Life In 19x19

hi, i run a small whole-year competition (Northern Bohemia Cup - excuse my poor English translation of the page) in my city, consisting of 4 qualification tournaments (swiss tournaments with reduced handicap) followed by a two-player final. players earn qualification points based on their placement in each tournament and two with most points at the end of a season qualify for final which decide winner of the Cup.
my dilemma is what scoring system to use. this year it was simply from the first place to eighth to get 10, 8, 6, 5, 4, 3, 2, 1 point and it worked quite ok. but it has at least two disadvantages: 1stly - players below 8th place don't get any points, no matter if they were 9th or last; and 2ndly - they get the same amount of points if there were 10 participants in the tournament or if there were 20 of them, while the more people participate, the more should be the place valuable.
so i proposed another system for the following year: every player gets 1 point, top 80% (rounded down) get another point, top 64% (=0.8^2) another, top 51% (0.8^3) another and so on... until 0.8^n falls under 1. for example, for 10 participants it means 11, 8, 6, 5, 4, 3, 2, 2, 1, 1 points, for 20 then 14, 11, 9, 8, 7, 6, 5, 5, 4, 4, 3, 3, 2, 2, 2, 2, 1, 1, 1, 1.
this looks surely better than current system, but i am not 100% satisfied with points for top places, as i think for first 3-5 positions the number of points should grow faster, but cant come up with an easy solution. i also tried various functions (quadratic, logaritmic) based on number of participants to dynamicaly generate number of points for each player, but none of them was really satisfying.

so i want to ask for your opinion on my qualification points system as proposed above and also for suggestions for any further improvement (while keeping the system simple enough so any ordinary player could understand it and could determine points for each place only with paper, pencil and calculator)

1stly - players below 8th place don't get any points, no matter if they were 9th or last;

did any 8th or lower place finisher, in a single event, ever got enough points in the other 3 tournaments to be close to the two-player final?

they get the same amount of points if there were 10 participants in the tournament or if there were 20 of them, while the more people participate, the more should be the place valuable.

it depends on the level of the player more than on the number of players.
I would make maybe make a system that depends on the number of dan degrees.

i also tried various functions (quadratic, logaritmic)

Why should it follow a mathematical function?


I did not look into it in detail but...
It might be an idea is to use a McMahon system (which basically is a variation of Swiss) and use the MMS points.
adding the MMS points of the 4 tournaments together will decide who gets to play the two-player final.
This way everyone gets points, and you can set a bar at a % of the total players to have X% above the bar for each event.
(as an extra advantage you also get tie-breakers if you need them.)

freegame wrote:Why should it follow a mathematical function?

Because it's a point system, and points are given by numbers. Perhaps you meant "a simple mathematical function"?

...sorry, I couldn't help myself.

freegame wrote:did any 8th or lower place finisher, in a single event, ever got enough points in the other 3 tournaments to be close to the two-player final?

i dont have enough evidence for a real statistics, we played only 3 tournaments of the first season so far, but current player #4 in overall standings has 1 first and 1 tenth place. on the other hand, i get your point, my main reason for "points for all" scheme was that it should be more motivating for the participants to get at least some points for their effort even if they couldnt reach top positions. it is not so important property of the system

freegame wrote:it depends on the level of the player more than on the number of players.
I would make maybe make a system that depends on the number of dan degrees.

true, this would be more precise and even more precise could be something like sum_of_participants_ranks, but i believe simple number of participants can measure level of tournament quite finely, especially with handicap swiss.

freegame wrote:Why should it follow a mathematical function?

i analysed several point systems (see below) before i started the event and they clearly share some characteristics, so i thought i could describe them by a mathematical function, which could be used afterwards as a base for the dynamic point system


thank you for your ideas, the proposal with MacMahon looks interesting

to be honest, when i compared standings from my current system with standings from my proposed system, they both give similar results as if i would simply use number of wins (= number of points scored in each tournament) as a qualification points, so maybe i shouldnt complicate it so much


attachment, several point systems from several competitions:

hyperpape wrote:

freegame wrote:Why should it follow a mathematical function?

Because it's a point system, and points are given by numbers. Perhaps you meant "a simple mathematical function"?

...sorry, I couldn't help myself.

While you do have a point I think you are not correct either.
If you would just award 1 point for the winner and nothing else this would be a point system that is theoretical usable (though not a good one) and it would not follow any function since it has no domain.
If a round robin system was used the winner would be based on just nr. of wins. This would give points to everyone, (though take way to many rounds) and it would also not follow a mathematical function because it consists of only a parameter.

In my case I meant that he should maybe not focus on trying to find an arbitrary function, but make one using dependent variables from the tournament results.

My proposed system (adding up McMahon scores) is not based on an arbitrary mathematical function but on number of wins and entry score (based on rank).
If this is used to determine the winner for a single event, why not use it to determine the winner over multiple events?

Anyway, I'm no real mathematician (focus on precise definition), but an engineer (focus on applicability).