Calculation aims to take risk out of deciding whether follow-ups to cinema hits will be a sure thing, or a disastrous gamble

Ever wondered why Spider-Man 2 triumphed and Basic Instinct 2 bombed? Now a group of academics have come up with a mathematical formula to predict the fortunes of a film sequel.

Hollywood has long known a follow-up is a fairly safe bet and franchises from Pirates of the Caribbean to Star Wars have dominated cinema schedules for years. But until now decisions about what to invest in a sequel or how much to pay for rights to a franchise have been based on some simple rules of thumb and a good dose of gut feeling.

Based on factors such as whether key stars are still on board, how long it has been since the last film and how that performed, the researchers say they can calculate what producers can expect to gross relative to a film in the same genre that is not a sequel.

"It is the industry of dreams, an industry of illusions, and lots of people go bust. The idea here is to put some more analytical thinking into the process," says Professor Thorsten Hennig-Thurau, of Cass Business School in London.

With follow-up films enjoying widespread box office success and strong DVD sales, financial investors and film companies compete aggressively to acquire sequel rights. The Teenage Mutant Ninja Turtles franchise was recently sold for $60m (£36m) and the rights to the Terminator franchise go on sale later this month. The academics hope their formula will help those participating in a growing trend for auctions for such franchises.

"I want this industry to recognise that it is not as different to other sectors as it thinks it is. What we are talking about here is brand extension. How else would you come up with an adequate value or price? Now everyone can work out what a sequel right might be worth," says Hennig-Thurau.

The research, which will be published in the Journal of Marketing this month, examined data from all 101 movie sequels released in North American theatres between 1998 and 2006 and a matched subsample of stand-alone films with similar characteristics. According to the formula, upcoming sequel The Twilight Saga: New Moon should be expected to return $34m more for the producers in its US run than a comparable vampire/ teen romance movie with the same characteristics that is not a sequel.

The figure is calculated by projecting an overall revenue of $267m in the US, of which $130.6m would flow back to the producing studio. Once this figure is adjusted for risk – at a level of 75% – the producers can expect to generate $109m in revenue. An alternative "twin" movie has projected revenues of $198m, leading to producer revenues of $96.9m, which, accounting for 75% risk, equals $65.5m.

"Movies like the Twilight sequel New Moon are highly lucrative and relatively safe bets if key parameters, such as original cast, are maintained," says Hennig-Thurau. Star continuity is where Basic Instinct 2 went wrong – no Michael Douglas. "The time difference between the two films was very, very long and actor continuity was halved in that you only had Sharon Stone and it was a pretty aged Sharon Stone," he added.

On the whole, however, sequels do well and often outperform the original. That is especially true now studios are presenting films as a franchise with a narrative woven throughout several instalments. "We are not really talking about sequels any more. We are talking about films that are conceived of as longer plays than one film... You are saying to the audience: 'This is a story, you have got to stick with it.' You buy into that particular number of films that will be coming out," says David Hancock, head of film and cinema at media research company Screen Digest.

Underlining that audience loyalty, Hancock notes that in the US last year, just 4.2% of releases were franchise films but they accounted for 20.6% of box office takings.

All this is a far cry from the law of diminishing returns of the 1970s and 80s. "The advent of home video around the mid-1980s changed the trend as larger audiences watched films at home and then flocked to see the next instalment when it arrived in local cinemas," says Mark Batey, chief executive of the Film Distributors' Association.

So in the 1990s the second film in the Austin Powers series grossed nearly five times the box-office take of the first one. A more recent example, the revival of the Star Trek franchise this summer, saw JJ Abrams's new film gross £21m in UK cinemas, which is more than double the return of any of the previous 10 Star Trek feature films.

"There is clearly a public appetite for new stories taking favourite characters on new adventures and from an industry point of view, there is arguably less risk in investing in the production and release of a property which has a proven track record," says Batey.

For film producers fighting lacklustre DVD sales, sequels bring an added benefit. Hennig-Thurau's research showed that DVD sales of the original movie often spike when a sequel hits the cinema screens. Once that sequel is out on DVD it also has a good chance of strong sales. The first week of DVD sales often outperforms the early days of cinema release, according to the British Video Association.

"It's clear, by straightforward comparison of sales data, that sequels comprise a growing proportion of DVD sales. The number of sequels that appear in the latest annual DVD sales charts has doubled since the mid-1990s," says BVA head Lavinia Carey.

DVD charts and cinema rankings packed with the likes of Shrek the Third, Transformers 2 and Ice Age 3 have, of course, incited the wrath of film critics worried about a lack of creativity. Cinema-goers have also complained of "sequelitis". Such criticism may have been justified in the days when making a sequel was a relatively lazy process of playing on the name, recognition and fan-base of the first successful film, says Hancock. But now studios have woken up to the perils of milking a brand too far.

"The nadir of sequels was Police Academy. What happened there was, hey we're essentially flogging a dead horse... But producers do learn from their mistakes. They know they flogged a dead horse in the 1980s and I don't think you are going to see us go to nine or 10 in franchises now."

The Film Distributors' Association is keen to argue, however, that sequel mania does leave room for original stories. Slumdog Millionaire is one of the top films of 2009 while The Full Monty remains one of the most successful British films ever released. "With 500 films released in UK cinemas each year, the blockbuster sequels tend to be concentrated in the top 40, but there's plenty of other choice for film fans during the year," says Batey.