A pirated copy of Sylvester Stallone-starrer “The Expendables 3hit the Internet last Wednesday. There have already been nearly 2 million illegal downloads of the film so far, with its theatrical debut still 16 days away.

Could this — counterintuitively — actually be a boon for the movie’s distributor, Lionsgate, and put more butts in theater seats when it bows Aug. 15? Some argue that piracy, in this case, could be a big win for Hollywood.

“Leaking a month before its release might just be the best thing that ever happened to ‘The Expendables 3,’” wrote The Verge’s David Pierce, who admitted he downloaded and watched a copy of the movie.

The “two-plus hours of near-flawless action porn” is tailor-made to be seen on the bigscreen, so the illicit copies floating around on torrent sites will only drive up ticket sales, in Pierce’s estimation. “I’m already counting down the days until I can see it in Imax,” he wrote. “Maybe one leak will change the industry, maybe it won’t. But it won’t hurt ‘The Expendables 3.'”

However, studies indicate that this isn’t true: Piracy is decidedly not an effective promotional tool.

EARLIER: ‘Expendables 3’ Leaks Online, Pirated Copy Downloaded 189,000 Times in 24 Hours

Indeed, pre-release piracy of this kind has a particularly harmful effect on box office, according to a study by Carnegie Mellon University researchers. On average, movies that are leaked before theatrical debut have 19% lower box-office revenue compared with titles pirated after theatrical release, the study found.

“There might be people who pirated the movie and will go see it anyway — I’m not disputing that,” said Michael Smith, a professor of information technology and marketing at CMU’s Heinz College school of public policy, and one of the report’s authors. “But the main effect is (piracy) hurts sales.”

Illegal downloads of “Expendables 3” clocked in at 1.89 million as of Tuesday at 6 p.m. Eastern, according to piracy-analytics firm Excipio.

Lionsgate has declined to comment on the leak of the film.

“The huge number of infringing downloads following the leak of this movie shows the extremely damaging impact of pre-release piracy and it reinforces the need for all players in the digital ecosystem to work together to help ensure an Internet that works for everyone,” said Howard Gantman, MPAA’s VP of global strategic communications.

Multiple studies indicate piracy has a negative effect on revenue. In a recent National Bureau of Economic Research book chapter, Smith and his CMU colleagues found that 16 of 19 papers published in peer-reviewed academic journals concluded that piracy harms media sales.

“The notion that piracy hurts sales is very much an accepted truth in the academic world,” Smith said.

The CMU team’s study was accepted last month for publication by Information Systems Research, which Smith said makes it the first peer-reviewed journal article to analyze the effect of pre-release movie piracy. The researchers applied standard statistical models for predicting box-office revenue, adding a variable for whether a movie leaked onto pirated networks prior to its release using data obtained from VCDQ.com, a site that monitors popular Internet file-sharing services.

The study examined 533 movies released between February 2006 and December 2008, of which 52 were subject to pre-release piracy (including movies that were released first in international markets). The few films that were pirated before their theatrical debut anywhere in the world represented a small subset, and included Fox’s “X-Men Origins: Wolverine” as well as “Star Wars Episode III: Revenge of the Sith,” Disney’s “The Avengers” and “Ratatouille.”

SEE ALSO: ‘Game of Thrones,’ ‘Breaking Bad’ Most Pirated TV Shows of 2013

The CMU researchers cautioned that piracy may affect different types of movies in different ways, and that its study relied on self-reported user data from a single website, VCDQ.com. The report also is based on data that is more than three years old; Smith said the research team expects to update the study.

And it’s worth pointing out that when it comes to TV shows, some industry execs have suggested that piracy might have a sliver lining. Time Warner chief Jeff Bewkes last year quipped that piracy of HBO’s “Game of Thrones” was “better than an Emmy,” while “Breaking Bad” showrunner Vince Gilligan claimed that illegal downloads helped the show gain fans.

For TV series, one or two pirated episodes out in the wild would mimic the free “sampling” strategy many networks use to drive up buzz — and might, theoretically, bump up audience overall. But if every episode of every season of “Game of Thrones” or “House of Cards” were readily downloadable in a high-quality format for free, that would likely depress signups to HBO or Netflix to some extent.

The research for CMU’s most recent paper, “An Empirical Analysis of the Impact of Pre-Release Movie Piracy on Box-Office Revenue,” was conducted as part of the university’s Initiative for Digital Entertainment Analytics (IDEA), which receives unrestricted funding from the MPAA (meaning the trade group does not have editorial control over any studies).

Smith noted that CMU researchers also have received grants from Google for previous piracy studies, funding that was also unrestricted.