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Offline Mu_

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Cton skill calculation - formula proposal
« on: December 13, 2009, 07:33:04 AM »
Thinking about calculation of skills after a cton, I came up with an idea which may solve the problem raised in a previous thread on this subject. Here it goes:

What are the problems with today's formula?

1. High skilled players are dis-incentived (sp?) to play ctons since, if they don't rank as #1, they lose skill points. Even if they do rank #1, they don't win much.

2. A very low skilled player can win skill points even if he is the last but one in a cton, provided that the one player he beat has high skill. Say, a player with 1200 skill gets #6 out of 7 players, but because Bonsai was unlucky and did not have horses, he died to his neighbor early. This way the said player gets a win. Should he? I think not. He did nothing to deserve it.

3. While a high skill player is expected to win a cton by the ELO system, the reward is too low even if he does. In fact, due to the luck factor in ctons, the larger the number of players, the harder to win the whole game (as opposed to getting 2nd, 3rd etc.)

What (in my opinion) should a formula achieve? (see next post)

Offline Mu_

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Re: Cton skill calculation - formula proposal
« Reply #1 on: December 13, 2009, 07:39:01 AM »
A "fairer" cton formula should achieve:

1. A higher return for winning the whole cton or placing higher
2. The incentive to not risk-all and die early
3. The incentive to finish as high as possible on the table
4. More reward if a higher number of players join

Now here is my proposal:

1. Calculate the average skill of all players in a cton - say it is 1550.
2. Award a win to all players above the midpoint (e.g. in a 7 player cton, 1, 2, 3, 4 get a win, 5, 6, 7 a loss; in a 6 player cton 1,2,3 win and 4,5,6 lose)

3. Once a win or loss is established, take the skill of each player and pit it against the average skill. Calculate the skill gain/loss that way.

4. Apply a modifier depending on which rank the player achieved. If the player achieved somewhere around midpoint, make the modifier a default value (say 1, or 0.4 or whatever). If the player placed one spot above or below, increase the modifier (say 2, or 0.8). And so on up and down from the midpoint, ensuring that a larger player base gets a larger modifier (as it is harder to win a large cton).

Offline Mu_

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Re: Cton skill calculation - formula proposal
« Reply #2 on: December 13, 2009, 07:56:32 AM »
And now, an example. Names and skills are fictional. The following order registers at the end of a 6 player cton:

1. Aplayer (skill 1700) 2. Bplayer (skill 1500) 3. Cplayer (1300) 4. Dplayer (1600) 5. Eplayer (1400) 6. Fplayer (1500)

Average skill is - 1500 (you can calculate it)
A, B and C get a win, D, E, F get a loss.

For A, the formula considers that he, a player with 1700 skill, beat a player with 1500 skill (average for the game). The base gain is therefore 4 skill points (Use skill calculator at RD=47 to convince yourself). But, because A gained 1st place, he gets a modifier of, say 5x - so 20 points.

B - 1500 skill vs. 1500 average skill - gain of 7 points (at 47 RD). Because he is only second, he gets, say 3x modifier - so 21 points.
C - 1300 skill vs. 1500 average skill - gain of 10 points (RD = 47 again in the example). Because he is only third, he gets 1x - so 10 points.
D - loss at 1600 vs 1500 - loss of 8 points, modifier 1x - so -8 points
E - loss 1400 vs 1500 - loss of 5 points, modifier 3x - so -15 points
F - loss 1500 vs 1500 - loss of 7 points, modifier 5x - so -35 points

I invite you now to comment and see if you think this system will generate differnt problems that I may not have foreseen. Keep in mind that:
A. This formula is easily code-able
B. It gives players incentive to finish as high as possible
C. The only big risk is to finish last or very close to last. High skill players, with very few exceptions, should be able to avoid that.
D. This thread is NOT for the "Who cares about skill?" crowd. Refrain if you think so please.

Offline Mu_

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Re: Cton skill calculation - formula proposal
« Reply #3 on: December 13, 2009, 08:10:51 AM »
And finally, consequences of the new formula (benefits as well as risks):

Benefits:
- Players know that they will get a win as long as they place higher than half of the other players in the cton - risk is lower than today, where you can lose in 2nd place

- Players have an incentive to place higher, as they will "grab" a larger modifier to their ELO skill calculation

- Players will do everything in their power to not die early - especially the higher skilled ones - thus eliminating the advantage that the neighbor of an early dead has

Risks:
- With high skilled players doing everything in their power to not finish low/last, low skilled players are more likely to finish last and lose points; however since their skill is low compared to the average skill of the game, their loss won't be that large anyway

Finally - I am a statistician by formation. Hopefully that will give more credibility to my method :).

Offline [KWT]fed1943

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Re: Cton skill calculation - formula proposal
« Reply #4 on: December 13, 2009, 02:25:24 PM »
I like your proposal and hope it will be accepted.

Because I like to play and like to play with/against better players than me.

Offline MiroMcDuck

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Re: Cton skill calculation - formula proposal
« Reply #5 on: December 13, 2009, 02:56:23 PM »
Actually, I don't think this would work. If I played OCC as I do now, I could grow my skill to infinity, because I would never lose this way. Point of Glicko system is that you stop growing when you achieve your own skill level. If it is enough to just place in top half, then you never stop growing. As a result, top players will be those who play most games and who play ctons on at least average level.

Also, as I said in previous post, the problem I see in current system is that it somehow works with average value. Beating two 1700-skilled guys isn't same as beating 2100 and 1300-skilled guy. This leads to such paradoxes as beating guy in a duel gives you more points than when you beat him and other 6 guys in a cton.

And btw I'm also a mathematician (analyst, not statistician); if anybody even cares.  ;)

Offline Mu_

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Re: Cton skill calculation - formula proposal
« Reply #6 on: December 13, 2009, 05:25:55 PM »
Miro,

You are actually correct. Do you have an alternative proposal? Yes, what you just said is true, and is a consequence i did not think about. Maybe a modification of what i said?

Best,

Offline MiroMcDuck

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Re: Cton skill calculation - formula proposal
« Reply #7 on: December 13, 2009, 07:17:12 PM »
I don't have alternative proposal because I don't know exactly how the system works. It seems to work fine, but it's not optimal. I wouldn't design new system from scratch, just modify the existing one to avoid those paradoxes and motivate people to play ctons.

diurpaneus

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Re: Cton skill calculation - formula proposal
« Reply #8 on: December 13, 2009, 07:20:45 PM »
How about we don't apply this for OCCs?

Offline CanuckSoldier

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Re: Cton skill calculation - formula proposal
« Reply #9 on: December 13, 2009, 11:21:41 PM »
I'm not sure there is a way to modify the glicko2 system for just Ctons without negatively effecting the skill rankings as a whole.  The Glicko2 system is working as it was designed after the initial tweaks me and Slaughter put in place after the first couple months of bugs and balance issues for the system.

MMD is right that always guarenteeing wins to the top half of a Cton would allow players to gain skill far above what they should be allowed in this system.

I'm not sure there is a way to encourage high ranked players to play in average skill ctons, this is not a flaw in the system but a problem with the randomness of player skill that are in the lobby at any one time.  The system is designed to encourage high skill players to want to play other high skill players, it is the only way to move up in skill once you have progressed out of the middle ranks.

Right now ctons are assigned skill points at only 40% of what teamers and duels get, that I can change.  But it's not going to change the risk factor for high skill players, it will just make skill points won or lost greater.  If a high skill player does win he will be rewarded more(and he should win if he's 100's of points better than everyone else) but if he gambles and has a bad day and loses, he will lose equally big.

I can run a poll on if Ctons should be weighted more, we orginially weighted them less because cton players were dominating the top 20 and it was felt by alot of players that they needed to be toned down to be more balanced with Teamers and Duels.

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Offline TheBadSeed

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Re: Cton skill calculation - formula proposal
« Reply #10 on: December 13, 2009, 11:36:05 PM »
Well, I still think the win/loss record should be disassociated with skill gain/loss in CTONs..

We all know that no matter who is in the game with you, if you place 2nd out of 7, you should't be saddled with a loss, even if you still lost skill points. Same thing if you placed 6th.. you shouldn't have that count as a win. It's basically like grading on a curve, which is not ideal in a competetive environment.

I think win/loss shouldbe based on your placement, and not on your skill gain/loss. That's a good place to start. At least one of the statistics will be more accurate.
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Offline CanuckSoldier

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Re: Cton skill calculation - formula proposal
« Reply #11 on: December 14, 2009, 03:02:16 AM »
Well, I still think the win/loss record should be disassociated with skill gain/loss in CTONs..

We all know that no matter who is in the game with you, if you place 2nd out of 7, you should't be saddled with a loss, even if you still lost skill points. Same thing if you placed 6th.. you shouldn't have that count as a win. It's basically like grading on a curve, which is not ideal in a competetive environment.

I think win/loss shouldbe based on your placement, and not on your skill gain/loss. That's a good place to start. At least one of the statistics will be more accurate.


Well I'll ask DTA and Speaker to look at that code and see how complicated that change would be.

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Offline Mu_

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Re: Cton skill calculation - formula proposal
« Reply #12 on: December 14, 2009, 10:35:16 PM »
How about changing the 0.4 modifier to depend on the placement too?

For example - let the system do the Glicko calculations, as DTA programmed, but:

-instead of multiplying everything by 0.4, multiply by factors averaging 0.4, such as:

1 and last place - 0.7
2 and 2nd to last place - 0.4
3 and 3rd from last place - 0.1
etc.

This way cton players do not dominate the rankings unless they consistently get 1st place? Of course, to keep the sum of the skills the same, the loss for getting last should be increased to, as shown above.

Offline RedPhoenix

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Re: Cton skill calculation - formula proposal
« Reply #13 on: January 12, 2010, 03:02:33 PM »
I definately think that CTON should be weighed more if we use current system. Top ranks are right now dominated by team players, because it simply isnt worth playing ctons to gain rank. Give cton a bit more value and top player start playing them more too, and we'll have a lot more interesting CTON games.

Offline Spyro

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Re: Cton skill calculation - formula proposal
« Reply #14 on: January 12, 2010, 03:33:11 PM »
Red I guess it won't work the way you think it will work. Since top player aren't playing anc ss or other teamgames cause those are faster and more fun with the right ppl playing them. It's just the nature of those 2 different styles of game which makes them be played differently often...
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