Balance decides that 2 purple + 1 blue + noobs = 7 blue. Then a silver throws a hissy fit because his cerb died and goes pure storage. Really great game.


Balance should not be done numerically, it should pick best player for one team. Then second two best players for other team, then another two best players for other team, and so on. Not this bullshit where it puts all coppers on one team and all blues on other.

Not numerically?!?

quote: Check that the edge cases make sense.

So you would rather have

3300
1801
1800
vs
1803
1802
300

than

3300
1803
300
vs
1802
1801
1800

?

Actually hang on. The spoiler says that team 1 had a 42% chance of victory. I suspect clans/parties were involved in creating this balance, as there is surely a more even win chance to create with 29 players.

See https://docs.google.com/spreadsheets/d/12juRYegGLi5y4JAbir_r8Hai0sylDIjFSFDwq6qf2Jo/edit?usp=sharing

(The replay may well be lying about ratings though).

Indeed 50% chances before game start were to be expected. I think it would be worth to look into how the code iterates through player constellations that produce equal win chances. Here is a starting point.

quote: Zero-K 1.10.6.0 Terra 2 (5+1/32) 7 hours ago: 4 players balanced Normal to 2 teams ( ( 1=71%) : 2=29%)). 4 combinations checked, spent 0ms of CPU time

quote: Zero-K 1.10.6.0 Into Battle v4 (9+5/32) 5 hours ago: 8 players balanced ClanWise to 2 teams ( ( 1=52%) : 2=48%)). 16 combinations checked, spent 0ms of CPU time

If the number of players in the room is large, the balancer will almost always manage to find teams with very nearly equal rating average, so you will almost always see 50% or occasionally perhaps 51% in large teams.

(Broadly speaking, this is because (a) the number of potential team assignments increases exponentially, and (b) even a randomly selected team assignment is increasingly likely to be pretty close to balanced as the number of players increases.)

If I remember the code correctly, the "empty" player is assumed to have rating equal to the average rating of all players in the room. Perhaps it should count for less than that. I am not sure if anybody has run the numbers to figure that out.

quote: Actually it's not exponential but a Binomial coefficient (N choose floor(N/2))/(2 - N mod 2).

According to Wikipedia this is ~ 2^(n)/(2*sqrt(pi*n/2)) for large even n; so there is a pesky sqrt(n) term in the denominator.

quote: Rather the average of all players in their team.

I think this is (implicitly) correct for the LegacyBalancer code used for large teams. I was thinking of the PartitionBalancer which explicitly adds a dummy player before choosing teams. The practical difference is probably minimal.

quote: I have the theory that the rating of players who tend to get 2nd coms is distorted to compensate the misconsideration on average.

As a ballpark estimate, even the #1 player only gets an extra commander about 1/4 of the time.
[Spoiler] According to DeinFreund's data the winrate in 4v5+ games for the larger team is less than 53% (and uneven games below that threshold are no longer played by default, though historical games do still affect rating).

By definition these games must be priced in to the ratings of higher-rated players, but it seems hardly sufficient to explain the 500-600 rating gap between the top of the casual and competitive ladders. I think the simplest explanation for that is that a high rated player influences much more of a 1v1 game than they do a teams game, even a 2v2, so they have more opportunities to turn superior skill into a W.

Chance of victory: 37.1%

I knew it was really bad, it keeps getting worse.