math bork

quote: So our team Elo is bork and should first convert to some sort of log function before the linear average.

Not exactly sure what you mean by this, but if you want X + X vs (X - 120) + (X + 120) to result in 4:5, we'd just have to use your formula:

playerstrength=2^(ELO/120)

This is the same as comparing players to a theoretical 1 elo player. The linear averages would then be off by this factor of 1.25.

One thing current balance theoretically allows is a <0 strength player. The exponential function wouldn't allow for this.

Forum broken, here's a closing bracket to fix it: >

The values would be between 2^10 (ELO 1200) and 2^20 (ELO 2400). Floating points shouldn't have any problem with this. Make sure to add them up in ascending order, to prevent floating point inaccuracies.

A higher adjustment rate for the first few games after the change should help with the recalibration.

The problem is that you can't compare it with that data since people's skill isn't constant, it changes over time.
Moreover, the balancing throughout that time was based on the flawed algorithm, which means that your sampling of battles is already heavily biased.

There's two ways you can go about this.

Way One: You can assume that an individual's rating at any point in time - as caluclated by the Zero-K infrastructure - is reasonably correlated to their skill at the game and the effectiveness of their contributions to their team's victory, i.e. you can assume that that individual ratings are basically correct. You then suppose that the problem is the BALANCING method for team games, not the rating-determination method for individuals.

If that's your approach, then you can come up with your own algorithm which takes as its input the list of individuals who are playing a game and their respective Elo scores as of the time they play the game, and which produces an expected probability of one side winning. You can then do this for every game in the database. Then you bin the games and your resulting predictions into buckets of, say, 2% or 3% or 5% width. Then you see how well your predictions for each bucket match the actual results for that bucket.

I.E. you end up with, say, 1,000 games where one side is predicted (by your algorithm) to win at 55% to 57%. If that side turns out to have won 560 of those thousand games, then your algorithm is pretty good. If that side turns out to have won 400 of those thousand games, then your algorithm is pretty bad.

Way Two: You can assume that not only is the balancing method broken, but the RATING method is broken as well. Now your task is more complicated, but still possible.

You'll have to use the historical data to construct a new rating for each individual for each game they play, as of the time that they play that game, using your new rating method.

THEN you can test your new balancing method as above, using the new ratings that your new rating method has produced.

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You should probably also study the literature before you undertake this journey. If you are not already intimately familiar with the details behind FIDE's Elo calculations, Glicko, and TrueSkill, then you are not yet ready to be offering useful suggestions here.

quote: You name it. Any other model will suffer from the same

[Spoiler]

I found the historic data files so I guess I'll present my results in the next week.

quote: I don't think this makes sense. You are essentially adding fractions by adding the nominators and denominators separately. It may make sense here on some level, but transforming the elo value into another measure yields no reason for why team elo should be linear in that measure instead of the other one.

I am not adding fractions. I assign values based on log2(elo/120) and each fraction is individually and separately satisfied. The reason why this measure should be linear and not Elo itself is because Elo uses exponent to find a person's value.

TrueSkill would solve the problem, sure. But there must have been some design reason why we chose to use Elo instead of TrueSkill and with that assumption in mind I'm interested in fixing our use of Elo instead.

This is a really interesting idea!

Note that what you call 120 is actually 400/log_2(10) and thus 2^(1/120) actually 10^(1/400) =: B.

quote: The values would be between 2^10 (ELO 1200) and 2^20 (ELO 2400). Floating points shouldn't have any problem with this. Make sure to add them up in ascending order, to prevent floating point inaccuracies.

Yes. And the scale can be multiplied with any factor, so that we can get numbers rather like Sprung proposed in his 1st post. [Spoiler]I will use a general factor B^-eloShift to get playerstrength=1 for elo=eloShift. eloShift=0 is easiest to calculate, eloShift=1500 is most elegant (because it compensates the non-elegance of 1500), eloShift=1380 is used in Sprung 's 1st example. Thus

playerstrength = B^(elo-eloShift).

teamstrength is the average of the team's players' playerstrength.
Actually the only thing that changes is that team elo is no longer the normal average, but

team elo = log_B(teamstrength)+eloShift.

My observation with concrete values in comparison to the current system:
For teams with no elo deviation it results in the same. The higher a team's elo deviation, the better its teamstrength.

I have proven that using this new kind of team elo in the current elo calculation for 2 teams of any size results in win probabilitites proportional to teamstrengths. Because I have recently calculated the correct solution for ZK's team FFA elo (currently a wrong one is used), I wondered if teamstrengths are still proportional to win probabilities that were calculated by inserting this new team elo in the FFA solution. This would show that "playerstrength" is really fundamental. Unfortunately it didn't hold true, even though both alternatives seem valid.

TheEloIsALie indicated that the transformation could be arbitrary. So let's assume a general function f with inversion g, where

playerstrength = g(elo)
teamstrength = average of team's playerstrength
team elo = f(teamstrength).

Then we have the possibility to use either team elo for a probability calculation as usual or probabilities proportional to teamstrength. I have shown that the equivalence of both even for team FFA is equivalent to

2/(N(N-1)) sum from k=2 to N (1/1+B^(f(teamstrength_k) - f(teamstrength_1))) = teamstrength_1 / (sum from k=1 to N (teamstrength_k)).

What is f? Does such an f even exist?
[Spoiler]