WinTD has a procedure built in for computing monetary prize distributions. One thing which I have not yet incorporated into this is the ability to provide person-by-person upper bounds on winnings, in part, because it’s not clear that there’s any clear consensus on how to handle that. There are three ways I can think of to handle this (all this is assuming that the players with limits are only eligible for overall prizes):
Method I – find point in prize distribution immediately at or below limit. Distribute everything from that point up to ties through that location by relatively standard means. (This is simplest when there is one prize which exactly matches the limit and only one player might conceivably receive it as their limit prize).
Method II – calculate normally from top down. Take excess winnings from the limited player and create extra prize from it for lower groups.
Method III – calculate normally from top down. Take excess winnings from the limited player and increase prizes at or below his score group proportionately.
There also is Method IV - calculate normally and the organizer keeps the excess, but I’m not sure that would go over well.
I show two cases of how I would see these applying to a distribution with the following prizes:
4000
2000
1000
500
300
100
In the first set of three, the limited player (marked with unr) was the clear winner. In the second set, he is clear 2nd. This looks at several different limit values—whatever is shown in his row.
My preference is Method III though that’s really close to impossible to do without a computer. Method I is the simplest if you happen to have a prize available that is exactly correct, but I’m puzzling over how to describe it in the general situation if you don’t. Method II is always fairly simple to execute but has very weird behavior, note how the 3rd place finisher gets the same as 2nd once the limit gets to $2000.
The CCA rule is “Balance goes to next player(s) in line”, which I think corresponds to your Method I although I haven’t looked at it in detail. Steve Immitt and I proposed an ADM at the 2011 Delegates Meeting which didn’t make it out of the Rules Workshop.
payout table with a two way tie for 1st, one player limited to $2000. “Balanced goes to the next player” sounds like either $9000 to the first player or $7000 to the third, neither of which sounds correct. Method I is sort of like drifting him down into the score group where his limit is located.
There is $11,000 in prize money in the top score group, but a player can’t win more than $6,000 because of the one prize per player rule (as I interpret it; not everyone sees it that way). Therefore of the two players tied for 1st, the rated player gets $6,000 and the unrated player gets $2,000, leaving $3,000 to go down into the next score group. Assuming one player has the second-highest score he has the $4,000 third prize plus $3,000 coming down for a total of $7,000, but can’t win more than $5,000 (clear second). He wins $5,000, with the remaining $2,000 moving down to the next player(s) in line. I think it amounts to the same thing as your Method I, but I don’t have time to look at it in detail right now.
Have you looked at rule 32C6 in the rulebook changes document? I think it supports Method I, and it certainly disallows Method IV, but it’s not entirely clear. Steve and I tried to make the rule more precise in 2011 but I think our proposal was too complex to gain support from the other delegates. Bill Goichberg’s description of how the prizes should be awarded was the same as your Method I, as I recall.
Thanks. That’s a clearer way of describing Method I, and yes, it appears that the two are identical. I assumed it was discussed somewhere, but didn’t hit the right search phrase.
Prize structure and prize restrictions are posted at http://www.chesstour.com/wo12.htm. The prize payout was about 85.4%. Let me know if you find any mistakes! This might be a good test case for WinTD except that I used SwissSys to pair the section. I didn’t use SwissSys to work out the prizes.
32C4. Based-on prizes. In tournaments in which prizes are based on entries, if the actual turnout is smaller than the based on turnout, the following rules apply:
32C4a. Proportional payout. Each prize must be paid at least in proportion to the turnout.
32C4b. 50% minimum. If the total advertised prize fund is greater than $500 (all sections combined), at least 50% of each advertised prize must be paid.
32C4c. Multiple-section tournaments. If separate based-on goals are announced for different sections, then the proportion paid in each section (32C4a) is treated separately. If a common based-on goal is announced for multiple sections, then the proportion paid in these sections is considered together. In either case, 32C4b also applies.
It doesn’t seem to specifically tell us whether a $100 limit on the amount an unrated could win would be changed to a $50 limit if a half of the based-on number showed up. I would tend to do that myself generalizing on 32C4a.
I would concur other than slight rounding differences on the prize fund.
I think perhaps a simpler way to describe it is to think of floating the players down rather than cascading the prizes. Suppose we look at the original prize distribution:
We start with the two 7.5’s who are limited to $1500. If you look at the top two prizes, both are too high, so we now act like they have 7.0 (but with an asterisk for dealing with their prize limit). With them added in, the "7.0"s would bring in 5000, 2500, 1200, 1200(U1100) and 1000, plus there’s now a $2000 limit player. Because this has enough prizes at or below their limit, we can handle all the limit players. The $1500’s get theirs first (because they are from the higher group), leaving $7700. Average is >$2000, so we give the $2000 his limit leaving $5700 for the other two to split, so $2850 each.
Suppose instead that the 7.5’s are limited at $500. They’re too high for top two prizes. They’re also too high for the top five so we tentatively drop them into the 6.5’s. The 7.0’s bring in 5000, 2500, 1200. The 1200 is below the $2000 limit. Average is above $2000 so the $2000 takes his, leaving $6700, with a two way split of $3350 each. The two 7.5’s plus the five actual 6.5’s now bring in 1200(U1100), 1000, 800, 700, 600, 600(U1100), 500.
We need two $500 or less prizes and don’t have them, so we’ll keep dropping the 7.5’s. The five natural 6.5’s will take the first four plus the 600 under money rather than the 600 overall. Since most are U1100, there’s no advantage to splitting them out, so you get $3300/5=$660 each. Now we’re down to the 6.0’s. We have left 600, 500, 400, 300. Obviously, we now have low enough values for the limits. We give them each $500, leaving a $800 split for the other 9.
As far as I know, all the CCA directors do it the other way, using the advertised limit as the actual limit rather than reducing it. Aside from any philosophical questions about how the rules should be interpreted I think it’s better from a customer relations point of view.