Scale points won by number of opponents in game

[Metsfanmax]

Concise description:

• When assigning points won or lost in a game, divide the standard formula by the square root of the number of opponents in the game.

Specifics/Details:

• The new formula would be: (loser score / winner score) * (20 / sqrt(number of opponents))
• For team games the number of opposing players is used, not the number of opposing teams.

How this will benefit the site and/or other comments:

• Winning a 12 player standard game gives one 11 times more points than winning a two player game, but is clearly not 11 times harder. Under this system a player would earn 3.3 times as many points instead of 11 times. This is significantly more reasonable than the current system.
• Parity would be better introduced across settings. Players who specialize in two, three or four player games would have a better chance of reaching the upper echelons of the scoreboard.
• Volatility in the scoring system is a serious limitation in the meaningfulness of a player's rating. In particular, because games where the winner takes 100 or more points are very common, it is difficult for equilibrium in a player's score to be established.
• Round up to one point won if the formula gives a value less than one for each individual player (i.e. for Battle Royales).

Edits:

- 2013-12-18: Changed formula to divide by square root of number of opponents, instead of number of opponents.

[Swifte]

I'll give you that 11 players doesn't make it 11 times harder than a 1v1... but it's still a LOT harder... I think this would very much under represent the skill shown in winning games with higher player counts.

I consider Aaarrrrggh (a former conqueror) to be very good at 8p games, for example, but for his career he wins at a 33% clip.. I imagine that's pretty high for a win-rate on 8p games.
Compare that to 1v1, and team, where folks can with at 70% or greater... your suggestion would see to say that he can have 20 points 33% of the time, while others can more easily get it 70% of the time... I don't think you've quite created an equilibrium there.

[Metsfanmax]

I'll give you that 11 players doesn't make it 11 times harder than a 1v1... but it's still a LOT harder... I think this would very much under represent the skill shown in winning games with higher player counts.

I don't think games with higher player counts are fundamentally harder. The main problem is one of probabilities: in a 12 player standard it's very easy to just get knocked out quickly. So a justification for the current system is that even though you earn more points, you're also a lot less likely to win them, so it evens out in the end. If all players are equal, you have a 50% chance of winning a 1v1 but an 8% chance of winning a 12 player, with both earning the same number of points. However, since you lose fewer points when you lose the 12 player game, the expected returns are still the same (that is, under random odds, the expected outcome in any game type is to exactly break even).

So the question instead becomes, do we value the skill inherently required to win a 12 player game more than we value the skill inherently required to win a two, three or four player game? Enough to give them more points for a victory? I do not, but the opinions of others are welcome.

I consider Aaarrrrggh (a former conqueror) to be very good at 8p games, for example, but for his career he wins at a 33% clip.. I imagine that's pretty high for a win-rate on 8p games.
Compare that to 1v1, and team, where folks can with at 70% or greater... your suggestion would see to say that he can have 20 points 33% of the time, while others can more easily get it 70% of the time... I don't think you've quite created an equilibrium there.

Let's run with this example. If you win 33% of 8 player games, then on average you gain 5 points per 8 player game ( 20 * ( 1/3 ) - ( 20 / 8 ) * ( 2/3 ) = 4.9 ). If you win 70% of 2 player games, then on average you gain 8 points per 2 player game ( 20 * 0.7 - 20 * 0.3 = 8 ). I think this is fair. I can't say for certain, but I guess that luck factors are more dominant for two player games than eight player games, on average. That is, since 1v1s are very often determined by drop and first round dice rather than skill, winning 70% of 1v1s is very difficult (at least, if you're playing people your own rating). It's a better accomplishment than winning 33% of eight player games (at least, by the probabilities). If you get to 70% wins on 1v1 by playing people who are lower rating than you, you also won't get as many points, so it balances out.

[chapcrap]

Let's run with this example. If you win 33% of 8 player games, then on average you gain 5 points per 8 player game ( 20 * ( 1/3 ) - ( 20 / 8 ) * ( 2/3 ) = 4.9 ). If you win 70% of 2 player games, then on average you gain 8 points per 2 player game ( 20 * 0.7 - 20 * 0.3 = 8 ). I think this is fair. I can't say for certain, but I guess that luck factors are more dominant for two player games than eight player games, on average. That is, since 1v1s are very often determined by drop and first round dice rather than skill, winning 70% of 1v1s is very difficult (at least, if you're playing people your own rating). It's a better accomplishment than winning 33% of eight player games (at least, by the probabilities). If you get to 70% wins on 1v1 by playing people who are lower rating than you, you also won't get as many points, so it balances out.

No way is that fair. Elite players earn less points for 8 player games than for 1v1 games?

The way it's set up now is that if players win the statistical probability of games (50% of 1v1 games; 12.5% of 8 player games) they end up with the same number of points. I don't see a problem with the system. Yeah, people can gain 100 points from winning an 8 player game, but then when they lose the other 7, it balances out.

[Metsfanmax]

Let's run with this example. If you win 33% of 8 player games, then on average you gain 5 points per 8 player game ( 20 * ( 1/3 ) - ( 20 / 8 ) * ( 2/3 ) = 4.9 ). If you win 70% of 2 player games, then on average you gain 8 points per 2 player game ( 20 * 0.7 - 20 * 0.3 = 8 ). I think this is fair. I can't say for certain, but I guess that luck factors are more dominant for two player games than eight player games, on average. That is, since 1v1s are very often determined by drop and first round dice rather than skill, winning 70% of 1v1s is very difficult (at least, if you're playing people your own rating). It's a better accomplishment than winning 33% of eight player games (at least, by the probabilities). If you get to 70% wins on 1v1 by playing people who are lower rating than you, you also won't get as many points, so it balances out.

No way is that fair. Elite players earn less points for 8 player games than for 1v1 games?

Consider the current system. A player who wins 33% of eight-player averages a net gain of 33.3 points per game. A player who wins 70% of two-player games averages a net gain of 8 points per game. If we accept those as similar levels of eliteness, then the current system is way more unfair than the proposed system. At most a 1v1 expert can win an average a net gain of 20 points every game -- if they win 100% of the time.

A compromise solution is to use the square root of the number of opponents:

Points won = (loser score / winner score) * (20 / sqrt(number of opponents))

Under this system, the elite eight-player expert averages 12.6 points gained per game, whereas the 1v1 expert still averages 8 points gained per game. Winning an eight-player game would net you 53 points instead of 140 points. This would also address Swifte's concern that it takes more skill to win an eight-player game than a 1v1. However, it mutes the volatility instead of eliminating it -- winning a BR would earn you 141 points instead of 1000. I have to admit that this aspect is better though -- winning a BR really is an achievement (even if a large part is the luck of not getting eliminated by round two) and you should win more than 20 points. What are your thoughts?

The way it's set up now is that if players win the statistical probability of games (50% of 1v1 games; 12.5% of 8 player games) they end up with the same number of points. I don't see a problem with the system. Yeah, people can gain 100 points from winning an 8 player game, but then when they lose the other 7, it balances out.

Players breaking even is also true in the proposed system. The problem with the current system is that you can chain together two or three 8 player wins in a row by getting lucky, and wildly distort your actual score, at least for a while (in addition to the problem mentioned above, of the incredible unfairness across game types). And if you win a Battle Royale you can win a thousand points all at once. Those things contribute to a volatile score system, which degrades the meaning of scores. So the proposed system captures the main benefits of the existing score system, but without the volatility.

[chapcrap]

I'm not opposed to a change in the scoring system. I actually like this suggestion: viewtopic.php?f=4&t=193115

But, I don't see this volatility as an issue. Going up or down a couple of hundred points isn't a big deal. I do think that BR's are skewed and a little lucky, so I wouldn't mind to see them muted somewhat. Overall, I'm not sure this is an issue.

[Metsfanmax]

I'm not opposed to a change in the scoring system. I actually like this suggestion: https://www.conquerclub.com/forum/viewt ... 4&t=193115

These two are actually not mutually exclusive. Let's represent the formula as:

Points Won = X * Y

where X = (loser score / winner score) and Y = 20. The exponential scoring system changes it to:

Points Won = sqrt(X) * Y

whereas my scaled points system changes it to

Points Won = X * (Y / # of opponents)

We can do both if we wanted to, or either one individually.

But, I don't see this volatility as an issue. Going up or down a couple of hundred points isn't a big deal. I do think that BR's are skewed and a little lucky, so I wouldn't mind to see them muted somewhat. Overall, I'm not sure this is an issue.

The volatility is one of two main issues. I contend that it is an issue mainly because you should be able to, at a glance, look at a player's score and estimate their skill. If I look at a player who just won two 12 player games in a row by luck, I'll get a poor representation of their skill.

I'd say the huge disparity between game types is a major flaw in the scoring system and needs to be addressed. Being an eight-player expert earns you four times as many points per game as being a 1v1 expert. This is just not fair. The exponential scoring system does not solve this problem.

[chapcrap]

I'm not opposed to a change in the scoring system. I actually like this suggestion: viewtopic.php?f=4&t=193115

These two are actually not mutually exclusive. Let's represent the formula as:

Points Won = X * Y

where X = (loser score / winner score) and Y = 20. The exponential scoring system changes it to:

Points Won = sqrt(X) * Y

whereas my scaled points system changes it to

Points Won = X * (Y / # of opponents)

We can do both if we wanted to, or either one individually.

I think that my issue here is that if there is a change, we wouldn't be awarding enough points to people who play multiplayer, singles games.

If I'm 2000 and all I play is people who are the same as me, then I gain 20 for every player I beat. So, an 8 player game nets me 140 points and a 2 player game gets me 20. One flaw here is that 33% is really super elite. Most players don't win that much. 20% of 8 player games is pretty good. I've won 19% and have +887 points from 587 games. That's averaging less than 2 points per game. That's not that much. For 2 player games I've won 60% and have -1123 points from 5860 games. That's about -0.2 points per game.

Now, I don't feel bad about this, because statistically, my percentages with 8 player games are a LOT better than with 2 player games. I'm achieving over 50% better in 8 player games than expected. In 2 player games, I'm only achieving 20% better than expected. So, the point gap makes sense.

But, I don't see this volatility as an issue. Going up or down a couple of hundred points isn't a big deal. I do think that BR's are skewed and a little lucky, so I wouldn't mind to see them muted somewhat. Overall, I'm not sure this is an issue.

The volatility is one of two main issues. I contend that it is an issue mainly because you should be able to, at a glance, look at a player's score and estimate their skill. If I look at a player who just won two 12 player games in a row by luck, I'll get a poor representation of their skill.

I'd say the huge disparity between game types is a major flaw in the scoring system and needs to be addressed. Being an eight-player expert earns you four times as many points per game as being a 1v1 expert. This is just not fair. The exponential scoring system does not solve this problem.

I don't think a couple hundred points changes what I think about a player. If it's a 800 or 1000. 2000 or 2200. If people are jumping a thousand points, then that's more of an issue, but that's not really happening is it?

I think I get where you're coming from with the different game types, but I think this formula is a little too extreme the opposite way to support. It would have to be something a little more complicated that weighted scores less and less as more people/teams were in the game. My issue with something like that is understandability. People shouldn't have to have a degree to get the system either...

[Metsfanmax]

Now, I don't feel bad about this, because statistically, my percentages with 8 player games are a LOT better than with 2 player games. I'm achieving over 50% better in 8 player games than expected. In 2 player games, I'm only achieving 20% better than expected. So, the point gap makes sense.

Your statistical thinking is inaccurate, which is where the discrepancy in our views come from. What's important is not the actual ratio of percentage won to expected percentage won when making comparisons across game types. For example, if we just took that raw ratio at face value, the person who wins 33% of 8 player games is winning nearly three times the expected rate. The best a 1v1 expert can do is twice the expected rate (if they win every time). A better metric might be: how much of the gap between the expected win rate, and 100% win rate, did you cross? There are 87.5 percentage points to grab in an eight-player game, and 50 percentage points to grab in a 1v1. The eight-player expert earns 20 percentage points more, or about 25% of the gap. The 1v1 expert also earns 20 percentage points more, but that's 40% of the gap. So by that metric, the 1v1 expert is actually significantly better, and therefore deserves more points per game.

[chapcrap]

Now, I don't feel bad about this, because statistically, my percentages with 8 player games are a LOT better than with 2 player games. I'm achieving over 50% better in 8 player games than expected. In 2 player games, I'm only achieving 20% better than expected. So, the point gap makes sense.

Your statistical thinking is inaccurate, which is where the discrepancy in our views come from. What's important is not the actual ratio of percentage won to expected percentage won when making comparisons across game types. For example, if we just took that raw ratio at face value, the person who wins 33% of 8 player games is winning nearly three times the expected rate. The best a 1v1 expert can do is twice the expected rate (if they win every time). A better metric might be: how much of the gap between the expected win rate, and 100% win rate, did you cross? There are 87.5 percentage points to grab in an eight-player game, and 50 percentage points to grab in a 1v1. The eight-player expert earns 20 percentage points more, or about 25% of the gap. The 1v1 expert also earns 20 percentage points more, but that's 40% of the gap. So by that metric, the 1v1 expert is actually significantly better, and therefore deserves more points per game.

So that's the more complicated formula that needs to be thought of.

Also, I think we should get away from talking about 33% win rate in 8 player games. That's unrealistic for almost everyone. 25% is on the very high end of achievable.

So, here are the gaps from 2-12 player/team games:

• 2 player: 50%
• 3 player: 67%
• 4 player: 75%
• 5 player: 80%
• 6 player: 83%
• 7 player: 86%
• 8 player: 88%
• 9 player: 89%
• 10 player: 90%
• 11 player: 91%
• 12 player: 92%
• 52 player: 98%

If a formula can be created involving those gaps, then we might have something. The number to use there is (1-(1/x)) where x is the number of players or teams in the game.

[betiko]

This suggestion doesn t make any sense at all. You are expected to win 1/2 of your 1v1 and 1/12 of your 12 player games. The payout goes accordingly.

[Metsfanmax]

Now, I don't feel bad about this, because statistically, my percentages with 8 player games are a LOT better than with 2 player games. I'm achieving over 50% better in 8 player games than expected. In 2 player games, I'm only achieving 20% better than expected. So, the point gap makes sense.

Your statistical thinking is inaccurate, which is where the discrepancy in our views come from. What's important is not the actual ratio of percentage won to expected percentage won when making comparisons across game types. For example, if we just took that raw ratio at face value, the person who wins 33% of 8 player games is winning nearly three times the expected rate. The best a 1v1 expert can do is twice the expected rate (if they win every time). A better metric might be: how much of the gap between the expected win rate, and 100% win rate, did you cross? There are 87.5 percentage points to grab in an eight-player game, and 50 percentage points to grab in a 1v1. The eight-player expert earns 20 percentage points more, or about 25% of the gap. The 1v1 expert also earns 20 percentage points more, but that's 40% of the gap. So by that metric, the 1v1 expert is actually significantly better, and therefore deserves more points per game.

So that's the more complicated formula that needs to be thought of.

I already did think of it. The 1v1 expert in this example is better, and earns more points. That's how it should be.

Also, I think we should get away from talking about 33% win rate in 8 player games. That's unrealistic for almost everyone. 25% is on the very high end of achievable.

So, here are the gaps from 2-12 player/team games:
...
If a formula can be created involving those gaps, then we might have something. The number to use there is (1-(1/x)) where x is the number of players or teams in the game.

It's not the size of the gap that matters, in this system: it's the percentage of the gap that you cross. This is what allows you to make a valid comparison across game types. In the ideal system, a person who crosses the same fraction of the gap in 8 player games as the fraction of the gap in 2 player games will earn the same amount of points. This is automatically true in my proposed system. If you win 25% of 8 player games, that crosses 14% of the gap. That is equivalent to winning 57% of 1v1 games. If we apply this metric, the person who wins 25% of 8 player games and 57% of 1v1 games earns the same amount of points (about 2.8 points per game). It may look unfair because of the raw, absolute difference, and so I'm not defending it as the best possible metric. But it's a lot better metric than just taking the ratio.

[Metsfanmax]

This suggestion doesn t make any sense at all. You are expected to win 1/2 of your 1v1 and 1/12 of your 12 player games. The payout goes accordingly.

The current system becomes flawed when you think about people who win more than the expected win rate. These people are rewarded with more absolute points for winning 12 player games than for winning 2 player games, even if they are the same caliber player, simply because there are more points available in the 12 player game. Think carefully about it, and read the posts above. If you still don't understand, I'll be happy to take it up with you over PM because this thread is already cluttered with arithmetic.

[demonfork]

I see this as a pointless change.

It does nothing to shift the balance between risk and reward. The ratio stays exactly the same.


With your system, In a 4 player game, all scores being equal, the winner will gain 20 points and the loser will lose 6.66 points. = 3:1

With current system winner gains 60 loser will lose 20 = 3:1


With both systems the player will risk 1 unit to gain 3.


Aside from not being sure how you will deal with a player losing a fraction of a point, the only thing that will change with this idea is that it will take more games for a player to inflate his score but fundamentally the scoring system will remain the same.

[Metsfanmax]

I see this as a pointless change.

It does nothing to shift the balance between risk and reward. The ratio stays exactly the same.


With your system, In a 4 player game, all scores being equal, the winner will gain 20 points and the loser will lose 6.66 points. = 3:1

With current system winner gains 60 loser will lose 20 = 3:1


With both systems the player will risk 1 unit to gain 3.

Yes, I don't want to change the balance between risk and reward. However, decreasing the total number of points won in larger player games has two benefits: 1) it's basically impossible for a player to have a 200 point swing, resulting in more stability of the points system, and 2) it makes smaller and larger player games much more equal: a 4 player game requires a similar commitment to a 12 player game but the latter can earn you nearly four times as many points. Under this system, the same amount of points are stake more or less independently of number of players.

Aside from not being sure how you will deal with a player losing a fraction of a point,

The system already deals with that: it computes fractional points won and lost and stores that on the server, and the number you see on the game page is rounded.

the only thing that will change with this idea is that it will take more games for a player to inflate his score but fundamentally the scoring system will remain the same.

Yes, it's not designed to fundamentally change the scoring system. The fact that it takes more games for a person to get a higher score is a valuable feature, to me. But I will stress that the most important part of this idea is to fix the fundamental inequality between large and small games.

[spiesr]

It seems like this, coupled with the other score suggestions that you are pushing lately, represent a drastic enough change that it would be better to just make a completely new scoreboard that is designed from the ground up to work with those ideals in mind. The backlash that implementing all the ideas you have proposed would probably be almost of high as that of adding a second second scoreboard, running it concurrently with old one and gradually making the new one more prominent, and doing the later would give a better end result...

[Metsfanmax]

I don't think that this, or the exponential scoring proposed by Lord_Bremen, represents a drastic change to the scoring system. It's fundamentally the same system, but fixes a serious flaw.

However, one could argue that it requires a full score reset to be fair to everyone, which is similar to you saying we need a second scoreboard. But I wouldn't go that far.

Also, most of my ideas are independent. We could meaningfully do this without the score floor (though, based on feedback from the other thread, I don't think we could meaningfully do the score floor without this).

[Geger]

I see this as a pointless change.

It does nothing to shift the balance between risk and reward. The ratio stays exactly the same.


With your system, In a 4 player game, all scores being equal, the winner will gain 20 points and the loser will lose 6.66 points. = 3:1

With current system winner gains 60 loser will lose 20 = 3:1


With both systems the player will risk 1 unit to gain 3.

Yes, I don't want to change the balance between risk and reward. However, decreasing the total number of points won in larger player games has two benefits: 1) it's basically impossible for a player to have a 200 point swing, resulting in more stability of the points system, and 2) it makes smaller and larger player games much more equal: a 4 player game requires a similar commitment to a 12 player game but the latter can earn you nearly four times as many points. Under this system, the same amount of points are stake more or less independently of number of players.

Aside from not being sure how you will deal with a player losing a fraction of a point,

The system already deals with that: it computes fractional points won and lost and stores that on the server, and the number you see on the game page is rounded.

the only thing that will change with this idea is that it will take more games for a player to inflate his score but fundamentally the scoring system will remain the same.

Yes, it's not designed to fundamentally change the scoring system. The fact that it takes more games for a person to get a higher score is a valuable feature, to me. But I will stress that the most important part of this idea is to fix the fundamental inequality between large and small games.

Also you want, it takes the same amounts of games (either 2-player or multiplayer games) to get a higher score. It sounds good. But you forget something, 2-player games finish much faster. So to gain points faster, people play only 1vs1 games, and the masters of 1vs1-games will be on top of the scoreboard

[Metsfanmax]

Also you want, it takes the same amounts of games (either 2-player or multiplayer games) to get a higher score. It sounds good. But you forget something, 2-player games finish much faster. So to gain points faster, people play only 1vs1 games, and the masters of 1vs1-games will be on top of the scoreboard

I didn't forget that, but your specific conclusion is not valid. In a sense, speed is irrelevant, especially for premium members. Yes, an eight player game usually takes longer than a 1v1, but we already have members at the top of the scoreboard. If someone is very good at eight player games, they'll reach the top of the scoreboard. They might not do so as quickly if they're starting from a low score as a 1v1 expert, but once either player gets there, they will stay there if they're actually good. The only reason this speed would be a serious concern is if we did a score reset, and then the first person to reach Conqueror would probably do it by playing 1v1s. But it doesn't matter at this point.

[betiko]

While i didn t fully understand your suggestion in the first place, now that i do i still think the same. Why is it a problem for someone to win 200 pts in a game?? Someone playing a large amount of games has by definition a very volatile score. Winning one of these hard games for 20 pts is ridiculous, too much time an effort for something you could win/lose in 5 minutes in a speed game.

[Metsfanmax]

While i didn t fully understand your suggestion in the first place, now that i do i still think the same. Why is it a problem for someone to win 200 pts in a game?? Someone playing a large amount of games has by definition a very volatile score.

A person playing a large amount of games will have more daily jitter in their score, but if they're in an equilibrium they'll never stray too far from their average if you can only win of order 20 points per game.

Winning one of these hard games for 20 pts is ridiculous, too much time an effort for something you could win/lose in 5 minutes in a speed game.

That's a valid point of view, even though it's one I do not share. For this reason I'm very willing to entertain the compromise solution (dividing by the square root of the number of opponents), because it rewards the effort involved in those games but not nearly to the same absurd extent it does currently.

[DoomYoshi]

Is this a yoshi trap thread?

[Night Strike]

While i didn t fully understand your suggestion in the first place, now that i do i still think the same. Why is it a problem for someone to win 200 pts in a game?? Someone playing a large amount of games has by definition a very volatile score.

A person playing a large amount of games will have more daily jitter in their score, but if they're in an equilibrium they'll never stray too far from their average if you can only win of order 20 points per game.

Winning one of these hard games for 20 pts is ridiculous, too much time an effort for something you could win/lose in 5 minutes in a speed game.

That's a valid point of view, even though it's one I do not share. For this reason I'm very willing to entertain the compromise solution (dividing by the square root of the number of opponents), because it rewards the effort involved in those games but not nearly to the same absurd extent it does currently.

Interpretation: "I don't share your view, so I'll settle with the less outlandish view of my own to push on others."

This whole notion that people should be punished with fewer points while playing larger player games is absurd. Your problem lies in the fact that the site added 9-12 player games, not the scoring system. If the scoreboard is too volatile because of the number of players in a game, limit those large size games to teams only.* Quit trying to take away points from those who work those very large games to get them. Besides, getting a big win like that is a great accomplishment for some people (like myself), so why make winning those games worth the exact same as winning smaller games? You're posting solutions in search of problems that don't exist.



*A suggestion as similarly outlandish as this thread.

[Metsfanmax]

Your problem lies in the fact that the site added 9-12 player games, not the scoring system.

That exaggerates the problem, but the problem has always existed.

Besides, getting a big win like that is a great accomplishment for some people (like myself), so why make winning those games worth the exact same as winning smaller games?

Do you think that a person who wins a 12 player game deserves 11 times as many points as a person who wins a 2 player game? I don't agree with that. But that's what the current system allows. For example, I just pulled up the first page of finished 12 player games. Here are the rounds they finished in:

8, 8, 6, 6, 2, 5, 8, 6, 6, 8, 7, 2, 3, 5, 7, 6, 9, 7, 5, 6, 6, 6, 8, 6, 8, 7, 8, 6, 6, 7, 6, 8...

It goes on. Out of the first hundred, five finished past round 10. Five. Yet people win 11 times as many points for such a "great" accomplishment? That's broken. Even 1v1s require more effort than that. My solution may not be the best solution, but the problem exists.

Edit: And if you're thinking of arguing that eight players are different and that it's the 9-12 player games that are causing the problem, don't bother. I did the same check for 8 player games that recently finished. I skipped the first two pages because there's like 150 results from the same group playing assassin on Jamaica. On the third page, there were also exactly five that ended past round 10.

[Geger]

Not "rounds" but "moves" are more important here.

10 rounds 1vs1-game = 19-20 moves, but 10 rounds 8-p game = 73-80 moves. Let's say speed games need in average 2 minute per move, so 1vs1-game takes in average 40 minute but 8p-game needs 160 minutes.

Hm... from this perception I can agree with you in some degree : 8p-games aren't worth 7x 1vs1-games, but 8p-game can't have the same value with 1vs1-game. Just find a better formula