#14455: "Ways to improve Elo/EAS for 3+ player and luck based games"
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细节描述
• 如果有的话,请将你在屏幕上所看到的错误信息粘贴出来.
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).• 请说明你当时想做什么,你做了什么,然后发生了什么
• 你的浏览器是什么?
Safari v13
• 请以英文复制/粘贴显示文字而非你的语言。 如果你有这个系统漏洞发生时的屏幕截图(画质不要太差),你可以使用Imgur.com来把它上传到网络,然后将链接复制/粘贴到这里来。
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).• 这段文本在翻译系统中吗?如果存在,它被翻译是否已超过二十四小时了?
• 你的浏览器是什么?
Safari v13
• 请简明而精确地解释您的建议,以便让人明白您想表达的意思。
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).• 你的浏览器是什么?
Safari v13
• 当你被封锁的时候,屏幕上出现了些什么呢?(空白的屏幕?部分游戏平台画面?错误的信息?)
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).• 你的浏览器是什么?
Safari v13
• 哪个规则没有被BGA的设计小组写进游戏里?
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).• 在游戏回放中,是否有不符合游戏规则的地方?如果有的话,请问是在哪一步呢?
• 你的浏览器是什么?
Safari v13
• 你当时是想做哪个游戏行动?
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).• 你在想做什么的时候,触发了这个游戏选项?
• 当你想这么做时,发生了什么事(错误信息,游戏状态信息,......)?
• 你的浏览器是什么?
Safari v13
• 请问这个问题发生在游戏的哪个阶段(当前的游戏说明是什么)?
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).• 当你想进行一个游戏行动时,发生了什么事(错误信息,游戏状态信息,......)?
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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).• 你的浏览器是什么?
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• 请以英文复制/粘贴显示文字而非你的语言。 如果你有这个系统漏洞发生时的屏幕截图(画质不要太差),你可以使用Imgur.com来把它上传到网络,然后将链接复制/粘贴到这里来。
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).• 这段文本在翻译系统中吗?如果存在,它被翻译是否已超过二十四小时了?
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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).• 你的浏览器是什么?
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案件历史
This actually exacerbates issues with how long it takes to reach an accurate EAS for long multiplayer games.
Currently, it is higher for people who finish in the middle of the pack and the P factor can even be different for the player who finish 1st than for the player who finish last. (see boardgamearena.com/bug?id=46582 )
when winning against 3 stronger players at once, elo-points are devided with 3. --> what for?
isn't that much more dificult that winning against one opponent?
see table 216760302
A better answer is to use a different curve altogether, or at least scale the asymptote away from 100%, preferably based on game data (which should be easy to extract).
One solution is to decrease the K factor for luck-based games. Then ratings would be more stable.
A better solution is to change the probability distribution for luck-based games. ELO is designed for a game like chess, where a casual player would have zero chance against a grandmaster. A rating difference of 400 points means a 90% chance of winning. A rating difference of 800 means a 99% chance of winning. There are games here where the weaker player always has a 25% chance of winning.
For example, the probability distribution could be
chance of winning = (your rating) / (your rating + opponent's rating)
using a minimum value of 100 for people who just started playing a game.
boardgamearena.com/forum/viewtopic.php?t=29584
I also provided there a few links to related papers for those interested in the maths.
增加一些新内容到这篇报告
- 其他的游戏桌 ID / 移动 ID
- 按 F5 是否解决了这个问题?
- 问题是否发生了好几次?还是每次都发生?还是时好时坏?
- 如果你有这个系统漏洞发生时的屏幕截图(画质不要太差),你可以使用Imgur.com来把它上传到网络,然后将链接复制/粘贴到这里来。