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 Post subject: A top down approach
PostPosted: Thu Feb 05, 2009 11:25 pm 
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Joined: Wed Nov 12, 2008 8:48 pm
Posts: 29
Let's try this differently.
Instead of suggesting a system and comparing with the current system let's start from scratch, list our goals, and develop requirements and then design.
This is in fact how I arrived at my suggestion here.

There are three primary goals:
G1: game quality
G2: more people
G3: desirable behaviour

There is some overlap, but I think in total this covers everything.

Now in order to achieve these goals we can identify certain principles.
For example:
P1: matching players of like strength. G1,G3.
This goes towards G1, and a bit of G3. Naturally any improvement in G1 and G3 helps in G2.

It is possible that the set of principles is not unique, and you could find another set that achieves these goals.
The aim of this discussion is to achieve these goals, as much as possible, through designing a ranking system.
There are of course other ways.

P2: simple interface. G2.
Whatever system is designed it should be simple to use.

P3: player incentive. G1,G2,G3.
We require some mechanism for controlling behaviour.
This only works if players are enthusiastic about this incentive.
If players become apathetic to this then the system fails.
For this reason rank accuracy is important, and other issues that plague veterans, such as inflation.

P4: player rank. P1,P3.
One possible form of incentive.

P5: betting system for matching players. P1,P2.

P6: variable game significance. G1,P4.

P7: player rank changes according to game outcome and game significance. P4,P5,P6.

P8: encourage participation within the game. G3.

Now we can realise one possible instance of these principles.
Current rank system:
Each player has a number of points. P4.
Player points are invested in games, with each player contributing the same amount. P5,P6.
The pay-out of each game is proportionate to the points invested and the outcome. P7.
There is an option to play PPSC or WTA. P8.

There are more things we would like from our system however.

P9: deter in-game behaviour that is counter to the spirit of the game. G1,G3.
Such as point maximization of the winning player that occurs in the current system.

P10: player incentive should be time-invariant. G2,G3,P1,P3.
Players should be penalised for joining late or for taking breaks.

P11: player incentive should rely on quality of play rather than quantity. P1,P3,P10.
Specifically avoid the problem of players getting high ranks by player many low ranking games. This is a serious criticism I have of the current system.

P12: distinguish strictly between winners, drawers, survivors, losers and quitters. P8,P9.

P13: encourage new players to participate. G2,G3.

P14: fast convergence to correct rank. G1,G2,P4.

P15: encourage competition. G1,G3.

P16: player rank should be stable. P4.

This list can be continued, and indeed the following system has benefits not listed here.

My system:
Each player has a rank. P4.
This rank is used to calculate the value of games he participates in and his earnings from such games. P5,P6,P7.
This is not a flat bet. Stronger players earn less winning against weaker players. P11.
The rank also limits which games a player may participate in. P1.
There are two separate contributors to the calculation of point distribution of games. I call these global and local contributors.

Global: the distribution of points at the end of a game is not zero-sum.
It is strongly positive for low-valued games and weakly negative for high-valued games. P13, P14.
This creates a fixed point in the system to which the average rank will tend. That means there is zero global inflation. P10.
If we assume that the population is growing we will see inflation of the top score despite the tug towards the fixed point. P15.
Success is always rewarded and failure is punished above some critical beginner level, where mere participation is rewarded.
Inactivity below the fixed point is not rewarded because of the tug upward to the fixed point.
Inactivity above the fixed point is not rewarded because of the inflation of the top score.
The average player however will not feel the need to keep up with inflation.
Veterans that fall behind the top score due to inactivity will be able to catch up since their above average status is maintained.

Local: the distribution of the points is even after an uneven investment (by player rank, P11) and global adjustments to game value are made. P7.
That is once the game value is determined and the initial investment is subtracted from players then players are treated identically without regard to rank. P2.
The initial investment is a percentage of the player's rank determined at the end of the game. P16.
This percentage is player adjustable. P6.
There are other parameters that allow for games between PPSC* and WTA, and also can reward mere participation. P8,P12.
(* not a true PPSC, rather the winner's reward is fixed to avoid in-game maximising by the winner.) P9.

Players are shielded from the complexity of the system by being given templates, such as WTA or PPSC*. There are other templates in my system as it is far richer. P2.

Ok, let's talk numbers.
How does this system work in practice?

When the game starts we set game parameters:
G = game significance = what portion of player rank is invested in the game
P = participation % = what portion of the game value is given to non-CDs, regardless of outcome. Also determines who can join a game. This is really measures the seriousness/friendliness of the game. Serious games assume no one will CD, friendly games reward mere participation quite highly. This parameter affects the extent of the global skewing. Friendlier games are skewed less. This is just to prevent abuse of the global skewing.
W = winner % = what portion of game value (after P) is given to the winner
S = survivor % = what portion of game value (after W) is divided flatly per survivor, the rest being divided per SC between survivors

When the game ends we calculate
R = player's rank when the game ends, but before this game is taken into account. New players start with R=0, and this is the lowest possible value.
C = player's SC count
K_i = i-th constant, to be defined later, greater than 0
T = total rank = sum of R's
U = total SCs = sum of C's, usually 34
V = adjusted game value = natural game value + global skewing = G * T + (1-P) * ( - K_1 * T + K_2 )
N = number of active players, usually 7
M = number of survivors, not including the winner

winner R = unspent rank + participation reward + victory reward
= (1-G) * R + V * P / N + V * (1-P) * W
= (1-G) * R + V * ( P / N + (1-P) * W )

defeated R = unspent rank + participation reward
= (1-G) * R + V * P / N

survivor R = unspent rank + participation reward + flat survival reward + relative survival reward
= (1-G) * R + V * P / N + V * (1-P) * (1-W) * S / M + V * (1-P) * (1-W) * (1-S) * C / U
= (1-G) * R + V * ( P / N + (1-P) * (1-W) * ( S / M + (1-S) * C / U ) )

CD R = unspent rank
= (1-G) * R

draw R = unspent rank + participation reward + flat survival reward + relative survival reward
= (1-G) * R + V * P / N + V * (1-P) * S / M + V * (1-P) * (1-S) * C / U
= (1-G) * R + V * ( P / N + (1-P) * ( S / M + (1-S) * C / U ) )

Templates:
G is freely adjustably by players, by default 0.1
We can define 18 templates using the following axies.
Friendly/Normal/Serious: P=0.4/0.2/0
WTA/Fixed: W=1/0.6
PSC/Mixed/Survival: S=0/0.5/1

suggested default: P=.2, W=.6, S=.5 (Normal/Fixed/Mixed)
classic WTA: P=0, W=1, S=1 (Serious/WTA/Survival)
simulated PPSC*: P=0, W=.6, S=0 (Serious/Fixed/PSC)

We can come up with better names for templates.
We could also allow for optional tweaking of parameters.
Setting P=1 makes the game unranked, but still penalises CD.
These templates are just examples. The actual ones will be better chosen.

So, to the choice of K_1 = 0.01 and K_2 = 210.
K_1 represents the amount of negative inflation we want to inject, and represents the added pressure on high-ranking players. This is small as not to be a nuisance.
K_2 represents the boost to game value, and ultimately translates to the encouragement new players receive.

Let's calculate the fixed point. We do this by considering a total draw scenario with no change in ranks.
R = (1-G) * R + V / 7
7 * G * R = V
We substitute for V and assume all R are the same.
V = G * 7 * R + (1-P) * ( - K_1 * 7 * R + K_2 )
0 = - K_1 * 7 * R + K_2
R = K_2 / K_1 / 7 = 210 / 0.01 / 7 = 3000
The gradient is: 1 - (1-P) * K_1 = 1 - (1-P) * 0.01, that is just slightly below 1.

Setting the minimum R to join at (creator R - 350) * (1-P) should prevent leeching.

An interesting thing to notice is that there is no limit to the number of games players play. There is however a built-in deterrent against playing too many games at once. Game value is calculated according to rank at the end of the game. This means that if you started many low level games against weak players you'll only benefit marginally after the first few wins and with too many games you may gather a few leeches since games are joined based on rank at start but scored based on rank at finish. The system really encourages players to play at their level. The P parameter gives players the option for friendly games.


Last edited by avinoam on Sun Feb 08, 2009 7:02 pm, edited 1 time in total.

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 Post subject: Re: A top down approach
PostPosted: Fri Feb 06, 2009 7:40 am 
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Joined: Wed Oct 08, 2008 12:47 pm
Posts: 726
Wow, thats a thorough writeup - i'll read it in more detail tonight, but you seem to have some good points.
Just as a side point, didn't Kestas write a list of requirements for the points system somewhere?


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 Post subject: Re: A top down approach
PostPosted: Fri Feb 06, 2009 4:44 pm 
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Joined: Tue Aug 26, 2008 8:46 pm
Posts: 249
I shall be splitting my comments into various different posts. I reject P6:

P6: variable game significance. G1,P4.

G1 being game quality.

P4 being player rank.

Now, more important games would have better play, but the flip side of this is that there are less important games with lower quality. This surely is not a good situation, where only with a great rating risk can you achieve a good game, and therefore only better players can really play good games.

P4. I don't see that this follows. You still have a ranking system if all games are of equal significance.


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 Post subject: Re: A top down approach
PostPosted: Fri Feb 06, 2009 5:53 pm 
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Joined: Tue Aug 26, 2008 8:46 pm
Posts: 249
There is one thing that this system does do, which is to change the WTA/PPSC division. I feel that that is very problematic indeed. WTA and PPSC are two viewpoints, and to make a scale between them is perhaps not useful.


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 Post subject: Re: A top down approach
PostPosted: Sun Feb 08, 2009 6:49 pm 
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Joined: Wed Nov 12, 2008 8:48 pm
Posts: 29
P6 variable game significance

This is a nice aspect of the current betting system.
Some games are friendly, some games are practice and some games are epic.
It's nice having the option to choose rather than the system designer choosing based on his personal taste.

Similarly, WTA and PPSC are two separate paradigms. It's nice being able to choose between them. However both of them have flaws.
By allowing a middle option you get a sharper division between 18 SCs and 16 SCs, and 1 SC and 0 SCs.
This is in the spirit of the game in my opinion.
In any case since this is user-defined each set of players can choose what suits them.
If you are a believer in WTA then play WTA. I don't see much benefit in restriction.

I also added the participation bonus as a way to separate between 0 SCs and CD.


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 Post subject: Re: A top down approach
PostPosted: Sun Feb 08, 2009 8:44 pm 
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Joined: Tue Aug 26, 2008 8:46 pm
Posts: 249
I am all for rated/unrated games. I am not for different significance of rated games however- it makes the rating system inaccurate, and it makes some games unimportant. Unrated games are good for variants or when you just don't have the time.

The problem with Blurring the gap between PPSC and WTA is that suddenly people don't know what they are exactly playing for, and that will make stuff more complicated.


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 Post subject: Re: A top down approach
PostPosted: Mon Feb 09, 2009 12:43 am 
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Joined: Wed Nov 12, 2008 8:48 pm
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Well, if you are against a continuum of possibilities that doesn't mean you will be against specific middle points.

I see WTA and PPSC as end-points of a natural scale.
WTA represents the true-to-game rating, but only works if players are committed to seeing the game through, even if their chances of winning become very small.
PPSC gives very little incentive to play in the true spirit of the game, but gives great incentive to play even when you're losing, although not so much when you're almost dead.
S=0.5 is precisely the middle ground.
Let's say W=0.6.
This means that 60% goes to the winner, 20% is split between survivors evenly, 20% is split between survivors PSC.
Let's try a few examples: (for these I use PPSC with fixed winner reward)

18:16
WTA: 100:0
PPSC: 60:40
Middle: 60:40

18:12:4
WTA: 100:0:0
PPSC: 60:30:10
Middle: 60:25:15

With my system 2nd place is not nearly as desirable as first, but 2nd player also has an interest in killing off the small survivors, although not as much as winning. Also notice that simply surviving gives you a reasonable amount of points.
There are very clear jumps between winner, sole survivor, survivor, defeated. I see this as a good quality in a rank system. I would certainly like to play this more than either PPSC and WTA. It's not wishy washy, it's fundamentally different.

I can understand your objection to variable middle ground, but don't agree to an objection to a single middle point.

I also don't agree with your Rated/Unrated distinction.
Again you can argue that a continuum of choices makes the importance of the game vague. Fine.
But I can still suggest that it should be Rated/Casual/Unrated.
Take a peek at my templates idea. There really is no reason to limit our choices to 2 templates. I think there are a variety. Here you can already count 7 distinct possibilities each giving a different flavour of game, and indeed for each flavour you will find players who will prefer it. There is also the participation reward which adds more possibilities, and creates the important distinction of defeated/quit. I don't think this should be built in either. I think it's ok to let players choose. If you think that it shouldn't be a continuum then even just 2 options already adds a lot to the system without making it ambiguous.

Basically your criticisms are taken care of with the idea of templates. :)


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