Elo Rework

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Re: Elo Rework

Postby Joacgroso » Thu Jul 15, 2021 11:35 am

If this is implemented and grinding becomes impossible, shouldn't elo ranks be closer to each other?
Joacgroso wrote:I feel like I went from Light Yagami to Keiichi Maebara.

I still hope one day the game will have private lobbies. They would really help.
Also, please nerf vampire hunters.
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Re: Elo Rework

Postby Superalex11 » Thu Jul 15, 2021 12:04 pm

Joacgroso wrote:If this is implemented and grinding becomes impossible, shouldn't elo ranks be closer to each other?

It depends on BMG's preferences. Assuming they're using the standard preference of 10x odds per 400 elo (which I did in my calcs a post prior), the current rank tiers are arguably too close/small. Though of course playercount does play a big role, so there's no easy answer.
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Re: Elo Rework

Postby James2 » Thu Jul 15, 2021 2:10 pm

alex1234321 wrote:
James2 wrote:This will be the case if each game is elo neutral. Which is why I proposed regularly cancelling out faction elo gains/losses (say, every day) rather than making each game non-inflationary/deflationary.


I thought about this, but I prefer the idea of forcing each game to be neutral. If cancel out factional changes at the end of the day, people will experience Elo changes without doing anything. It would be extremely infuriating to find out you made Master Elo only for your Elo to decrease at the end of the day. Players would be rewarded or punished based on the outcome of other games that they have no control over. I know these would balance out in the long run, but the ToS playerbase is small and you'd have to balance minimizing random deviations with keeping Elo up to date.

I agree with the priority list that you previously mentioned although I would order the points 1, 3, 2, 5, 4 in terms of importance. Having a daily correction would slightly violate your second point while preventing the fourth one from being violated. Also, I would argue that Mafia should have a larger K-factor than Town since each Mafia member has a larger influence on who wins the game than each Town member. That's also why Mafia leavers are so much more annoying than Town leavers.

The thing is elo gains/losses from things outside a player's control (such as the quality of eight other townies) will cancel out in the long term. Whereas giving mafia wins/losses a greater impact on elo substantively favors those who are better at mafia and worse at town. The issue is clear if we look at the extreme cases:

1. A player who always wins as mafia and always loses as town while playing people with the same elo. This player wins 4/13 games (leaving neutrals aside), which is by definition less than average. Yet under your system he'd neither gain nor lose elo.

2. Individual townies have no control whatsoever over whether they win or lose. In this case, town wins and losses are effectively noise that cancels out in the long term. Thus even if town wins/losses have the same impact as mafia wins/losses, players' elo would still represent their skill as mafia (which is as it should be in this scenario).

Regarding the psychological aspect of it, people would gain elo as often as they'd lose it (assuming a decent algorithm). If frustration were enough of an issue you could just refraining from updating people's scores in real time (or label real time elo "provisional elo" or something else that sounds less important).
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Re: Elo Rework

Postby Superalex11 » Thu Jul 15, 2021 2:37 pm

James2 wrote:The thing is elo gains/losses from things outside a player's control (such as the quality of eight other townies) will cancel out in the long term. Whereas giving mafia wins/losses a greater impact on elo substantively favors those who are better at mafia and worse at town. The issue is clear if we look at the extreme cases:

1. A player who always wins as mafia and always loses as town while playing people with the same elo. This player wins 4/13 games (leaving neutrals aside), which is by definition less than average. Yet under your system he'd neither gain nor lose elo.

2. Individual townies have no control whatsoever over whether they win or lose. In this case, town wins and losses are effectively noise that cancels out in the long term. Thus even if town wins/losses have the same impact as mafia wins/losses, players' elo would still represent their skill as mafia (which is as it should be in this scenario).

Absolute winrate in an asymmetrical game design is meaningless with regard to elo. Elo is meant to reflect expected outcomes, meaning if, for example, one expects to lose with 100% confidence, they should lose 0 elo on a loss and gain infinite elo on a win. The faction-based k-factors OP suggests work assuming town and mafia have equal win chances (of course right now they don't, so the k-factors would need to be tuned). Without introducing faction-categorized elo scores, the only way to adequately balance elo changes to net zero (in population) is to explicitly control for it. Your proposal of cancelling factional differences at regular intervals post-game will still result in mafia players' games being more impactful towards their elo, since both mafia's winrate and the probability of any given player being mafia are below 50%.
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Re: Elo Rework

Postby alex1234321 » Thu Jul 15, 2021 3:50 pm

Superalex11 wrote:
Joacgroso wrote:If this is implemented and grinding becomes impossible, shouldn't elo ranks be closer to each other?

It depends on BMG's preferences. Assuming they're using the standard preference of 10x odds per 400 elo (which I did in my calcs a post prior), the current rank tiers are arguably too close/small. Though of course playercount does play a big role, so there's no easy answer.

I would argue that the tiers would have to be closer together. I doubt that a group of master-tier players as Town would be able to beat average Mafia players more than 90% of the time. Even that feels like a lot. So I'd say Master would have to be somewhere around 1600 Elo and the other tiers would also have to be brought about halfway towards 1200 from where they are now.

James2 wrote:
alex1234321 wrote:
James2 wrote:This will be the case if each game is elo neutral. Which is why I proposed regularly cancelling out faction elo gains/losses (say, every day) rather than making each game non-inflationary/deflationary.


I thought about this, but I prefer the idea of forcing each game to be neutral. If cancel out factional changes at the end of the day, people will experience Elo changes without doing anything. It would be extremely infuriating to find out you made Master Elo only for your Elo to decrease at the end of the day. Players would be rewarded or punished based on the outcome of other games that they have no control over. I know these would balance out in the long run, but the ToS playerbase is small and you'd have to balance minimizing random deviations with keeping Elo up to date.

I agree with the priority list that you previously mentioned although I would order the points 1, 3, 2, 5, 4 in terms of importance. Having a daily correction would slightly violate your second point while preventing the fourth one from being violated. Also, I would argue that Mafia should have a larger K-factor than Town since each Mafia member has a larger influence on who wins the game than each Town member. That's also why Mafia leavers are so much more annoying than Town leavers.

The thing is elo gains/losses from things outside a player's control (such as the quality of eight other townies) will cancel out in the long term. Whereas giving mafia wins/losses a greater impact on elo substantively favors those who are better at mafia and worse at town. The issue is clear if we look at the extreme cases:

1. A player who always wins as mafia and always loses as town while playing people with the same elo. This player wins 4/13 games (leaving neutrals aside), which is by definition less than average. Yet under your system he'd neither gain nor lose elo.

2. Individual townies have no control whatsoever over whether they win or lose. In this case, town wins and losses are effectively noise that cancels out in the long term. Thus even if town wins/losses have the same impact as mafia wins/losses, players' elo would still represent their skill as mafia (which is as it should be in this scenario).

Regarding the psychological aspect of it, people would gain elo as often as they'd lose it (assuming a decent algorithm). If frustration were enough of an issue you could just refraining from updating people's scores in real time (or label real time elo "provisional elo" or something else that sounds less important).


My system definitely does break down when you consider players who are much better at one faction than the other. If you assume that everyone has an intrinsic "true Elo," then it would make sense for Mafia games to count more since you have a larger influence over the outcome. Of course, that's not the case in real life. Ideally, there would be faction-based Elos, but those would take a very long time to calibrate. It might work if you combine it with inflation cancellation.

Let's see how your proposal would work. I'm going to assume a true Town winrate of 60% at a given Elo level but an assumed baseline winrate of 50% for each faction. In that case, someone who wins 4 games as Mafia and loses 9 as Town (assuming K=30 and all games are even) would get -75 Elo. However, the average Town player would gain +3 Elo per game and the average Mafia player would get -3. Over the 13 games, this player would have a correction of -15, so they would really lose 90 Elo. That checks out.

So I think your proposal would more effectively prevent inflation while being robust against different factional winrates. The only other issue is the possibility of there not being enough games. There are around 100 ToS games going on at any one time. Assuming 1/4 of those games are Ranked (just picking a number out of thin air), there are 25 Ranked games happening at a time. If each game takes 20 minutes, that's 1,800 Ranked games happening per day. Let's conservatively assume there are only 1,000 games. Using the same winrates as before, Town will win an average of 600 games with a standard deviation of 15.5. If K=30, on average a Townie would win +3 extra Elo and the average player would win +1.15 Elo per game with a standard deviation of 0.18. Someone who plays 5 games in a day would have an average correction of -7.75 with a standard deviation of 0.89. Over a year, the standard deviation of the total correction would be approximately 17 Elo. If each game was against equal opponents, the player would have a standard deviation of 319 Elo over the course of the year, so the error caused by the corrections being off is not large.

tl;dr: I think you might be right.
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