Some other things to note from inspecting that contour plot:
When your AAF score is very low (by losing almost all your games, lower right of the diagram), you have little to gain by continueing to play, because even if you win, your AAF score will hardly improve.
When your AAF score is very high (by winning almost all your games, upper right of the diagram), you have little to lose by continueing to play, because even if you lose, your AAF score will hardly deteriorate.
I think those aspects are in the spirit of a sort of melee fight in an Arena: the defeated are progressively getting eliminated, leaving the victorious to fight each other.
You jump between contours with each game played, since your score can’t stay the same in a single game.
So if the top left contours flatten out, being up there and moving right with a loss, you stay on a similar ish score because of how flat neighbouring contours might be.
If the bottom right contours become more diagonal, you move diagonally with a win, and stay on a similar score with a nearby contour.
score can't stay the same
(game+1)(win+1-loss)=game(win-loss) => game+win+1-loss=0 but game = win +loss (assuming no no results or draws )
(game+1)(win-loss -1)=game(win-loss) => -game+win-loss-1=0 but game = win +loss.
I suppose that sounds quite discouraging for the person on 20/100 wins
Indeed. Your AAF score always goes up by a win and it always goes down by a loss.
But if your score is already low, it goes up very little from a win, and if your score is already high, it goes down very little from a loss. So there is an incentive to keep playing when your score is high and there is also an incentive to stop playing when your score is low.
In that sense it is sort of a “soft” knock-out system.
Very cool! I’m going to have to look into this more and run some simulations. However, based on the other comments, it seems like it has the desired outcome (encourage play even if you are winning).
In practice, there aren’t really situations where someone’s has a 10/10 record and loses to a 12/100 player. What more often happens is there are a few people who go 8/8 or something while others go a more normal 5/6.
That 8/8 person is usually a mis-ranked kid. So they have the double effect of kids playing fast and sandbagging (accidentally or not) leading to wins. However, that sort of person would win anyway in a different style of tournament.
For tie breaking I use the average SOS, which I think generalizes nicely.
Also thanks to the mod who split this out into it’s own thread!
If you don’t mind playing that other game that starts with a C… lichess has a good implementation of arena tournaments. I’ve played that once before and I enjoyed it quite a bit (even though I got thoroughly crushed)
In that case, maybe I have some leftover privileges from being a moderator.
But I am confused about that, because in my recollection I did have some forum editing tools available before I became a moderator. I just didn’t use them then, because I was afraid to mess things up.
You had the “moderator” flag removed but you are still trust level 4 leader. It’s probably fine for you to keep that if you like, but if you would prefer to be a normal regular I can do that for you. LMK
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