them, those with female leaders or even just the ones based in the UK, the same general rule applies: "Highly ranked universities have leaders who are more highly cited."

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Although Goodall scrupulously adds that this is only "on average", her research allows her to make some bold and specific statistical claims. "One extra point on a (university leader's) citation score", adjusted for differences between disciplines, "is associated with ten extra places up the world's top ranking of universities."

Something similar, perhaps more surprisingly, applies to business schools. According to Goodall: "An increase of 65 citations obtained by a dean is associated ... with a one-point move up the research assessment exercise for a UK business school."

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These are, of course, statistical associations that say nothing about the direction of causation. But Goodall goes further in her analysis of what she calls "a natural laboratory": the performance of 55 UK research universities in the RAE in 1992, 1996 and 2001. Over the relevant period, each university averaged almost exactly three vice-chancellors (or equivalents). These were all given a "P-score" (a president's individual lifetime citation score normalised for discipline).

Goodall then asked whether putting a better scholar in charge produced better results in subsequent RAE returns. The answer was a resounding "yes". "A hypothetical ten-point move in a vice-chancellor's P-score (averaged over the period 1990-94)", she writes, "is estimated to generate four excellent departments in 2001 - or three extra departments when other variables are included."

In other words, a vice-chancellor's world-class expertise in, say, biochemistry can generate excellence in quite unrelated disciplines.

Although the core arguments of Socrates in the Boardroom are rooted in detailed statistical analysis, Goodall acknowledges that they are also informed by her "professional experience of having worked in an administrative capacity with university leaders over a number of years".

Her own background is highly unusual. One kind of MTA, the model-turned-actress, is something of a cliche. The other sort of MTA, the model-turned-academic, appears to be pretty much unheard of.

Goodall left school at 16 and worked as a fashion model. In the mid-1980s, she switched track to become a development project worker in India, and then a political campaigner. Aged 33, and after a false start in law, she embarked on a degree in social policy and administration at the London School of Economics.

She found the atmosphere instantly congenial. "You were assessed by the piece of work on the table," she recalls. "Your past and everything else didn't matter. I found that really liberating and felt at home. It matured me and made me see the world objectively."

If she arrived at the academy comparatively late in life, Goodall now speaks about universities with the zeal of a convert.

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"The thing that's most divine about universities - apart from the stuff that comes out of them - is that people are obsessed by ideas," she explains. "That's incredibly refreshing. We strive to let the data drive our thinking. Some of the individuals may seem a bit odd, but that's just because they are so interested in what they are doing - and that's a fabulous thing to see."

There is also the question of Socrates in the bedroom. This would be nobody else's business, except that Goodall, unprompted, offers a warm but surprising tribute to her partner, Andrew Oswald, professor of economics at the University of Warwick. "I live with someone who works, lives, sleeps and dreams regression equations. He is so driven; he cares so much about what he's doing and how valid the data are. We talk social sciences in the middle of the night."

After getting a first in her undergraduate degree, she decided not to embark at once on a PhD and instead spent seven years working with three different university leaders. Her first post was as special assistant to Anthony Giddens, then director of the LSE.

"He's an obsessive researcher," she says of the acclaimed sociologist who is now Lord Giddens, a Labour peer. "And he continued to write while he was director. He would get on the blower, phone up academics around the world and say: 'We want you to come to the LSE. What do we have to do to get you to come here?' He got involved in the hiring process big time."

It was precisely Goodall's experiences of the various "emphases and preferences" of the three leaders she worked for that led her "to ask questions about what works and what doesn't, their differences in research backgrounds and the impact these had on the roles they performed". This became the topic of her doctoral research at Warwick, and now her book.

The statistical detail in Socrates in the Boardroom may be complicated, but the headline news could hardly be more clear-cut: "In universities, where the majority of employees are expert workers, having a leader who is also an expert is likely to be beneficial to the institution's long-term performance."

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On one level, this may not sound too unexpected. If we look at what economists call "revealed preference" - what top universities actually do - we find an overwhelming dominance of leadership by prominent scholars (although the LSE and the universities of Glasgow and Oxford at various times have been notable buckers of the trend). So, consciously or unconsciously, they know what works and are doing the right thing.

Yet Goodall argues that the correlation has never before been demonstrated so conclusively. She also believes that the message is still far from being universally understood.

When meeting university leaders for her research, she says, she would conduct the bulk of her interviews and only then reveal her evidence that "better scholars make better leaders".

"Some were genuinely surprised or even, in the case of non-academics, shocked," she reports. "Some people's faces dropped. One looked as if the floor had just opened underneath him."

"I would say it's not a given that people already know," Goodall notes. "In the past few years, the thrust of managerialism means that expert researchers have been pushed into the background. There has been a view that if you're a great manager you can lead in any sector." This, she speculates, may have led to some of the recent problems in the banking sector, where many directors had little understanding of the latest financial instruments.

Socrates in the Boardroom includes a case study about the hiring of the leader of a British research university, where the person specification seemed to emerge rather haphazardly from headhunters' interviews with faculty. "The board appeared not to be marrying the applicant with a predetermined strategy," she adds. Although the preferred candidate and eventual appointee was a top scholar, the runner-up was far less distinguished. High-level academic achievement was simply not given the prominence it should have had.

People who have spent a good deal of time in what is sometimes called "the real world" often find the atmosphere in universities eccentric, slow-moving and rarefied. Goodall does not see it like that at all. She admits that one does come across the occasional absent-minded professor. She even accepts that "a lot of academics think: 'Leadership is nothing to do with me. My loyalty is to my discipline.'"

But she also believes that stereotypes about academic unworldliness are greatly exaggerated. "It is convenient for managers and managerialism to make assumptions about what experts can and can't do," she argues, although "there's no evidence that they can't lead". A young scientist's life is all about "raising money, communicating what you're doing, co-ordinating huge teams of researchers, managing your grant, even in your twenties. Managing and communicating are part of what the academic world does and how it exists.

"Among the top people there are always some who can learn the art of leadership and management. There are those for whom a leadership role is not right, but there are far more people it is right for than we give credit to."

For institutions, the key to getting quality leadership is not to assume that it will spring up naturally from among the academic ranks, nor to think that it should simply be brought in from outside, says Goodall. What they must do is offer "short, very focused courses that potential scholarly leaders can go on at an early age".

All this leaves unanswered the big question of why the best researchers make the best leaders. British vice-chancellors present and recent include world-class experts in everything from molecular electronics to chemical thermodynamics, from social change in rural England to the lemurs of Madagascar. Could it be that the qualities of tenacity, dedication and sheer brainpower that got them to the top in such fields are likely to be transferable, and that they will tend to excel in pretty much any field they decide to turn their hands to?

That is no doubt part of it. But Goodall and the many university leaders she cites place the emphasis elsewhere.

A number of themes recur. One is credibility. "Being a good scholar", Goodall is told by one interviewee, "means that I can look a Nobel or Pulitzer prizewinner in the eye." Another is expert knowledge. "Because I am an academic," another interviewee says, "I am driven by the academy and the development of ideas and knowledge. It is my business. It is not possible for someone external to the academy to understand this." A third important factor is the signalling effect: putting an academic in charge sends a message to the world, and crucially to other high-flying scholars, about the university's real values.

A final issue is the role of vice-chancellor as standard-bearer. Goodall is sympathetic to the RAE, at least inasmuch as it has had "the consequence, intended or not, of giving leaders more power - and I do believe ... they have to have more power. I don't believe in the democracy argument and big committees." Those such as Giddens who found the time to submit research to the RAE while running their institutions make particularly inspiring role models.

In making such a powerful case for leaders who have "acquired a deep, inherent, instinctive understanding of the core business", Goodall presents a substantial challenge to our research universities. Yet the rewards can be equally substantial.

Take the case of the Rockefeller University in New York, which has been led since 2003 by Sir Paul Nurse, the British-born Nobel laureate. There were crucial moments in the institution's history, Goodall says, when "it took very clever people, with deep expertise in the relevant scientific areas, to pick some of the scholars to come and work there. They were the ones who knew that sparks would fly if you put them all in the same place."

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