“DEADPOOL”, which so far has taken more than $500m in cinemas worldwide, is an atypical blockbuster, a foul-mouthed anti-hero film with a mature “R” audience rating. But in one important respect it is typical of many of Hollywood’s most successful movies: it does not rely on a world-famous star to sell it.

In contrast, two recent “star vehicle” films struggled to attract audiences despite heavy promotion and high-profile openings on Christmas Day in America. “Joy”, with Jennifer Lawrence, and “Concussion”, with Will Smith, both failed to earn back their production budgets at the domestic box office and also fared poorly overseas. What happened? Ms Lawrence is by the reckoning of some the biggest star in Hollywood’s firmament; Mr Smith held that unofficial title for years. Have film stars lost some of their lustre?

Overall, the cinema business’s health seems as rude as ever. Revenue from the American box office grew by 6.3% in 2015, to a record high of $11 billion. Thanks to droves of new filmgoers in China, where the market grew by 49% last year, global revenues increased by 4% to $38 billion. The industry has held up well against increased competition from streaming services that give people plenty of options to watch films at home. The stars with the biggest global profiles, such as Tom Cruise and Leonardo DiCaprio, are instantly recognisable in lucrative overseas markets.

But much of the industry’s recent success, at home and abroad, comes from the rise of the big special-effects event film: franchises like “Fast and Furious”, “Avengers”, “The Hunger Games”, “Jurassic Park”, James Bond and “Star Wars” led a group of 14 films with more than $500m each in worldwide box-office takings last year, up from just five such films in 2006.

Such productions are more likely to make stars than to be made by them. “You really don’t want to have a movie star” in certain big franchises, says a senior studio executive: the films will be hits either way, so why pay more? Jennifer Lawrence was not “Jennifer Lawrence, biggest female movie star in the world” until she made the first “Hunger Games” film.

An analysis by The Economist of two decades of box-office results in America and Canada does not refute Ms Lawrence’s status as one of the biggest box-office draws (see article). But it is hard statistically to disentangle her singular appeal from the massive success of the franchise films she has been in. By the same token, she should perhaps not be blamed for the poor performance of “Joy”—“without Jennifer Lawrence in it, it would have been a flop, a total flop,” says the executive.

Hollywood executives still want to believe in stars’ power to get bums on seats, so they will bet again on a headliner even after a few flops. There is some risk-aversion in this: if they make a flop with a big name in it, they are less likely to have to defend their decision to green-light the film.

This conservatism tends to favour the white male actors that have already attained superstar status over the selection of new and diverse talent (as does the fact that the decision-makers are predominantly white males too). The controversy over the lack of any black actor (among other omissions) in the nominees for this year’s Oscars ceremony, on February 28th, is in part the fruit of that mindset.

Academic studies in recent decades have generally failed to find any conclusive evidence to support studio bosses’ faith in stars’ pulling power. Our own analysis suggests only that a few of them do add a bit to box-office receipts. Number-crunchers at Epagogix, a company in London, use an algorithm to project box-office takings of films based on their story elements—including the use of special effects, a surprise ending or a cool location. And they reckon that as long as the stars look good and can act, they make scant difference, with at best a very few exceptions. It helps to have a damsel in distress, but it does not really matter which damsel.

Among the few stars who do, by common consent among studio bosses, producers and agents, seem to be guarantors of success are the biggest comedy actors—names such as Kevin Hart and Melissa McCarthy. This is in part because they signal to the audience precisely what kind of entertainment is on offer, and are good at delivering. Our analysis backs this, with a bunch of leading comedy actors strongly outperforming industry averages. But the trajectories of star careers leave a lot of room for guesswork. Bruce Willis was paid $5m to make “Die Hard” in 1988; some in Hollywood were aghast, but the movie was a huge hit. Then Mr Willis made more flops than hits (excepting the “Die Hard” sequels) before hitting it big again with “The Sixth Sense”. But this time, was it the star or the story?