Ways to improve Elo/EAS for 3+ player and luck based games

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sprockitz
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Ways to improve Elo/EAS for 3+ player and luck based games

Post by sprockitz » 22 January 2020, 17:08

Edit: Vote for suggestion here - https://boardgamearena.com/bug?id=14455

Here is the current elo eas formula
For a Win:
RatingChange = K*P/(1 + 10 ^ ((YourRating - OpponentRating)/400)))
For a Loss:
RatingChange = -K*P/(1 + 10 ^ ((OpponentRating - YourRating)/400)))

K is a weight for each game (first 10 games is 60, next 10 is 40, after is 20 for Elo. All games are 40 for EAS)
P is a multiplier by number of players. P ~= 2/NumberPlayersInGame (more players decreases the amount gained or lost for each individual matchup, but increases the total amount of points at stake for a given game) (if you play with more players than the recommended number the P value actually becomes slightly lower than the above formula.

Proposed Changes
1 Adjust the 400 factor for number of players. Change it to 400*sqrt(numberOpponents).
Motivation: Equalize expected Elo/EAS for multiple player counts, could allow for a fair Arena competition where different player counts are allowed.

Under the current system players who only play 2 player matchups have a significant advantage over players who play with more than 2. This is because as the number of players goes up, the variance of a game goes up as well. Altering the 400 value based on number players compensates for the increased variance so that (on average) players in different player counts should be able to achieve similar ratings.

This would allow an arena mode competition to allow setups with multiple players. This would alleviate some of the wait time angst in arena mode.

2 Adjust the speed at which ratings change (K factor) depending on the length of the game. For EAS, make it a game length based variable between 20-50 (also a variable K value by games played wouldn’t be a bad thing)
Motivation: Too much variance in short generally luck based games, too much time required (too much time spent playing mismatched opponents for all players from weak to average to strong) in longer high skill games.

Right now EAS K factor is 40, Elo starts at 60 but drops to 20 after 20 games are played.

Some games take 2 minutes, others take 2 hours. Having the ratings move at the same rate per game means you can achieve a balanced rating in a few hours for some games (i.e. Backgammon, Can’t Stop, Reversi, 7 Wonders, Lost Cities), while for long games (Terra Mystica, Clans of Caledonia) it will take more than 100 hours. While longer games should take longer to reach a ‘true’ rating adjusting the K factor can be used to slightly mitigate the issue. You can’t make K factor too big otherwise the game to game
ratings swings would be too wild.

3 Normalize the ratings system so each game has roughly the same distribution of ratings by adjusting the 400 value based on the game luck factor.

Motivation: This would give a more realistic distribution of player skill from average through master in each game. Right now games with luck can’t have experts or masters (w/o matchup manipulation or a statistically improbable run of good luck anyway). Right now you could be a ‘perfect’ backgammon player but stall out at around a +100 rating because the luck factor in the game is large.

In a game like backgammon or can’t stop a strong player can expect a win rate of about 60% against average players. So this limits players ratings under the current system to about +100 from the base rating (a 100 rating point advantage indicates a 64% probability of winning). With the ratings volatility players can get on a lucky streak to get to +200 or rarely even +300, but will come back down to an average of around +100. Yet somehow players achieve +400-+500 ratings in these games...that can only be done by strategic opponent selection (or blatant cheating but we will ignore that for this argument). Basically you want to play only other high rated players and then get lucky by winning a few in a row to gain significant points. Arena mode should already mitigate this opponent selection tactic.

This idea isn’t as completely hashed out as the other 2 above, so I won’t offer concrete numbers, but there are a few ways to achieve this. The best is likely to increase the base 400 value for high luck games. A range from 400-900 based on luck factor (already games are ranked as 0-5 luck..could change 400 to 400 + 100*luck lvl). Combining this change with a change based on player number would however be more tricky, multiplying them together wouldn’t be great, it would likely be better to take the maximum of the two values. For this one to work luck ratings would have to be revisited b/c many of them aren’t very accurate (in checking about 8 games I saw at least two that were well off...kingdomino at a 4 and king’s guild at 3 both are definitely too high and lost cities at 2 is too low).
Last edited by sprockitz on 13 February 2020, 23:14, edited 2 times in total.

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dschingis27
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Joined: 27 June 2015, 18:30

Re: Ways to improve Elo/EAS for 3+ player and luck based games

Post by dschingis27 » 23 January 2020, 17:21

Thank you for all your thoughts! After going through it, I like all 3 ideas very much und would really welcome changes into this direction.

DavisV
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Joined: 19 September 2019, 06:21

Re: Ways to improve Elo/EAS for 3+ player and luck based games

Post by DavisV » 23 January 2020, 17:30

I'm for all those suggestions!

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asd123321
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Re: Ways to improve Elo/EAS for 3+ player and luck based games

Post by asd123321 » 26 January 2020, 00:18

what does the ^ do and the effect of the 400 in the formula.

I have always thought that the more games played the less effect of the last one rather than have it based so much on recent games. Then recalculate all ELO from the beginning in 2013. Ha!

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sprockitz
Posts: 285
Joined: 23 October 2014, 02:22

Re: Ways to improve Elo/EAS for 3+ player and luck based games

Post by sprockitz » 26 January 2020, 05:08

asd123321 wrote:
26 January 2020, 00:18
what does the ^ do and the effect of the 400 in the formula.

I have always thought that the more games played the less effect of the last one rather than have it based so much on recent games. Then recalculate all ELO from the beginning in 2013. Ha!
The ^ is an exponent symbol, so 10^2 is 100 (10*10) while 10^3 is 1000 (10*10*10).
The 400 is divided by the rating difference. So the portion in the power with the exponent. 10^((600-400)/400) = 10^(200/400) = 10^(1/2) = 3.16
The 400 number is a divisor for the rating difference and is the rating difference that means the higher rated person should win 10 times for every 1 time the lower rated person wins.

DavisV
Posts: 22
Joined: 19 September 2019, 06:21

Re: Ways to improve Elo/EAS for 3+ player and luck based games

Post by DavisV » 13 February 2020, 16:43

Is this added in "Bug and suggestions" feedback? I want to vote

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sprockitz
Posts: 285
Joined: 23 October 2014, 02:22

Re: Ways to improve Elo/EAS for 3+ player and luck based games

Post by sprockitz » 13 February 2020, 21:07

I can copy it over there when i get a chance. Will link here when I do.


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