You know those single player RPGs that you have a ton of fun with, but when you're completely done, there's not much of a reason to do another playthrough, aside from self-made challenges, nostalgia, and perhaps understanding the story better? That's why I'd like to have this thread dedicated to thinking up an idea that involves competition with other players through an online server that is NOT simply your team versus another player's team.

An idea I had was have randomly selected party members, who have randomly selected gear/items, fight a certain amount of randomly selected enemies per battle, and for every win, you get points. Throw in a time bonus for winning under X minutes/seconds to get even more points. Once you get a game over, your record gets submitted to an online server for X total battles/X total points, so players can compete for the highest score. The more wins a player racks up, the more enemies are present in future battles. I can see how randomly selected party members, gear, items, and enemies per battle could screw you over if you have bad luck, but I thought it'd also be too boring to retry for a higher score with everything being similar, so that's why everything is random.

Do you think this idea works? Do you have any input to polish it up? Can you think of another idea that'd be even better for the concept of player competition?

I like the idea of leaderboard competition, but I am not so sure about how nice it is to make things random like that. A couple of ideas below:

You could have timed leaderboards (say, weekly) and present a specific challenge, such as limited party members, spells only, double damage, or whatever. Make enemies and the scenarios of the week fixed, so players can optimize their strategies for the given challenge. Then, score can be based on how fast players finish the challenge.

I also wouldn't fully disregard team-vs-team battle. One thing I thought about was either having time turns to force players to think quickly, or even alternating actions. Such scheme could be combined with the challenges I mentioned above.

Of course, in theory all of this has the potential to be fun, but I would expect a lot of prototyping and tweaking to make any such competition work. 

I'd recommend keeping the randomness out to keep it feeling like an even playing field, if you include character customisation you get all the feeling of randomness you need from your "random" opponent which is always the player's main focus. Plus people feel far more attached to a character they made themselves, increasing the probability of players coming back again.