Prize Distribution -- Shoulda Hadda V-8

Running Chess Tournaments
1

In another thread, James Schuyler highlights various flaws in the standard methods of distributing place prizes and class prizes.

These flaws have also been pointed out in other threads, such as:

Distribute Prizes
http://main.uschess.org/forums/viewtopic.php?f=2&t=208

and

Prize Distribution Revisited
http://main.uschess.org/forums/viewtopic.php?f=2&t=6710

Various solutions have been proposed, making use of complicated proportional or fractional methods. Understandably, however, TDs don’t want to add 6/13 of one prize plus 4/7 of another when players are milling around asking for their money so they can begin the long drive home.

Before I go any further, let me make a fervent plea. Please do not hijack this thread with posts about the inherent unfairness of class prizes. I actually agree with that point of view (at least to some degree), but that’s not the purpose here. If you want to rail about class prizes in general, please do so in one of the following:

Splitting Money Prizes
http://main.uschess.org/forums/viewtopic.php?f=2&t=7365

or

Counterplay: Letters to the Editor
http://main.uschess.org/forums/viewtopic.php?f=24&t=7661

Suddenly, just the other day, I slapped my forehead. “I could have had a V-8.” An idea struck me which was so simple, and yet so logical, that I wondered why nobody had thought of it before. Stay tuned, and find out if you, too, should have had a V-8.

Ideally, a prize distribution method should:

  1. be continuous. A small change in the prize structure should result in only a small change in the actual prize won by any player.

  2. be monotone. An increase in one of the prizes should never result in a decrease in the actual prize won by any player.

  3. award class prizes to the players in that class.

  4. be in agreement with the philosophy behind class prizes.

  5. be simple to apply in the heat of tournament aftermath.

Here’s my brainstorm:

A. First award the place prizes, without regard to the class or “under” prizes. In other words, figure out what the place prizes would be if there were no class prizes.

B. Next, award the class or “under” prizes to the players in those classes. If some players already receiving a prize in step A would now have their prize increased, get the increase from the class prizes, rather than tinkering with the place prizes already calculated. Observe the limit-one-prize-per-player rule, awarding any leftover amount to other player(s) in the class.

C. If there are class or “under” prizes in multiple classes, award prizes in the more inclusive categories before those in the less inclusive categories. For example, figure the under-2200 prizes before the under-2000 prizes.

How would this work in James Schuyler’s example?

1st $200
2nd $100
3rd $50
1st U2000 $60

p1 2200 5.0
p2 2200 5.0
p3 1900 5.0
p4 2200 4.5
p5 1900 4.0

A. First award the place prizes. This one is easy, because there is a 3-way tie for the 3 place prizes. p1,p2,p3 each get $116.67.

B. Next, award the under-2000 prize. p3 has already won more than $60, so his prize is not increased. The under-2000 prize goes to the next under-2000 player. p5 wins $60.

Here is one of the examples from the Distribute Prizes thread:

1st $150
2nd $101
1st U1800 $99

p1 2100 5.0
p2 1700 4.5
p3 1900 4.0
p4 1650 3.5

A. Award the place prizes to p1 ($150) and p2 ($101).

B. Award the under-1800 prize. p2 has already won more than $99, so this amount goes to the next under-1800, p4.

Here is a slightly different example from the same thread, an example originally designed as a companion case to expose the flaws in the standard prize distribution methods:

1st $150
2nd $99
1st U1800 $101

p1 2100 5.0
p2 1700 4.5
p3 1900 4.0
p4 1650 3.5

A. Award the place prizes to p1 ($150) and p2 ($99).

B. Award the under-1800 prize. p2 has already won $99, so he is entitled to an additional $2. (More would violate one-prize-per-player.) This $2 comes from the U1800 prize. p2 wins $101 total, with the remaining $99 (of the U1800 prize) going to the next under-1800, p4.

Finally, here is the example that started the Distribute Prizes thread:

1st $32
Class B (1600-1799) $20
Class C (1400-1599) $20
Class D/E (under 1400) $20

p1 1707 3.0
p2 1575 3.0
p3 1688 2.5
p4 1322 2.5
p5 1584 2.0
p6 1541 2.0
p7 1114 1.0
p8 830 0.0

A. Award the place prize to p1 and p2 ($16 each).

B. Next, award the class prizes, beginning with the most inclusive class. In this case, no class is inclusive of any other; in fact, the three classes are pairwise exclusive, so it shouldn’t matter which class is calculated first. Starting with class B, p1 gets his prize upped from $16 to $20 (using $4 of the $20 class B prize), and the remaining $16 goes to p3, the next B player in line.

C. Likewise, p2 gets his prize upped from $16 to $20, and the remaining $16 of the C prize goes to p5 and p6 ($8 each). p4 wins nothing at this point, as D players are not eligible for B and C prizes.

D. Finally, award the D prize to p4 ($20).

As far as I can tell, this algorithm solves the discontinuity and anti-monotonicity problems of other methods, while still respecting the limit-one-prize-per-player rule. It also awards class prizes to class players, and is in harmony with the basic philosophy of class prizes (which is that class players can earn more than higher-rated players for the same score).

Additionally, this method seems simpler and less arbitrary than the artificial “standard” ways. Division by N is required only when there is an N-way tie for the same prize. And I have a hunch that it will be possible, more often than at present, for TDs to calculate some of the prizes even before all the games finish.

One and all, please cast your examples at this algorithm, and let’s see how it works. You can even try to break it, if you want to.

Bill Smythe

2

I’m not sure what you mean by “break it.” Your system divides the prizes and is not especially difficult to use. I can demonstrate that leads to results I find highly undesirable, but you can answer that by simply not agreeing with my value judgment.

!st: 200
2nd: 100
U2000: $125

2200 4.5
2100 4.5
1900 4.5
1800 4

Your system: 2200, 2100 and 1900 get $100 each place prize. Since this is less than the $125 U2000, 1900 gets an additional $25. 1800 gets the remaining $100 from the U2000 prize. The result of this is that the class player gets more than the other players with whom he is tied. I think this is grossly unfair, but if you don’t then you won’t see a problem.

Standard system: ($200 + $100 + $125)/3 = $141.66, which is more than $125. 2200, 2100 and 1900 get $141.66 each, and 1800 (with 4) gets nothing. I just can’t accept that a system which filters more money down to lower-rated and lower-scoring players is an improvement.

3

Well, I don’t think you’ve broken it, not yet anyway. Let’s take an even simpler case (same prize structure):

1st: 200
2nd: 100
U2000: $125

2200 4.5
2150 4.5
2100 4
2050 4
1900 4

Here, too, the class player gets more ($125) than the other players with whom he is tied ($0). This remains true even if 2nd is changed to $150 (to make it more than the class prize). It also remains true regardless of which system (mine or the standard version) is used to distribute prizes.

It is inherent, with class prizes, that a class player can win more money than other players with the same score. Apparently, you find this more repugnant if the amount won by the other players is non-zero than if it is $0. In other words, you seem to be accepting (at least within the context of class prizes to begin with) the extreme case, while disapproving of the more moderate case.

Bill Smythe

4

That’s true. I’m not arguing that your system is necessarily worse than the standard one, just that I don’t see any reason why it should be an improvement. There is also the point that your system tends to push more money down to lower-scoring players, which I also consider undesirable.

A more practical objection is that any organizer using this distribution method should really have to announce it in advance. Since he’s obviously not going to put the whole thing in the TLA, this would be difficult unless the system were published somewhere.

5

It’s an improvement, not primarily because of any significant differences in philosophy, but simply because the present system has a whole bunch of technical glitches, such as discontinuities, non-monotonicities, illogic, strange results from time to time, etc. To see these glitches, just read the Distribute Prizes thread, or James Schuyler’s original Chess Life article (available from the Counterplay thread in the Articles forum).

I think it’s more accurate to say that my system pushes less money up to higher-rated players. Because of the way the standard system handles ties between place winners and class winners, a lot of class money often ends up in the hands of players not in the class. With my system, class prizes stay in the class, where they belong. See James Schuyler’s example, in which the standard system awards the class players a total of only $3 more than they would have won without the class prizes.

That would be true only until USCF adopts this system as the standard. Even before then, a change in the distribution details (as opposed to the prize list itself) is not likely to keep any players away, so it might be sufficient simply to post the distribution method at the tournament, during registration and before the first round.

Bill Smythe

6

But your system has other glitches, as I already pointed out. You don’t mind those, and you dislike the ones that arise from the current system. I have no problem with that, just with your trying to turn your preferences into soemthing more than a personal preference.

Yes, that’s probably an equivalent way to phrase it. I still find it objectionable. I think any system that increases the prize money to lower-scoring players is flawed. And before you argue the point, I agree that all prize splitting systems that involve both place and class prizes are flawed. Some are just more flawed than others.

I doubt that’s going to happen. However, including your system as an acceptable variation would answer the objection.

I also disagree that using a non-standard prize distribution system would not keep some players from entering. This came up a few times when I played more frequently, and I can recall a few incidents where players and TDs nearly came to blows over weird prize divisions.

7

John’s Example:

and the subsequent dialogue would be avoided if you followed the rule of thumb of never having a class prize larger than a place prize.
I think this method works great as long as you follow the rule of thumb.

The only thing I found odd about it is this situation and want an opinion:
this is from a 7 round tournament with lots of draws.

1st: 200
2nd: 100
U2000 1st:80
U2000 2nd:60

2210: 5.0
2190: 5.0
2150: 5.0
2100: 5.0
2050: 5.0
1980: 5.0
1950: 4.5
1920: 4.0

The Top 6 would split the 1st & 2nd of $300 for $50 each.
The 1980 player would get $30 of the 1st U2000 to bring him up to $80.

In this situation would you then Give the 1950 $60 ($50 left from 1st U2000, and $10 from the 2nd U2000) and the 1920 player $50? ( this could get crazy looking if one of the Class prizes went down several places in a larger tournament, but is fair under the logic of this payout system)

Under the standard Prize structure in the rule books the division would be like this
1980 player would get $80(1st U2000), the other 5 tied with 5.0 would get $60 each, 1950 would get $50(2nd u2000), and the 1920 would get nothing.
So it tends to let the up top players benefit from the class prize funds

8

The rule book standard is to maxmize the payout for the prize winners. It was designed for equity. If a class player ties for a place prize, the rule of thumb is that he get his maximum prize money. If that is the class prize, then fine. But if his prize would be higher by sharing the class prize with the place prizes, then this is beneficial to that player. Under the rulebook standard in most cases the top players are not benefiting, and are probably being hurt by sharing the class prize, but it is the most equitable way to distribute the prizes. This is the method that most players understand and find fair.

Where the TD/organizer runs into problems is when he monkeys around with the prize fund and the rulebook standard. Then the players become suspicious and wonder if there is hidden agenda behind the distribution. That is when the arguments start. The ill will that is created then can hurt future attendance at events organized by that individual.

If you want to know what really hurts tournament attendance, its based on prizes. Why should class players attend an event when they are sure their prizes will likely be cut in half by the organizer? And why would a class player play for a prize, given in an example above, of $20? Players are voting with their nonattendance at such weak events. Clubs that do not respect players and provide such low quality events watch their members drift away. Players now have the alternatives of the internet or strong computer programs to sate their desire to play. Only the real addicts will go to the poor events.

9

I have to totally disagree with you that in ‘most cases the top players are not benefiting from class prizes’. I think the very nature of the way rulebook splits occur (and basic math) tells you everyone is going to benefit from the split if more money is added to it or less people are in it. My example above that I gave (which is what happens most of the time). Under the Rule book structure, the ties at top get $60 each as opposed to $50 a piece under the proposed alternative.

The only logically way to agree with you that class prize splits tend to take away from top place money is if you are meaning to say that if we did away with class prizes and put all that money into place prizes, then I would agree with you. But that is not really an option.

They get more money by the class prize player dropping out of the split and taking his own prize (he in turn gets more money as well).
The thing that people are fussing about is that money that was set aside as ‘class prizes’ in the pool is theoretically going to the benefit of non class players.
Under the proposed alternative more people will end up getting some sort of prize usually as well.

10

JediJoshua, under your own example, the 2000+ rated players with 5 points do not benefit from any class prize. They split $300 and get $60 each. The 1980 gets $80 and the 1950 gets $60. The class players are the ones benefitting from the existence of the class prizes. Per the rulebook this is an ordinary distribution. Most players would see this as very fair. The 1920 rated player should expect to get $0. Do you have some sort of bias against players who are strong and tie for first? The suggested fractioning of prizes under the several alternatives offered do not conform to standard practice. You can, as an organizer, do what you like if you publish it in advance. Just don’t expect many players to come to an event that doesn’t conform to USCF rules. What the TD can expect is a claim made through the TDCC for failure pay out stipulated prizes according to the rulebook. Sanctions have been applied in the past to TD’s for not paying out prizes properly.

11

So far, so good.

That sounds right, too. The 1950 was clear 2nd U2000, so is entitled to at least $60 (the 2nd U2000 prize). $50 remain from 1st U2000, so that plus $10 from 2nd U2000 will do the trick. That, in turn, leaves $50 from 2nd U2000, which would go to the next player in line.

You hit the nail on the head again. If there were ten U2000 prizes, 1st U2000 could win parts of a place prize and 1st U2000, then 2nd U2000 could win parts of 1st and 2nd, while 3rd would win parts of 2nd and 3rd, etc. 10th U2000 would win parts of 9th and 10th, and the remainder of 10th could then be awarded to an 11th U2000 player.

Crazy, maybe, but the standard system would be even crazier, trying to divide a whole bunch of prizes (both place and class) among an even bigger bunch of players, some in the class and some not, all the while making sure each player gets at least the minimum to which he is entitled, but still observing the limit-one-prize-per-player rule. :neutral_face:

As you also pointed out, the proposed distribution would also keep the class prizes within the class, whereas the standard method would allow a few of the class dollars to leak up to players outside the class.

Bill Smythe

12

Though the 200+ players are technically not ‘touching’ the class prize, because of the class prize, they are getting $10 more each. If the 1980 were above 2000 as well, or there were no class prize, they’d only be getting $50 each. So availability of the class prize helps them by getting them a better split.

I went over the rules in the rule book and compared them to the theory in this. I also like it better than Schuler’s proposed method as it is far simpler and has less hiccups to iron out with all the fractions. I would like to see the wrinkles ironed out and have this submitted to the rules committee to be a named alternative to the conventional money split. Call it the Cascade Method. Then all an organizer would have to do was advertise they would be using the Cascade Method of prize distribution. People’s opinions differ as to whether this would have to be in the TLA or other advance advertising or simply posted at the tournament. I guess the rules committee would have to rule that one in their discussion.
If for some reason they would not adopt it we could put a website up with the methodology and simple direct people to that website in pretournament advertising.

In my are, this would fair very well since we have mostly class players in the tournaments. If a class player ties for first he’d get his ‘share of first’ a portion of the class prize, and the rest would go to the next in class.

13

I have a counter-proposal: design prize funds so that correct prize distribution is obviously correct in all situations.

Most prize distribution questions can be answered by:

… E. Shoot the Organizer

14

Ditto

15

Asked to respond to this thread, I will say “Amen” to this post was all that I would have contributed earlier, as I’m not sure its succinctness can be improved upon. However, maybe the good professor would be so kind as to publish some guidelines for distribution to help the rest of us - similar to his excellent analysis earlier this year on ratings. Next comment is to try to hold events under $5 so no one cares about prizes and only about chess (I know I’m the elephant in the room on that one). More ideas later.

16

1st: 200
2nd: 100
U2000 1st:80
U2000 2nd:60

This seems like a decent prize fund - it would take a four-way tie for first, one of whom is under 2000 for their to be a problem.

Ken, would you say this is decent enough or could the organizer have reasonably improved upon it?

Edit: maybe the problem stems from having 2nd prize and first U2000 too similar in amounts. Maybe make 1st/2nd prizes as Master/Expert Class prizes with no overall first place prize. That would improve clarity at the cost of fairness, except that U2000 players knowing the prize fund, play with the knowledge of ineligibility for 1st prize. Does anyone have good prize structure ideas beyond the rulebook?

17

Unfortunately, the term “obviously correct in all situations” is not something that everybody agrees on (at least as long as there are class or under prizes in addition to place prizes).

Simple example:
First 200
Second 100
Top A 60

All the prizes flow smoothly. The A prize is less than any place prize.
If a master (Marc), expert (Ed) and A player (Al) tie for first with another A player (Andy) a half point behind then you have the following options:

A) Marc, Ed and Al split 360 for $120 each per the current rules (my preference)
B) Marc and Ed get $100, Al gets $120 and Andy gets $40 (Bill Smythe’s preference and I think this is also JediJoshua’s preference)
C) Marc, Ed and Al get $100 each and Andy gets $60 (I think JediJoshua lists this as Schuler’s preference)
D) Marc and Ed get $100 and Al gets $160 (this was proposed by somebody on another forum)

If you shoot organizers over prize split disagreements about such a straightforward prize fund then it won’t be long before surviving organizers limit their tournaments to class-only events or to events with no class prizes (not a goal that I would agree with).

18

Actually Under Bill’s you award 1st and 2nd first, so $100 each to Marc, Ed, Al. then you award Class, since the Class prize is $60 and Al already won more than $60, the $60 goes to Andy. Only if Al’s Split got him less than the class prize does he draw from it.

Schuler’s method involved fractions to not add up to more than one whole, so under Schuler’s method, the top 3 each get 1/3 of 1st and 1/3 of 2nd($100), now Al only has 2/3 of a prize at this point so he gets an additional 1/3 of the other prize he techincally qualified for so he gets $120 total, and then Andy gets the 2/3 left of $40.

19

Hello Bill,

I have been following the thread and I am interested in “The Smythe” method of prize distribution. I’m never good at looking at hypothetical results, so I’ll look at my previous tournament so see how the method would work.

In tie-break order (we also had trophies):

The prizes for this tournament were:
700-400-300-200 U2200:150-75 U2000:150-75

1-4th are the same for both systems. It’s the U2200 and the U2000 that we see the difference.

Under the current USCF system I believe the prizes are as follows:
450/6 = $75 which is less than the $112.50 that Thompson and Peck would get if they split the U2000 separate.

So. $225/4 = $56.25 for the Experts and the 2 A players get $112.50 each.

5 Thompson, N. 1948 3.5 - $112.5
6 Lin, A. 2067 3.5 - $56.25
7 Aceil, J. 2109 3.5 - $56.25
8 Balkum, A. 2046 3.5 - $56.25
9 Peck, J. 1940 3.5 - $112.5
10 Marmont, B. 2057 3.5 - $56.25

Let me know if I calculate the correct prizes under the Smythe method.
Step b. Calculate the U2200 prizes
225/6 = $37.50

5 Thompson, N. 1948 3.5 - $37.50
6 Lin, A. 2067 3.5 - $37.50
7 Aceil, J. 2109 3.5 - $37.50
8 Balkum, A. 2046 3.5 - $37.50
9 Peck, J. 1940 3.5 - $37.50
10 Marmont, B. 2057 3.5 - $37.50

Step c1. Calculate the U2000 prizes
225/2 = $112.5 minus the money they already won.
5 Thompson, N. 1948 3.5 - $112.50 - $37.50 = $75 (in addition to U2200 Prize)
9 Peck, J. 1940 3.5 - $112.50 - $37.50 = $75 (in addition to U2200 prize)

The remaining money from the U2000 prize would go to the U2000 players who scored 3 points.

Step c2 Calculate the remaining U2000 prizes
225 - 150 = 75
Five U2000 players scored three points, so they would get $15 each.

I believe this to be a “real world” example of the method. I’m sure both methods have their pros and cons. Seeing the two distributions after the fact and side by side, I would choose for this tournament the current method. The biggest drawback is that I can’t use two methods and choose the result I like best when I have to advertise variants in advance.

  • Enrique
20

For prize funds, I think, as others, you need to start place first, then class. If someone is eligible for more than one prize, what they receive needs to come out of the various prizes they are eligible for in proportion. This sacrifices complexity for a more level spread. Let me take Bill’s examples from the first post.

My solution says that the p1 and p2 are eligible for 1st and 2nd prize and so those two prizes clearly go into the top prize split. p3 is elgible to bring in both the 3rd place prize and the u2000 prize into this combined split. What p3 actually brings up should be done in proportion. 3rd place + u2000 prizes = $110. U2000 is $60 which is 54.54% of that $110. So 54.54% of the U2000 prize needs to move up and 46.46% of the 3rd place prize needs to be moved up (why the complicated math, why not just split the portion that moves up 50/50? - because this is fairest, if 3rd place had been just $1 and U2000 $50 it would be unfair to move 50% of each prize up). 54.54% of the U2000 prize of $60 is (rounded) $32.72 moving up, leaving what’s left of the U2000 prize as (60-32.72) $27.23. 46.46% of the 3rd place prize of $50 is moved up, that is $23.23, leaving 3rd place prize fund as (50-23.23) $27.77. In all ($32.72 + $23.23) $55.96 moved up as p3’s contribution to join the $300 already there. $355.96/3, or $118.65 each is divided among p1, p2, and p3. The remaining 3rd place prize fund of $27.77 is clearly awarded to p4, whereas the remaining U2000 prize fund of $23.23 is clearly awarded to p5.

Now I know that was a lot of extra math to move up just an additional 96 cents instead of splitting it down the middle and having half of each prize go up to the top pot. Unless a computer can be fed an algorithm to do the work, no one is going to do all that, as moving 50% of each prize is hard enough for a lot of people. Fortunately the 2 prizes involved here are similar ($50 vs $60) so even doing it wrong (moving half of each prize up instead) wouldn’t have cost more than $1, but I wanted to do the example purely.

Anyways, bottom line, when someone is eligible for more than one prize, moving a proportion of multiple eligible pots up instead of all of one pot up is BY FAR the more equitable way to split the prizes.