Gender bias in popular movies – A computational approach

One of the movies in which they mention men are overrepresented is Pirates of the Caribbean (2007). I don't think overrepresentation indicates gender bias in that movie. It's a movie about pirates in 1728. Most of the characters in the movie are pirates, and only one pirate was female, if I remember correctly.

I wonder if a completely unbiased movie industry would still have an overrepresentation of men simply because historically, a lot of "exciting" jobs, such as pirates, were done mostly by men. It would be hard to make a historically accurate film about gangsters, bank robbers, politicians, war, etc. without a lot of males roles.

A similarly blunt-but-informative measure is counting "he"s vs "she"s. In Nabokov's Favorite Word is Mauve, Ben Blatt found that among New York Times bestsellers, "he" appears more often than "she" in 90% of those written by men and two thirds of books written by women.

A very biased article on gender bias, only talks about one gender. Is this inclusive? Is there similar research for the other people?