Fallacy of Division

"The whole is greater than the sum of its parts."

- Aristotle, averting the fallacy.

Fallacy of Division
 * Generalizing from a whole to the parts.

"A colony of ants can destroy a tree. Therefore, this ant can destroy that tree."

Pretty much opposite to Fallacy of Composition, which argues that the whole must have the same traits as the sum of its parts, among other things. In reality, it depends on the parts; peanut butter and chocolate might taste better together than any one component, while ketchup and chocolate, not so much.

Film

 * Trail of the Pink Panther, Curse of the Pink Panther, Son of the Pink Panther: Everyone likes a Pink Panther movie regardless of whether Inspector Clouseau (as played by Peter Sellers) is actually in it, right?
 * The film studio in Looney Tunes: Back in Action makes this fallacy by firing Daffy Duck from their next movie, based on the fact that Bugs Bunny has far more fans than he does. It ends up a spectacular failure without the classic Bugs/Daffy interaction.
 * Star Wars: The Clone Wars: a Clone Wars movie? The Warsies will love it, even though it is not directed by Genndy Tartakovsky or George Lucas and it's CGI. (the derivated TV series fared better, though)

Live-Action TV

 * Spinoffs are frequently based on such logic. When a Long Runner wraps, producers often try to build a new series around one or more characters.
 * The supposed Seinfeld curse is a classic example disproving this fallacy.
 * Joey: A spin-off of Friends that flopped horribly. Apparently the developers fell afoul of this fallacy.
 * "Hey, MythBusters is popular, and it has explosions in just about every episode! Let's make a show centered around Stuff Blowing Up!"
 * Leads to a great deal of Follow the Leader behavior. For any successful premise, particularly in cheap-to-produce game shows and reality shows, expect to see numerous imitators.
 * Subverted in the M*A*S*H episode "Rumor at the Top" in which the gang thought the Army was planning to send one of them to a new MASH being set up because the 4077th was so efficient. However, it turned out that the Army was planning no such thing as they realized that the 4077th only worked so well because of the combination of people.
 * Applied full-force to the M*A*S*H television franchise itself, which had two unsuccessful spinoffs - AfterMASH and W*A*L*T*E*R - that, for the most part, banked on the popularity of the second-tier cast and connections to the parent show itself. A third, Trapper John, M.D., was somewhat more successful than the other two, but did not include any of the original actors and was legally recognized as a spinoff of the movie.

Music

 * Many side-projects and solo works made by musicians who are/were part of bands that have already established a popular reputation can fall into this when they don't live up to the glory of their other/former, more popular band. i.e. Sid Vicious' solo project and Billy Corgan's band Zwan.

Real Life

 * Happens in sports all the time. It's almost guaranteed that some starter from a championship team, regardless of how much they contributed to the actual championship, will land a huge contract that next off-season.