In general, as I look at competitive games, I see two big styles emerge, that which I call efficiency races, and rock, paper, scissors. I believe that good competitive games are a blend of both, but that RPS should generally take priority over efficiency races.
A classic quote from Sid Meier, creator of civilization, “A [good] game is a series of interesting choices.” An interesting choice is a choice that has advantages and drawbacks so as to make it not explicitly better than any other choice the player has, except in the context of a specific situation. Ideally players must carefully evaluate their situation and make the right choice to come out on top.
By contrast efficiency races are not about making interesting choices nearly so much as perfect performance. Racing games are inherently efficiency races most of the time. There is a definitive path to victory and may woe befall all those who do not copy it as perfectly as possible. The issue with efficiency race style games is they end up with brain dead gameplay. In a shooter styled as an efficiency race, the game becomes, who can fire first and hit most consistently, without any other sort of mitigating factors.
Without RPS interactions, a multiplayer game cannot have strategy, comebacks are only possible by the lead player screwing up, or an external comeback mechanic forcing that player out of the lead, like the blue shells or lightning in Mario Kart.
Having a mix of RPS and efficiency race styles of play is generally speaking ideal, because it enables a depth of interaction, while giving players a basis to make their predictions on. When they know how much payoff their opponent gets from particular options, they can see what their opponent is biased to pick. Things based purely on efficiency (like tricky to perform execution based techniques) are often looked down upon by outsiders but they help create a sense of progression in the game and enables a whole range of interesting choices to be made that couldn’t otherwise that are balanced on the basis of how tricky they are to perform.
Quake 3 is an example of a great mix of efficiency and RPS. Quake 3 is a game about map control. In any other game this would be camping the best powerups, but in Quake 3’s speed prevents effective camping from ever being too viable. Essentially map control consists of grabbing power ups, like the red armor, yellow armor, and megahealth, so that you get an advantage over the opponent in battle. Beyond this, Quake champions watch the clock to determine when these power ups Respawn so they can be there when it happens to keep their advantage up. Quake is a massive battle of information. Metagame tactics include delaying when you pick up a power up to change the timing of that power up so it is harder for the enemy to pick it up and monitoring the timings of the power ups so you can predict where the enemy will want to go in the future.
Another example is in fighting games, where you have efficiency in the maximum combo punish you can pull off when you hit your opponent, and RPS in trying to hit them at all.