More examples from Bill using the proportionate pot system.
p1, a 2100, clearly receives 1st place. p2 is eligible for both pots and his prize should come from both, to have the most equitible distribution. The 2 pots combine to equal $200 - with a slight mathematical weight to the 2nd place prize over the U1800 prize. I showed how the percentages worked in the post above, so I will merely estimate here. Of the $101 2nd place prize approximately 50.5% moves up which is, say, around $50.55, leaving the rest for others. Of the $99 U1800 prize, 49.5% or so moves up, which is around $49.45. So, in all, ($50.55 + $49.45) $100 moves up which is what p2 receives. p3, next in line, is only eligible for the remaining 2nd place prize and receives that which is ($101 - 50.55) $50.45. p4 is next in line and is eligible for what’s left of the last remaining prize of U1800, which is ($99 - $49.45) $49.55.
Here is where my system looks like a genious - switching around $2 in the prize fund makes practically 0 difference in the prize fund distribution, as it should be, whereas in the other systems violent changes results based on which order you award the prizes often leaving some people out in the cold entirely. P2 would get his highest eligble prize, the $101, but this is taken proportionately from the 2nd place and U1800 prizes.
The proportionate system says that the players over 2000 get some split of 1st and 2nd and that the player under 2000 who also tied with them gets the highest prize he is due but at a proportion of each pot. This player must earn $80 total which is the highest pot for which he is solely eligible. His share of the overall pot is $300/6 or $50. His share of the U2000 pot is an undivided $80. His shares combine to $130. The $80 prize is 61.53% of his pot and the $50 prize is the remaining 38.47%. These percentages tell us how much need to come out of each prize to best make up the $80 he is due. 61.53% was the percentage of the $80 prize that he is due that needs to come out of the U2000 prize. This total is $49.22. The remaining part of the $80 he is due, which is 30.78, comes out of the 1st-2nd prize. So 1st-2nd prize is now ($300 - $30.78) $269.22, which should be divided equally between the five highest rated players who would each receive $53.844.
There is still ($80-$49.22) $30.78 remaining in the U2000 1st prize and an unawarded U2000 2nd prize left of $60. The 1950 is next in line to receive prizes, and he is eligible for both, but since they are the same category of prizes, there is no need to split them proportionately. He would receive the higher prize of $60 and the 1920 player would receive the $30.78 as the next highest eligible scorer with just that one prize remaining.
That was a lot weirder than the first two. Anyways, checking progress here: does anyone think I am remotely on the right track?
I apologize - I meant “obviously correct in all situations to anyone who has read and understood the rulebook - but may perhaps need to double check the details”. A properly designed prize structure eliminates the need to check the details.
As soon as you introduce the idea of proportional prize distribution, all bets are off.
This is not about details - this is about changing fundamental concepts of prize distribution. Once you open the door to that idea, the sky’s the limit. Fun to discuss - but probably a serious non-starter of an idea. I’d put it in the same class as “why isn’t USCF run more like MENSA?”
On a historical note, am I correct in my assumption that the current system of splitting prize funds was started so no one needed to calculate tiebreaks? Spread the prize money love? This would make sense prior to laptops running pairings and calculating distributions, but I don’t have any rulebooks prior to 5th edition so not sure how far back the distribution system goes.
Not really. A consensus was formed at least 30 years ago that using tiebreaks for cash prizes was unacceptable. The standardization of prize fund distribution methods came later.
This can be addressed by adjusting the prize structure to award more dollars for place prizes and less for class prizes. Doing this in combination with the distribution method proposed by Smythe still accomplishes the stated intent:
The Smythe method is simple relative to alternative proposals to reduce discontinuity and other perceived inequities. More class players will be able to understand why they did or did not share in their class prize, which is a win for both players and directors. I agree with Bill that this approach is an improvement.
There’s probably an Arrow impossibility theorem floating around here. I think you’re always going to have potential problems with discontinuities in the money flowing down to lower score groups. If you have $x for U2200 and $x for U2000 and a player is eligible for both, epsilon changes to either prize will shift the proportions from all coming out of one to all coming out of the other. So both continuity and monotonicity are out the window.
Technically, the current USCF distribution system solves a sequence of optimization problems. Starting with the highest score group, maximize the amount awarded to that group (though not necessarily in equal amounts) subject to (1) the total shares across players of any prize is no more than 1.0, (2) the total shares across prizes for each players is no more than 1.0 and (3) in case of multiple ways to solve the maximization given (1) and (2), take place prizes first and class prizes from highest to lowest. Take whatever’s left and repeat for the next score group; continue until the money is gone.
It sounds as if almost everyone agrees on constraints (1) and (2). I think most people would agree in principle with the notion that the payout to the highest score group should be maximized. The “problems” all arise in what flows down to the lower score groups. But as long as you stick with constraints (1) and (2), you can always construct problematic situations. And a proposal that discards the maximization at the highest score group (see John Hillery’s example where there are three prizes and three players in the top score group) and still doesn’t really fix the problems with the lower score groups doesn’t seem to be a step forward.
Mr. Doan, just the person I was hoping was watching this thread. I would claim that the proportional prize system I have been espousing has been by far the fairest with the most continuity. The problem is that the time-consuming math involved is a real turn-off, almost to the point of impracticality. Is there any way from a programmer’s perspective to fix this? I suspect there are just too many variables to just plug in all the prizes and amounts and have the program spit out the correct prize distributions, using any algorithm, much less the proportional system. Still, it doesn’t hurt to check. Peace.