Is this a Probabilities Question?

[EasilyFound]

If one is devising a point system for a poker league, is there an objective way to comparatively value winning tournaments of different sizes?

Let's say you give 100 points for winning a 10 player tournament. Must winning a 20 player tournament have a value a certain value compared to 100?

For instance, I came across a formula that gave 101 points for winning a 9 player tournament and 150 points for winning a 20 player tournament.

Is there an objective measure to compare those two achievements? Is winning a 20 player tournmanet only 50% more difficult than winning a 10 player tournament?

Is this a probability question?

Good lord, I hope I've explained the question well enough.

Thanks for your time.

[AaronBrown]

It's twice as hard to win a 20 player tournament as a 10 player tournament, all other things being equal. Therefore, it should get twice as many points.

My guess is the formula you have also gives points for coming in below first place, and goes deeper for larger tournaments. As long as the total number of points is proportional to the number of players, the system makes some sense.

For example, suppose you gave 101 points for 1st in a 9 player tournament, and 70 points for 2nd. That's 171 total points, or 18 per original player. You should then give 360 points for a 20 player tournament. You might divide those up 150 for 1st, 100 for 2nd, 60 for 3rd, 35 for 4th and 15 for 5th.

There's no obvious rule for how to divide up points among finishers, although Fibonacci rules are pleasing (each place earns the sum of the points of the next two places; like 180, 105 ,65, 40, 25, 15, 10 for seven places).

[EasilyFound]

So will it also be three times as hard to win a 30 player tourney? ANd 50% harder to win a tourney of 15 players?

So, if we start with awarding points 100/60/40/20 in a ten player tourney, follow Fibonacci rules, and keep the total number of points proportional to the total number of players, we'll have a system that makes some sense? That is all that we want.

[EasilyFound]

As I crunch some numbers, I see that following the Fibonacci rule, and keeping total points proportional to total number of players, nobody below 4th place will ever get points. As the number of tourney players increases, I think I'd want a point system that rewards more than the top four players, and to do that, the points for the first four places would have to be reduced.

[AaronBrown]

Yes, keeping points proportional to number of players and using Fibonacci shares makes sense.

To award more places (and I agree with you that's a good idea) start your series smaller. Say you want to give points for 40% of the places. You just take that many Fibonacci numbers.

So if you want 8 players to get points (20 player tournament), your payoffs will be proportional to 1, 2, 3, 5, 8, 13, 21, 34. That adds up to 87. If you want 18 points per original player (that's arbitrary, you could use any number you wanted), you need to scale that up to 360. 360/87 is about 4, so you could start with 4, 8, 12, 20, 32, 52, 84 and 136. That adds up to 348, so you have 12 extra points which you could ignore, or add to first place, or distribute somehow.

It may sound complicated, but with a little Excel trial and error, you should be able to come up with point distributions for all tournament sizes from 2 to 10,000. You only have to do it once, then make that the official list. You can use round numbers if you want, or stick to strict mathematics.

[EasilyFound]

Thanks.