Royalties are payments made to owners of creative properties... songwriters are a good example.
Your question appears to be about residuals, a different animal entirely. Producers of motion pictures and television programming become "signatories" with SAG and/or AFTRA, meaning that they agree to abide by the terms of these unions' (and other unions') collective bargaining with the organizations that represent the studios and networks.
When the owner of recorded entertainment generates income through the re-sale of a program, the directors, writers, performers and certain other craftspeople who were integral to the creation of the entertaiment share in the new income.
There are literally dozens of different contracts that detail different formulas for computing the minimum residual payments to be made; depending primarily upon the nature of the original production and its initial purpose (theatrical, network, cable, etc.) as well as the outlet on which it is to be re-broadcast (net, cable, DVD, in-flight, foreign markets, etc etc.). The Associate Producer on a show is the person who is at the front lines in knowing the various contracts their shows are produced under. And all those big buildings at the networks and studios are filled with accountants who do these computations all day long as movies and TV shows are continually repurposed.
In most situations, certainly those related to network game shows like TPiR or the network incarnations of "Pyramid", the residual is a percentage of the performer's/writer's/director's/etc's original compensation for their contribution.
And don't nobody try to screw with any of it! ;-)
Randy
tvrandywest.com
