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Amun Re Leagues - Scoring System
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Wildfire2099



Joined: 20 Aug 07
Posts: 122


PostPosted: Wed Sep 30, 2009 11:17 am    Post subject: Reply with quote

Looking a little closer, I think it's just the top and bottom that's of concern. In the 4 player, for instance, yoseph is 36 points ahead of the last person in div 1, which is the maximum you could lose (if you finish last every game).. that's a pretty big gap after just 4 seasons... the same at the bottom, where Adriaan and ats could win every game and perhaps still be in the bottom division.

Perhaps an upper and/or lower limit on points carried over would work? It's probably premature to change anything, but maybe some modelling would be worthwhile.
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Alexfrog



Joined: 26 Oct 05
Posts: 77


PostPosted: Wed Sep 30, 2009 2:54 pm    Post subject: Reply with quote

I think its great as it is. It allows climbing to your correct position more quickly (it was annoying to start at the bottom, 5-0 a division and barely move up into another division that you are goign to crush again - and its not fair to the other people in that division either).

ALso, if someoen has earned a ranking at the top by dominating that division, they deserve to stay there even with one bad season.

If Tiger Woods has a bad golf tournament, he doesnt fall of the Tour and have to requalify. Similarly, the winner of divison 1 should have enough leeway the next month that doing poorly wont necessrily kick them out.
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Knave



Joined: 28 Jun 08
Posts: 258


PostPosted: Wed Sep 30, 2009 7:28 pm    Post subject: Reply with quote

I wonder if Gaditus is referring to me... I had a terrible season in the 4-player league, but I'm still holding on to my division like grim death... mostly due to some built-up points.

There is a lot of churn in the top division of the 3-player league, only 3 of us were able to hang in there, and powermorph is hardly a long-time resident (though he did play very very well and probably deserved to win). Domster did not have that bad of a season, and he is dropping down a division regardless. Anyone can get into the top division, and to stay there all you have to do is win some games. I really do not think there is an issue.

A caveat... I no longer play in the 5-player league, so things might be a little more fossilized over there, I would not know.
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mdp



Joined: 14 Nov 05
Posts: 22

Location: Wichita

PostPosted: Thu Feb 25, 2010 3:50 pm    Post subject: Re: Amun Re Leagues - Scoring System Reply with quote

Gaditus wrote:

Points will be awarded for positions in games:

5 Player 1st:20 2nd:4 3rd:-4 4th:-8 5th:-12
4 Player 1st:12 2nd:0 3rd:-4 4th:-8
3 Player 1st:12 2nd:-3 3rd:-9

Points will also be awarded for finishing first in a division. The number of points awarded will be equal to the number of players in that division.

The points will be carried forward to future seasons but will be reduced by 20% so that more recent results will have more weight.


I think these quotes account for all of the points awarded or taken away from players in the leagues. The issue I'm seeing (I'll call it "point decay") is that over time, the overall trend in the league will be for the middle division to settle at zero points, and for divisions below that one to be negative.

What I mean is that every game awards a "net" of zero points. A small number of points are awared to one person for winning a division, but a large (relatively) number of points are deducted FROM EVERYBODY. The result is that, over time, scores will gradually decrease until the deductions equal the additions. Since the additions consist soley of the bracket winners bonus, scores will approach that bonus (6 to 8 points).

The natural distribution between brackets will mean that the upper divisions will probably settle in at a hundred points or so, and the lower divisions will settle in at minus one hundred or so.

To demonstrate this effect, I've gone back to season 5 of the 5 player league (first season that this point distribution was in place for) and taken the average points of each division after the season ends. The trend is for this average score to decrease.

Division 1

Season 5: 644.375
Season 6: 624.375
Season 7: 621.625

Division 2

Season 5: 619.875
Season 6: 596.5
Season 7: 586.625

Division 3

Season 5: 599.7778
Season 6: 585.25
Season 7: 570.25

Division 4

Season 5: 574.6667
Season 6: 566.125
Season 7: 559.75 (only 4 games finished so far)

Division 5

Season 5: 558.3333
Season 6: 547.625
Season 7: 532.375

The remaining lower divisions are not very complete in Season 7.

So far, without exception the average is going down.

Now, it's only going down by an average of 2.48%, which was confusing to me until I looked at my own scoring history.

I ended Season 5 with 611 points. I began Season 6 with 588 (a decay of 3.8%). I ended Season 6 with 560 points. I began Season 7 with 548 points (a decay of 2.1%). For an overall decay rate of 2.95%. Between Seasons 5 and 6 I lost 23 points. Between seasons 6 and 7 I lost 12. I confess I don't know how this number is being calculated.

So, I'm not quite sure what's happening here. It doesn't look like 20% of our points are being removed between seasons. More like 2.5%. But that 2.5% is dragging down the average division scores by the same amount. At this rate it'll take quite awhile, but eventually we'll settle out around zero for the league average score.
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Gaditus



Joined: 05 Feb 07
Posts: 1924

Location: Canterbury, UK

PostPosted: Sun Feb 28, 2010 5:29 am    Post subject: Reply with quote

The reason your scores only seem to have decayed by a small percentage is that the 'underlying' score is really 500 less than that shown. 60 x .8 = 48 for example. The 500 is added for formatting reasons (all scores are now 3 digits so the tables line up!).

The exact mechanics of the scoring method are not as important as the effect - which is how players move from division to division. At the moment it is working OK, but I am monitoring it to see if the top (and to a lesser extent bottom) division(s) do not change enough.
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