The most seductive theory in sport has had one hell of a hearing during the past month. As the Women’s World Cup captured more hearts and minds, so the assumption intensified that England’s run will be a gamechanger, with elite success encouraging large numbers – particularly girls – to play football and get active. It sounds logical enough. Lucy Bronze, Megan Rapinoe, Wendie Renard and Rose Lavelle are fantastic role models, after all. There’s just one problem. There isn’t much evidence for what academics have called the “role‑modelling” or “trickle-down” effect.

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Remember when Boris Becker, Steffi Graf and Michael Stich brought an unprecedented number of grand-slam victories for German tennis? There was a decline in membership of the German Tennis Association afterwards. Similarly, in the run up to London 2012 people such as Colin Moynihan, then chair of the British Olympic Association, promised a home Games would “motivate a whole generation of young people as they seek to emulate their Team GB heroes”. The reality has been less rosy. A recent Sport England survey found one in three children do less than 30 minutes of activity a day – such as walking, using a scooter, or playing sport – with the sports minister, Mims Davies, calling it “simply unacceptable”.

We should not be surprised. Long before 2012 researchers looked at Australia’s Olympic results between 1976 and 1996, and identified no correlation between national sporting achievements and “sedentariness” rates in the population. Meanwhile a systematic review of public health initiatives after the 2000 Sydney Olympics suggested there was no evidence that the euphoria of the Games turned into increased activity, despite the silky rhetoric and promises.

Other research has found a slight negative correlation between Olympic success and mass sports participation. As the authors of another study put it: “It is a well‑known assumption that the success of professional athletes increases sport participation in their home country. However, the theoretical support for such a relationship, as well as the empirical evidence, is shallow.”

Read that again. Let it marinate. Across the globe, politicians and public authorities partly justify investment in elite sport based on the effect it has on the ordinary population. But the evidence that such trickle‑down effects in sport work is as elusive as trickle‑down economics was in Ronald Reagan’s America.

Of course some of us are inspired to take up a sport after watching it on TV but studies suggest much of this comes from a “substitution effect”, with already active people switching from one sport to another, or from encouraging lapsed players to dig out their racket or golf clubs again during Wimbledon or the Open. The challenge is getting more people to become more active more of the time.

What about women’s football? Clearly it is growing in popularity, so it can be tricky to disentangle increasing participation with the success of a national team. However a study looking at the after‑effects of Japan’s Women’s World Cup victory in 2011 does just that. The academic Hideaki Ishigami examined all extracurricular activities recorded by 1.5m female Japanese students in the years leading up to and after the tournament – helped by the fact the Nippon Junior High School Physical Culture Association, a national governing body, compiles registration data for 99% of schools in Japan by type of sport.

Facebook Twitter Pinterest Despite having fantastic gold medal-winning role models such as Jessica Ennis at London 2012, UK children now do less than 30 minutes of activity a day. Photograph: David Davies/PA

As Ishigami noted, more girls played football in Japan after 2011. But there was a blunt kicker: his research also found it was “no greater than expected by chance” once growing participation levels before the 2011 tournament were taken into account. As he put it: “We found no quantitative evidence supporting the role-modelling effect. This implies the increase in their participation following the 2011 World Cup would have been observed regardless of whether Japan won.”

As Ishigami notes, gender is clearly a factor. The Daichi Life Insurance Company has conducted annual surveys with 13-year-olds in Japan since 1989. According to their findings, girls’ dream jobs have consistently included teaching, the medical profession and catering – with sports never ranking in the list, even after the 2011 World Cup. That contrasts markedly with boys of the same age, who always include baseball or football. This difference in genders for sporting role models has been found in other countries, too.

The Recap

There is a message here for the Football Association and the government. Women’s football in Britain is clearly going the right way – given a record FA Cup final attendance, a new £10m Barclays sponsorship for the WSL, and a thrilling World Cup. But as we learned when England finished third in Canada in 2015 this is not enough. The Lionesses have again inspired the nation but now the harder work begins.

The game needs to better fertilise its grassroots – the FA’s new national strategy for girls aged five to 11 is a start – and get more consistent exposure. Stories that neither the FA nor Premier League considers itself capable of expanding the appeal of the WSL don’t bode well, given average crowds were under 1,000 last season, but just imagine the effect of a women’s match shown every Sunday on BBC2?

Meanwhile the fundamental point remains: elite success is not enough to get more people active. After Britain won only one Olympic medal at Atlanta 1996 there was a revolution in government funding that catapulted Team GB towards the top of the table. Is there a relentless desire for a similar upheaval when it comes to getting the rest of us moving, too?