As far as I can see, there are two types of Luck Manipulation, both of which should be noted in some way.
I'm going to use movies that I worked on for the sake of examples, since I know how luck manipulation factored into their making.
1.Luck manipulation that affects the moment-to-moment gameplay
This is doing things like manipulating enemies using the RNG to do favorable actions for the runner (e.g. move out of the way or not spawn at all). Another example is manipulating bosses to do quick patterns.
It can also be purely superficial, like making several enemies drop One-Ups in a Mega Man run.
[1756] MSX Contra by scrimpeh in 10:21.37 is an example of this, as enemy spawn timers and turret spawn positions are manipulated between screen transitions to reduce lag. Here, luck manipulation factors inside nearly the entire run, as most screens contain enemies that need to be manipulated. However, it is hardly visible to the player, as most luck manipulation happens as idle input during screen transitions.
2.Luck manipulation that affects the game's route
This naturally goes hand in hand with route planning and tends to be of the "manipulating drops" variety more often. While this type of luck manipulation is more common in nonlinear games, even very linear games can exhibit this type of luck manipulation (e.g. manipulate a health drop from an enemy so you don't have to go out of your way to get health later).
Generally, this type of luck manipulation allows the runner to take a route through the game they otherwise wouldn't be able to. Sometimes, that is the only part of the game that actually uses luck manipulation in a significant way.
Also, any movie that involves grinding in a way uses this type of luck manipulation.
[2158] MSX Lupin III: The Castle of Cagliostro by scrimpeh in 07:15.86 is a good example of a movie that uses luck manipulation in its route. Several detours are avoided by getting items needed to complete the levels from random enemy drops.
Movies can contain a healthy share of both types of luck manipulation, too. The Arsene Lupin run linked above, for example, not only uses luck manipulation to influence the route, but manipulates several enemy spawns and item drops to go through the screens quicker.
The question becomes where to draw the line between "heavy" luck manipulation and "regular" Luck Manipulation, which will probably have to be done on a case-by-case basis. With the first type, I believe movies should be tagged in which a significant portion of the run involes luck manipulation. In the case of luck-based routes, movies should be tagged in which there is a significant and visible route difference compared to a non-luck based route. My 2 cents, I guess.
Lastly, while they may often look alike, Luck Manipulation is not to be confused with Enemy/AI Manipulation. To the uninitiated, this damage boost in Castlevania (.gif taken from Grincevent) may look like luck manipulation, but the Medusa Head's spawn is in fact entirely fixed and dependent on your y position, which is not RNG-based.
P.S: While this is unrelated,
this movie is the one movie I did which got tagged with Heavy Luck Manipulation that literally did not involve an ounce of luck manipulation. If the tag could be removed, that'd be grand.
