A website called BoxOfficeQuant put together an intriguing graph last month. The Sequel Map charts Rotten Tomatoes' average scores for various sequels against the films from whence they sprang. Forget Alien vs. Predator; this is Alien vs. Aliens.
You'll find a clickable version of the graph in BOQ's post. Hit it and you're taken to a larger image; hit that image and it zooms in wherever your cursor is to the extent that you can actually read the movie names amidst the circles. If, as happened with me, the graph doesn't quite register with you at first, all you have to do is realize that it's been shifted 45° to make the dotted line horizontal — just cock your head to the right.
I haven't examined it comprehensively, but despite the aim of only using the second film in a series of more than two the author has included The Muppets Take Manhattan instead of The Great Muppet Caper. My guess is that mistakes like that are rare, how-ever, since many of the sequels in existence are either labeled numerically (making a second effort pretty easy to determine) or the only sequels in their franchises.
An observation not included in the BoxOfficeQuant post itself is that, while sequels
as a general rule may not live up to their predecessors, a surprising number of sequels to highly acclaimed films are themselves well reviewed. There's fact a real glut at the apex of that dotted line, in fact with very little daylight between several high-scoring second installments and their firsts. Toy Story 2, Pink Panther sequel A Shot in the Dark, and The Godfather Part II are all up there, of course, and the known trend of initial sci-fi and superhero sequels often equaling if not bettering their predecessors in critical and audience reception is on display, from The Empire Strikes Back to Termin-ator 2: Judgment Day to the more recent The Dark Knight, Spider-Man 2, and The Lord of the Rings: The Two Towers.
Updated and revised January 2019
Sequel Map image © 2011 Edmund Helmer.
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