

Tue Mar 31, 2009 4:32 pm 

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MrCrabbs Guest

Post subject: How to allocate points in a tournament final 


My suggestion, FOR A 4P FINAL:
4th place: Fee returned (5000 points)
3rd place: 15.5% of total fees
2nd place: 30.5% of total fee
1st place: 54% of total fee
If the next tournament had the same amount of entrants paying fees as this one, 23, and as in this tournament each entrant payed 5000 points, then there would be 115,000 points total.
4th place gets 5000, which is just fee returned.
3rd place gets .155x115,000 = 17825 points
2nd place gets .305x115,000 = 35075 ponts
1sr place gets .54x115,000 = 62100
The arguments for it:
 The points system used last time was intended to solve the problem of players who get to the final not being bothered how they finished and settling for 4th. My system still solves that problem, since you only get your fee back for 4th, so settling for 4th would not be a rational strategy.
 There is a strong incentive to try to climb a place, since for any position, climbing one place offers a greater reward than what you would lose if the gamble failed and you fell back one place. This should make for a game that is exciting and competitive, and also that bears a strong relation to usual 4p games played under the Kreso points system.
 It is noninflationary. A tournament with 20 players in it (assuming 3 drop out), involves 4 games of 5p for the first round, with two going through from each game. Then 2 games of 4p for the semis, with 2 going through again from each game, and a final of 4 players.
Now, since players get 200 bonus points for just staying in a game for 10 minutes*, then there would usually be 200x20 points created for 4 5p games, 200x8 points created for the 2 4ps in the semis, and 200x4 points created for a 4p game (the final). That's 200x32=6400 points which would usually be created for this number of players playing this number of rated games. The only points created in my suggested points system is the 5000 created to be given for 4th place. Since 5000<6400, the tournament is noninflationary. Points out=Points in+5000.
* I am slightly unsure whether it is 100 or 200 points that a player gets for staying in a game for 10 minutes or more. In the event that it is 100, then we get 32x100=3200 points that are usually created for this number of players playing this number of rated games. Since 3200<5000, my system would be mildly inflationary. But the last tournament gave was inflationary to the tune of 30,000 points=the sum of the bonuses given to 1st, 2nd and 3rd. Although the bonuses were a oneoff easter special, the 30,000 that was created dwarfs the 50003200= 1800 points that would be created in the system I propose.
 What my system does NOT do: It does not say anything about how players get to the final, but assumes that the knockout system remains the same as in previous tournaments, ie: the top two going through to the next round.
 Bill, please post the system that was used this time round, for comparison and discussion. 



Tue Mar 31, 2009 5:06 pm 

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MrCrabbs Guest

Post subject: 


How this points system was designed
***ONLY READ THIS POST IF IT INTERESTS YOU, please give my first post priority over this one. This post explains that my suggested points system was arrived at using Kreso's system as a model.***
My starting point was to try to make a points system for the final that would make the game as similar to a 4p game as Kreso designed as possible.
To do this, I imagined that 4 players all had 10,000 points exactly, and played a 4p rated game together.
Under Kreso's points system (see http://www.galacticmag.com/docmiscellaneous.php), the payoffs at the end of the game would be:
4th player gets (.24x10000)= minus 2400
3rd player gets one third of the 4th player fee, 2400/3, but pays a fee of .17x10000.
Thus 3rd player gets 8001700= minus 900
2nd player gets (2400/3)+(1700/2)(.11x10000)
Thus 2nd player gets 800+8501100= positive 550
1st player pays no fee and gets 800+850+1100= positive 2750
The difference between what 4th and 3rd gets is 1500
The difference between what 3rd and 2nd gets is 1450
The difference between what 2nd and 1st gets is 2200.
Now, since in a tournament final we want every player who got to the final to earn strictly nonnegative payoffs, set the fourth place equal to 0, but keep the differences between the payoffs to each player the same.
Then:
4th gets 0 points (0%of 10,000)
3rd gets 1500 points (15% of 10000)
2nd gets 2950 points (29.5% of 10000)
1st gets 5150 points (51.5% of 10000)
Sum of percentages = 96
So what would they each get if it was out of 100, istead of 96?
4th still gets 0
3rd gets (15/96)x100 = 15.5%
2nd gets (29.5/96)x100 = 30.5%
1st gets (52/96)x100 = 54% (all figures to nearest half %).
Sum of percentages = 100
Thus, for a tournament final, 3rd should get 15.5% of the winnings, 2nd 30.5% and 1st 54%.
Since even 15.5% of 115,000 is 17825, there would still be a danger that if 4th place were zero, the game would again be a game of "dodge last place". To avoid that, I return the 4th place players fee to him or her, so they get that 5000 back. I do this without taking the 5000 out of the pot from which players 13's winnings are calcualted, so not reducing their payoffs. To do this we have to "print" 5000 points. 



Tue Mar 31, 2009 5:41 pm 

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MrCrabbs Guest

Post subject: 


Responding to this thread:
To have a sensible debate, I have outlined 4 benefits of my system. They are:
1) No incentive to settle for 4th
2) A "normal" incentive to gamble to climb a place
3) Noninflation (ie: the system doesn't create too many new points, reducing the value of points)
4) Similarity to Kreso's system
Please feel free to add your own criteria of what a good system should aim to achieve, and to say how you think different criteria rank in terms of importance.
In that way competing systems can be judged according to how they meet the criteria that are most important, and we can find the best system of any proposed.
Last edited by MrCrabbs on Tue Mar 31, 2009 8:45 pm; edited 2 times in total 



Tue Mar 31, 2009 5:54 pm 

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trace567 Guest

Post subject: 


Sorry Crabbs but I still think the way Bill divided the points was both fair and easy for players to understand.
The odd percentages are just going to be confusing for people who enter I think. Which was what I was attempting to say to you last night, that it seems complicated.
The Sunday tournament had extra amounts added, Bill has stated that it was for that one tournament.
However I do like the idea of no point charge for the player who comes 4th.
50% 1st place
30% 2nd
20% 3rd
as Bill did, is both straight forward and fair imo. 



Tue Mar 31, 2009 5:59 pm 

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Bill2k06 Ex Moderator
Joined: 20 Mar 2006 Posts: 2675 Location: Manchester UK

Post subject: 


nice cnstructive post, and good to see you havent left like you said.
i knew you couldnt let this rest crabbs, i know this has been on your mind all last night and all today.
then the 2 hrs spent constructing and writing this post backs up my theory that you wont go, (or havent gone) and also backs up my theory that :
a) you was drunk yesterday
b) you have adhd
c) you have some other compulsive condition
this is just my theory because of your persistence.
but anyway as i said, nice constructive post _________________




Tue Mar 31, 2009 6:01 pm 

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MrCrabbs Guest

Post subject: 


If simplicity is a value (and I think you are right, it is), then the system could be made:
4th pace: Fee returned
3rd place: 15%
2nd place: 30%
1st place: 55%.
That is a hybrid of Bill's system and mine, and meets well the 4 criteria I lay out as important, plus the 5th criteria you add of simplicity. 



Tue Mar 31, 2009 6:06 pm 

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MrCrabbs Guest

Post subject: 


Bill2k06 wrote:  nice constructive post 
Well, I wish I could say the same. I was not drunk yesterday, and I outlined this system and its merits to you just as I have done today. i emphasized that the points as done in Sunday's game made for a game of "dodge last place, and forget the rest".
You are free to think I have a personality disorder, just as I am free to think you are permadrunk, both on power and booze. 



Tue Mar 31, 2009 6:15 pm 

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MrCrabbs Guest

Post subject: 


On a related point, I had not read that Bill was giving out 50%, 30%, 20% and zero. Instead, I went off the points he handed out, and it seems he has either not used the forumla trace quotes, or has miscalculated the points.
115,000 points.
50% of 115,000 + 15,000 bonus = 72,500 for 1st
30% of 115,000 + 10,000 bonus = 44,500 for 2nd
20% of 115,000 + 5000 bonus = 28,000 for 3rd
Whereas what Bill gave out was 70k, 35.5k and 28k.
I hope it will be clear to you that I am not here simply to denigrate the winners. I have just shown that ingeras and sim are owed points! 



Tue Mar 31, 2009 6:27 pm 

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MrCrabbs Guest

Post subject: 


The hybrid system better meets criteria 2) and 4), ie: it is closer to Kreso's system than the points system used on Sunday, and it provides a normal incentive to try to gamble to climb a place, by taking 5% from 3rd and giving it to 1st. It also meets criteria 2) and 3), and the new criteria 5) Simplicity. 



Tue Mar 31, 2009 6:32 pm 

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trace567 Guest

Post subject: 


Right I have just checked the points given for Sunday's tournament.
By my calculations ingeras is owed 2500. However all other points given are correct.
I would like a second moderator to double check my calculations, if she is owed 2500 I will happily make the alteration. 



Tue Mar 31, 2009 6:51 pm 

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MrCrabbs Guest

Post subject: 


You are reverting to type Trace. I have put my calculations here, and they are right. Please put yours.
Ingeras is owed 2500, sim is owed 9000.
Once more, the benefits of open discussion are demonstrated. 



Tue Mar 31, 2009 7:46 pm 

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Magflag12 Moon
Joined: 11 Jan 2008 Posts: 373

Post subject: 


Thank you crabbs for this. May I point out a few points of my own in this 'debate'.
I am glad that you followed a debatelike format, I appreciate that because I am an academic debater in College so its something I am familiar.
Firstly, we assume Bill's system is the status quo, and that your plan is the solvency for the harms you mentioned in the status quo.
Your harms in the status quo were (briefly and mostly assumed)
 The point system used last time did not solve the problem with settling with a nonwinning game
The status quo is inflationary
 The status quo is not consistent with Kreso's guideline for a game
Now I won't go over your plan as you have outlined it efficiently for us.
However, I will go over the benefits (solvency) that you have outlined for us.
1) The incentive to settle for 4th is, and correct me if I am wrong, removed because the final would typically be a 4p, and getting 4p only insures you getting a return on your point investment
2) It provides a natural incentive to gamble to climb a place
3) Noninflation is prevented by not creating artificial point value
4) Similar to Kreso's system (You sort of fail to impact the benefit of this, even after considering your second post)
Now, I see your point system as a decent way to run things, and I wouldn't be opposed. But the significance of it is not as great as your are making it out to be.
In the status quo we have 2 out of 4 criterias that are definately met. 1 and 2 are met because there is obviously no incentive for settling for 4th, because you get no money if you do. 2 is met because any increase in points received is in and of itself an incentive to do better in the game.
3) is not solved in your plan because to solve this problem you have to remove the bonus that Bill adds to the tournament. If you do that, you may remove some inflation, but you also remove some incentive for players to play in the tournament and take it seriously.
4) Is not an essential criteria, as you have provided no way of showing that it is. I would say that it is nice that it is modeled after Kreso's model, but it is not essential. Any progressive system is similar to Kreso's model, so therefore, the status quo meets this nonsignificant criteria in a sense.
So, bottum line, you have provided just another system that contains the same problems, the only thing you fix is that getting 4th does not go unrewarded. If you will look at any particular system in which points or some sort of capitol is gained from competing (such as Poker or any tournament style) you will almost never see a system in which a place gets your money back. In online poker if you play a 9p tournament and get 3rd, you double your money. The reason for this is because you should have either wasted your money and your time, or you should have benefitted from your time and your money. I believe that this criteria should be the one to be upheld.
If anything, if you waste your time and points (materially speaking) you learn how to play the game better, but if you just waste your time (getting 4th) you are less likely to learn anything. _________________ If you're in a war, instead of throwing a hand grenade at the enemy, throw one of those small pumpkins. Maybe it'll make everyone think how stupid war is, and while they are thinking, you can throw a real grenade at them. 



Tue Mar 31, 2009 8:27 pm 

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MrCrabbs Guest

Post subject: 


To players who read my above posts and understood them this post is unnecessary. But I write it mainly as a response to Magflag's, which is at times confused.
5 criteria so far.
1) No incentive to settle for 4th
2) An incentive to climb a place
3) Noninflation
4) Similarity to Kreso's system, and thus "normal" incentives
5) Simplicity.
A new 6th criteria:
6) Avoiding a game where all players just focus on not coming last.
The status quo
1st  50%
2nd  30%
3rd  20%
4th  zero.
The Crabbs version, adjusted for simplicity as per Trace's post
1st  55%
2nd  30%
3rd  15%
4th  0% + 5000
How they meet the 6 criteria:
1) Bill's provides the strongest incentive not to settle for 4th. But my version also means no player is likely to settle for 4th. Why accept just your points back when you could get more? It is clear that in neither system is settling for 4th a good strategy.
2) Bill's system provides insufficient incentive to try to climb a place compared to my own. Consider you are in 3rd, and you are considering whether to gambe to get 2nd. If it works, you get 10% extra. If it fails, you lose 20%. The incentive is NOT to take a risk.
Under my system, if you are in any place whatsoever, except 1st, you have an incentive to gamble to try to finish higher. Try it  take a scenario of your own choosing, and look at the loss versus the gain of a gamble.
The only other case in which it is not worth a gamble under my system is if you are in 2nd and a gamble for 1st might mean you finish last. In that case you would gain 55%30%=25%, but lose 30%5000 if you fell to last.
55%30%= 25% of 115,000 = 28750 if you win
(30% x 115,000)  5000 = 34500  5000 = 29500 loss if it fails and you slip from 2nd to last.
But even in this case, since 1st place is clearly the most glorious, many players would still take the gamble, since there is only 750 points in it.
Thus, unambiguosly, my suggested points system better meets criteria 2) of an incentive to try to improve your rank. This is not a opinion, but mathematically true.
3) My system is noninflationary as I showed above. The same is true of Bill's except when bonuses are added, as they were this time. Then, the bonuses are inflationary. But the same would be true if we adopted my system but added Easter bonuses. The bonuses are not an integral part of Bill's system, but a oneoff. Thus it was not part of my critique of the status quo that it is inflationary, since hopefully the bonuses will not be repeated.
4) Similarity to Kreso's system. My system is closer, as I show above. Hence players will have incentive more similar to those in a normal game, and there will be the usual competitive element. Players who like 4p games and 5p games as Kreso has made them should prefer my system.
5) Simplicity. Bill's system and my own adjusted one are simple to implement.
6) The game is far less likely to become a simple game of "dodge 4th" under my system. That is mathematically true and verifiable.
Magflag12 wrote:  So, bottum line, you have provided just another system that contains the same problems 
Is thus unambiguosly incorrect.
A reply to magflag
Magflag please review your analysis since it should now be clear to you why Bill's system does not meet criteria 2  it is a question of cost/benefit analysis. 1st getting more than 2nd, who gets more than 3rd, who gets more than 4th, is not alone enough to make for a competitive game. Instead you need to consider how much a player would gain or lose from a gamble, as I do in this post.
3) Is met in my suggestion, contrary to what you say Maggy. It is noninflationary and hence 3 unambiguosly is met.
4) Is an important criteria in so far as we think Kreso's points system tends to produce good incentives and a competitive 4p game. Since players in the tournament are mainly players who enjoy playing 4 and 5p games in GM, it seems very likely that this criteria would be a popular one.
Briefly, this is not poker this is GM. Poker is there to make a profit, and hence incomparible to the points given out in GM, where points in equals points out, more or less. It is naive to assume that the reason players don't get their points back for, say, 4th in poker is to "teach" poker players. The payoffs are chosen to maximise the profits of the house. Players not learning is good, not bad, for the house.
Finally, please refrain from replying again for a while maggy since I want other contributions. I do not want this thread to die because it becomes me and you writing 800 word replies to one another, with you practicing your college debating techniques. I have met the points you raise and hope others will contribute.
Last edited by MrCrabbs on Tue Mar 31, 2009 9:18 pm; edited 9 times in total 



Tue Mar 31, 2009 8:35 pm 

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Yiles Moon
Joined: 24 Feb 2008 Posts: 441

Post subject: 


Magflag12 wrote:  I am glad that you followed a debatelike format, I appreciate that because I am an academic debater in College so its something I am familiar. 
I guess then you are also familiar with an "argumentum ad verecundiam" argument?
Please continue... _________________
Bruce Lee wrote:  “When the opponent expands, l contract. When he contracts, l expand. And when there is an opportunity...l do not hit...it hits all by itself”  



Tue Mar 31, 2009 9:11 pm 

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Magflag12 Moon
Joined: 11 Jan 2008 Posts: 373

Post subject: 


lol I actually am Yiles.
I meant to finish that sentence with a 'with' by the way.
However, that particular sentence was not an Argumentum ad Vercundiam. I was not justifying my claim with my knowledge of debate theory. I was saying that I can easily relate to his format.
More specifically,
By crabbs following that format I was able to be more precise in my arguments. If he hadn't of followed that format it would have more likely been a novel than an argument lol.
Bottum line: it was just a thank you. _________________ If you're in a war, instead of throwing a hand grenade at the enemy, throw one of those small pumpkins. Maybe it'll make everyone think how stupid war is, and while they are thinking, you can throw a real grenade at them. 


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