Distribute Prizes

Running Chess Tournaments
41

This really gets into a secondary area, the one I wanted to put on hold for a while, in which multiple players are tied for multiple prizes, but some of the players are ineligible for some of the prizes.

The original discussion was concerned only with the case where ONE player was eligible for multiple prizes, and what should be done with the remaining portion(s) of the remaining prize(s).

But, since you brought it up, here are some thoughts.

First, let’s take a simpler example:

Prizes:
1st: $200
2nd: $150
Under-1800: $100

Results:
1950 5.0
1900 4.5
1700 4.5
other players with 4.0 or less

Here the 1700 is eligible for the $100 prize, and also for half of the $150 prize. The 1900 is eligible for half of the $150.

The book method is to combine the two prizes and split them equally between the two players. The 1900 and the 1700 each get $125. This obeys the “limit one prize per player” rule because two players are splitting two prizes (the number of prizes in the pool does not exceed the number of players splitting the pool).

I think we can all agree (not just because it is the rule, but because it is right) that, indeed, these two players should split the $150+$100 in some way, and that no other player(s) should get a share of this $250.

The book method, however, awards part of an under-1800 prize to a player who is not under 1800. The 1900 and the 1700 end up with the same award. Yet, the organizer has declared (by having an under-1800 prize in the first place) that, under some circumstances, a player rated under 1800 may be entitled to prize money not available to a higher-rated player with the same score.

So a method more in line with the organizer’s intentions might be to divide the $250 unequally, with the 1700 getting more than the 1900.

The 1900 is obviously entitled to a minimum of $75, and the 1700 to a minimum of $100. This accounts for $175 of the $250. What should be done with the remaining $75?

If it is split equally, the 1900 would get $75 plus $37.50, for a total of $112.50. The 1700 would get $100 plus $37.50, or $137.50 total. This scheme awards the entire $250, while still recognizing the philosophy behind “under” (or class) prizes, namely, that class players are sometimes eligible for more money than higher-rated players with the same score.

Another option would be to split the excess proportionally, rather than equally. Doing it this way, the 1700 would receive 100 / 175 of the excess $75, or $42.86. The 1900 would receive 75 / 175 of the $75, or $32.14. Total award would be $142.86 for the 1700, and $107.14 for the 1900.

Either of these methods would, I believe, be better aligned with the philosophy of class prizes than is the current method.

Bill Smythe

42

OK, well you haven’t convinced me that the current rule is flawed. Perhaps it is, but you haven’t convinced me yet.

The 1900 has no claim to an u1800 prize (that’s why it’s called “u1800”).

Why wouldn’t the 1650 be eligible for the u1800 since the 1700 took 2nd place by outscoring him?

Perhaps, in my old age, retardation has reared it’s unfortunate head - I just don’t get it! I’m not opposed to suggesting rule changes, if they are indeed flawed, but how you think the 1650 is not supposed to be eligible for the prize is beyond my comprehension.

43

Right away this is more like the corollary case (multiple players tied for multiple prizes) rather than the case which started this conversation (one player eligible for multiple prizes). But here goes.

We have seven players tied for two prizes. In the case of one of the prizes, only one player is directly eligible for it.

Under the present rule, the $799 total is divided equally among the seven players.

Following the logic in my last post, we would divide the $799 total in some not-necessarily-equal way, with the under-2000 player possibly getting a little more than each of the other six.

But, unlike the previous (two-player) example, each of the seven is due the same minimum ($100). So the $799 in this case would still be divided equally among the seven.

If the under-2000 prize were $120 instead of $99, then things would be a little different. The total minima would be six times $100, plus $120, or $720. The total prize money involved would be $820. So, after awarding each player his minimum, the remaining $100 could be divided equally ($14.29 for each player) or proportionally (100/720 for each of the six, plus 120/720 for the seventh). The latter comes out to $13.89 for the six and $16.67 for the one.

So, depending which method (linear or proportional) you wanted to use, the divvy-up (in the case of the $120 under-2000 prize) would be as follows:

Linear:
$114.29 for each of the six
$134.29 for the one

Proportional:
$113.89 for each of the six
$136.67 for the one

I don’t agree with this at all. There are two prizes for seven players (number of prizes does not exceed the number of players) so under no circumstances would you award any part of the two combined prizes to anyone outside the group of seven.

Bill Smythe

44

Any time a $2 shift in the prize structure results in a $99 difference for each of two players, in my book, that’s a flaw. Prize-awarding algorithms should be continuous – small changes in independent variable X should result in only small changes in dependent variable Y.

And, don’t forget, it was this discontinuity (which I consider a flaw) that started the whole argument in the first place.

By the same token, the 1650 has no claim to a 1st-u1800 prize, either. Remember, it really is a “1st-u1800” prize, not just a “u1800” prize. Otherwise, every u1800 player in the tournament would be eligible for part of that prize, regardless of his score.

So, because of the “limit one prize per player” rule, we have some prize money left over. One or more players with no real claim to that money will end up getting it anyway, no matter which way you figure it.

Well, why wouldn’t the 1900 be eligible for 2nd overall since the 1700 took the u1800 prize by outscoring him? As I see it, it’s exactly the same thing.

Bill Smythe

45

Sorry, it’s been awhile since I’ve been on the boards, but I’ve been reading Smythe’s nuts and bolts of his idea with much enjoyment, providing rejoinders for any counterarguments both circumstantial and philosophical. That Bill really knows how to use his cerebellum. I say let’s invoke those rules lawyers, and get this tidied up, and shipped out to the 6th edition! Bill, do we have a final wording yet?

46

If the chess lawyers work on the 6th edition, could be over 6,000 pages.

47

Yes, and that will also mean that every chess club will have to hire another lawyer to interpret the darn book. :slight_smile:

48

OK, I’ve revived this thread. Welcome to those coming over from the Prize Calculation thread. Look especially at pages 2 and 3.

Bill Smythe