So in my mod Uber Arena, one of the taglines I emphasize in promoting it is that it "uses no random number generators" in its game mechanics. That is, every new mechanic is designed to be 100% deterministic and predictable - in theory. But I've been thinking about this and wondering, just because something is not using RNG, does that mean it is indeed 100% skill-based and predictable?

One counterexample I can think of is the headshot system in Unreal Tournament, something that has proven to be a point of major controversy between the UT and Quake crowds, likely because of disagreements about the nature of predictability in game mechanics. So in UT, if you can headshot a player, you will almost always instantly frag them (or at least do significant damage). Obviously, to accomplish this, you have to "go for the head" (as Thor/Thanos would put it). Now, in theory, this is a 100% deterministic mechanic; it is based on a predictable variable - the position of the enemy player's head on the screen and how much screen space the head is occupying (closeness of the player). It seems like there would be no issue. Yet, headshots are often regarded as "random" despite, technically speaking, not being so at all.

The argument here is that, even though it is theoretically predictable, the amount of precision required to pull off headshots using actual skill rather than luck is so great that it exceeds human capabilities, even at top-level tournament play. The railgun, on the other hand, while also requiring good aim, is not so "hard" that a skilled player can't learn how to become a good RG user, as the area that needs to be hit is larger.

It seems, then, that there is a point at which, if a deterministic mechanic becomes sufficiently complex, it "degrades" into randomness because the player cannot feasibly track all of the variables, a phenomenon we'll call "decay into randomness". And to be fair, it's not like RNGs used in games are really random either; it's common knowledge that they use pseudo-randomness generated by seeding the computer clock and performing complex math to output a seemingly random result. Obviously, no one would seriously be expected to calculate RNGs like this on-the-fly in the middle of a heated arena FPS match.

The question is, at what point does "decay into randomness" occur? Where do you draw the line? What are the variables? Is there a formula or algorithm to describe it? For example, in the case of the headshots vs. RG, how small does the area to be hit need to become before it "becomes random"? There is disagreement here, since some argue headshots are skillful and you just need to be good enough to aim at the head consistently, and others feel that is too much to expect out of even the most skilled players and thus it's pure luck. Who is right?

There is also Miller's Law from psychology, or the "Magical Number Seven, Plus or Minus Two", from George A. Miller's famous 1956 paper, where he postulated that the human short-term memory capacity (roughly) ranges from 5 all the way to 9. This principle does put a cap on how many variables a player is reasonably expected to track in an arena FPS match. In a duel, for example, the player is likely timing the RA and MH, as well as attempting to derive the other player's position based on sound cues, which already takes up 3 "slots". If they're tracking another, lesser armor, that's another slot taken. And likely other, more subtle variables too. Once the capacity is exceeded, the player will have to start "dropping" game variables to keep track of and leave them to chance. Adding more things for a player to keep track of adds more skill up to a point, but once you reach the memory limit (which is made more complicated by its fuzziness), it could be argued that too many mechanics/variables might actually decrease skill. Is this true?

Finally, it seems there are some random game mechanics that do appear in competitive play, but are generally considered to be "acceptable". For example, in TDM, while the respawn times for power-ups are fixed, the initial spawn times are randomized. Why is this "okay"? Wouldn't it still be better if they were fixed as well, so players could time the initial spawn as well? Or is there something to be gained from making it random that somehow adds more skill, contrary to the intuition that randomness removes skill? (In Uber Arena, it's worth noting that initial spawn times are also fixed, at 45 seconds into the game, making them completely predictable)

I think this is a really fascinating topic and it would give some good insight into the nature of arena FPS design. Is there anyone with a good background in psychology that could provide more insight? Has there been previous research done on this?