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Explaning the New League Points System (S6 and on)
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Barfo  





Joined: 10 Oct 2006
Posts: 2596

PostPosted: Sun Aug 26, 2007 3:59 am    Post subject: Explaning the New League Points System (S6 and on) Reply with quote

Hey just thought id drop this little post in so that people arent confused when they see the new points system.

What i wanted to do was make a system that would scale better with different number of people, and particularly so that the same numerb of points were equally possible no matter how many people there were. So what i did was create a normalized scoring system, so that it could scale based on any number of people. So points are based on the percentile you finish, so finishing first is always worth the same number of points, finishing exactly in the middle also, and any other place you can think of. Your normalized place (nP) is just your place (X) minus 1 divided by the total number of people (T) subtracted form 1 (aka percentile) nP = 1 - ( (X-1)/T ). As you can see finishing first is = 1, while finishing last will be close to zero, but not quite zero depending on how many people there are - so everybody who turns in a score gets at least some points.

From there i needed to just make a funciton that gave a number of points based on your nP that would be pretty similar to the old system, for congruency. So taking 30 people as the ideal participation in the old formula (i liked that the best), i plotted up what the total number of points was for each nP, normalizing those points by the total number of points (finishing in first). Then i just played around until i found a polynomial that fit that really nicely:


the Y axis of that chart is normalize points, the X axis is normalized place, as you can see it fits really nicely.

Of course 1st place isnt goign to be worth 1 point so for the real scoring system it just multiplies that scoring by 100, so that finishing first in a song will always give 100 points. So the max possible score for one week is 400. Also all points are rounded to two decimals (rounded up) to make later calculations easier.

For math nuts, the final formula is:

F(x)= 62.5 * x + 7.5 * x^4 + 30 * x^7

a nice 7th order polynomial that gives the same linear behaviour for the first half o thte chart but also a really steep points growth near the top.
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dragonmas682  





Joined: 05 Apr 2007
Posts: 17

PostPosted: Sun Aug 26, 2007 4:05 am    Post subject: Reply with quote

im a bit confused, never really understood the old version either (this is my first season, which so far seems good to start out with because everything is changing) but i'll just keep trying to get the best scores i can ;)
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muna  





Joined: 04 Jun 2007
Posts: 2929
Location: South Florida

PostPosted: Sun Aug 26, 2007 4:11 am    Post subject: Reply with quote

I still don't rally get it. Does this meant that if there are 3 people in the league (which I know is impossible) ant they are like this.

Total score-

1. HellAshes (101348)
2. Muna (100)
3.JCirri (50) jk

that I woud get 0.5 points, JC would get none and HA would get 1?
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TarLaPaN  





Joined: 11 Aug 2007
Posts: 148
Location: SoutH CAli

PostPosted: Sun Aug 26, 2007 4:12 am    Post subject: Reply with quote

to much math -_-
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Barbaloot  





Joined: 02 Feb 2007
Posts: 1583

PostPosted: Sun Aug 26, 2007 4:21 am    Post subject: Reply with quote

muna wrote:
I still don't rally get it. Does this meant that if there are 3 people in the league (which I know is impossible) ant they are like this.

Total score-

1. HellAshes (101348)
2. Muna (100)
3.JCirri (50) jk

that I woud get 0.5 points, JC would get none and HA would get 1?


It looks like HellAshes would get 100, Muna would get about 44, and JCirri would get about 20 in that scenario. (I just looked at the graph; I didn't actually plug any numbers into the polynomial.)

If there were a tie at first, would both players get 100, or would their normalized place be the average of normalized first and second places?
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Barfo  





Joined: 10 Oct 2006
Posts: 2596

PostPosted: Sun Aug 26, 2007 4:40 am    Post subject: Reply with quote

Barbaloot wrote:
If there were a tie at first, would both players get 100, or would their normalized place be the average of normalized first and second places?

Ties (at any place) get the average of all the palces that are involved int eh tie. So if 4 people tie for first, then they all get the average of 1st-4th place points. Thats not actually a change, i used to do it that waybefore (but rounded sort of funny) but sort of on the sly (and i had to do it manually, so elx and such maybe didnt do it that way).
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RocketMan  





Joined: 01 Jan 2007
Posts: 1189
Location: Rapid City, SD

PostPosted: Sun Aug 26, 2007 4:43 am    Post subject: Reply with quote

Just my idea, as far as scoring goes...
Why not just start the winner of the song at, say 100 points, no matter how many people are entered. Then -1 for each place down. ...or you could -2 for the first ten, then -1 for the rest, whatever. To the best of my knowledge there has never been more than 100 people in one division. Hey, for anything, you could start at 50...then -1.
I just think it would be a lot easier to figure out, it would keep the overall rank a little closer, and overall it would make more sense (or at least it does to me).
Anyway...thats just my 2 cents...take it for what its worth.

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PDPablo  





Joined: 04 Aug 2007
Posts: 27
Location: Las Vegas, NV

PostPosted: Sun Aug 26, 2007 4:44 am    Post subject: Reply with quote

muna wrote:
I still don't rally get it. Does this meant that if there are 3 people in the league (which I know is impossible) ant they are like this.

Total score-

1. HellAshes (101348)
2. Muna (100)
3.JCirri (50) jk

that I woud get 0.5 points, JC would get none and HA would get 1?


w/ this new system, the points aren't set in stone since it's based on the number of ppl in the league...
basically "x" from the formula is a fraction (how many ppl you beat/tied w/ divided by the number of ppl) so you're almost always getting a decimal answer...
lengthy math formulas aside, this is what the points would be in that example:

3rd = 20.9 (JC)
2nd = 44.9 (Muna)
1st = 100 (HA)

but the only reason for the huge gap between 1st & 2nd is b/c there's so few ppl in the league.
in a larger-sized league (say, 100 ppl) finishing 2nd would give you 97.04 points so it's less of an issue in bigger leagues, though it still pays to come in first.

EDIT: at least Barbaloot's answer agrees w/ me...
maybe my math hasn't been horribly skewed over the summer after all
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mamlfj  





Joined: 27 Feb 2007
Posts: 77
Location: São Paulo, Brasil

PostPosted: Sun Aug 26, 2007 4:45 am    Post subject: Reply with quote

If I'm understanding the new point system correctly, you could be out of the playoff by a 0.01 difference, is that it?

Apart from that it's very intersting new way, lots of points to get first and not so much to the last one, this will make for more challenging leagues I think, and much more humilliation for me when I see the leader is 1000+ points away
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Barbaloot  





Joined: 02 Feb 2007
Posts: 1583

PostPosted: Sun Aug 26, 2007 4:45 am    Post subject: Reply with quote

RocketMan wrote:
Just my idea, as far as scoring goes...
Why not just start the winner of the song at, say 100 points, no matter how many people are entered. Then -1 for each place down. ...or you could -2 for the first ten, then -1 for the rest, whatever. To the best of my knowledge there has never been more than 100 people in one division. Hey, for anything, you could start at 50...then -1.
I just think it would be a lot easier to figure out, it would keep the overall rank a little closer, and overall it would make more sense (or at least it does to me).
Anyway...thats just my 2 cents...take it for what its worth.


You don't want the last place score (or really any scores in the bottom half) to be such a huge percentage of the first place score. Under your system, if there are 20 players, the first place player gets 100 and the last place player gets 81.

Also, the difference between, for example, first and second, is much more significant than the difference between, say, 18th and 19th, and this should be reflected in the number of points (which Barfo's system does).

[edit] Wow, double ninja'd.
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Matt276  





Joined: 05 Sep 2006
Posts: 1242
Location: Princeton, NJ

PostPosted: Sun Aug 26, 2007 5:23 am    Post subject: Reply with quote

Nice job barfo, that is a pretty nice polynomial - I have no idea how you came up with that, but whatever, it definitely does the job.

RocketMan wrote:
Just my idea, as far as scoring goes...
Why not just start the winner of the song at, say 100 points, no matter how many people are entered. Then -1 for each place down. ...or you could -2 for the first ten, then -1 for the rest, whatever. To the best of my knowledge there has never been more than 100 people in one division. Hey, for anything, you could start at 50...then -1.
I just think it would be a lot easier to figure out, it would keep the overall rank a little closer, and overall it would make more sense (or at least it does to me).
Anyway...thats just my 2 cents...take it for what its worth.


The system you're suggesting is very similar to the system the leagues have used before. The problem with the old system is that it had to be slightly adapted for each different number of players. Your system has the same problem - what if there are 101 players? You would need to adjust for different numbers of players. Barfo's system works for any number of players.
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AVG00  





Joined: 07 Jul 2007
Posts: 42

PostPosted: Sun Aug 26, 2007 5:36 am    Post subject: Reply with quote

I'm just wondering, how long did it take you to create that formula?
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McDog3  





Joined: 25 Oct 2006
Posts: 466
Location: St. Peter, MN....in my dorm

PostPosted: Sun Aug 26, 2007 7:04 am    Post subject: Reply with quote

I enjoy math and all *cough*nerd*cough*, but i'm glad I don't have to worry about using the point system.....and this should make it more intense for those top players because doing even just a little better is all the difference, and the lower players will be constantly near each other because ot the small pt differences. Awesome work!
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schmegery  





Joined: 19 Jan 2007
Posts: 103
Location: Hampton, VA

PostPosted: Sun Aug 26, 2007 9:38 pm    Post subject: Reply with quote

How exactly did you come up with this formula anyway? Random trial and error or other methods?
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Barfo  





Joined: 10 Oct 2006
Posts: 2596

PostPosted: Mon Aug 27, 2007 7:47 am    Post subject: Reply with quote

schmegery wrote:
How exactly did you come up with this formula anyway? Random trial and error or other methods?

Well i mean i just took a league of 30 people in the old method and calculated up the scores and then normalized the x and y axes to get the red line. And so i knew right away that i wanted a polynomial function (just by inspection its obvious that thats whats going to fit it), and you need an x^1 term due ot the linear nature of the first 2/3rd of the old function, and i figured two higher order terms was enough to get the desired other behaviour so i drew up the basic form:

f(x) = Ax + Bx^y + Cx^z.

Right away its obvious that if you want f(1) = 1, then A + B + C = 1, and since the middle term is going to be smaller, i just wrote it as:

f(x) = Ax + (1-A-B)x^y + Bx^z

then what i did was just plug in various values and plot them in excel in the chart like you see above until i got enough agreement. Obviously i started by getting the linear part ot match up, you want A to be only slightly less than the slope of the linear part (since near 0 the funciton behaviour is obviously dominated by the first order term), and also concomitant with this its obvious y and z need to be at least a few integers above 1 to get a decent match in the linear secton. THen i tried to fit the third term in order to get a decnt fit to the behaviour near 1, using B= 1-A with the A form before. i tried basiclaly z=5 thru 8 and 7 looked the best, with a whole family of z=7 you can fit both ends of the line, with varying levels of off in the middle. Obviously hte last step was to take y= a middle value between 1 and z, in order to bring up the middle part of the equation. once i setlted on y and z, i just played around with it a lot to get the match i liked the best. There are porbably even better matches if i had bothered to do like a linear regression fit, but the end result was prety damn good and probably within 10% variance from whatever the eventual best fit woul dbe so i just settled at doing it the sloppy, imprecise way.
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