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Mathematical proof that ranks cannot reach 1000

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blutch
blutch
Posts: 1,089
05:14 Sat 13 Dec 08 (GMT)  [Link]  
I've always wanted to proof formally that the ranks are guaranteed to never reach 1000. That's why I decided to make this mathematical proof.

It's important to note, though, that as stated in the document's introduction, this focuses only on the mathematical side of the ranking algorithm, and doesn't take into account the possible rounding errors due to computer usage.

I've never written any mathematical stuff in English, so feel free to correct any notation/terminology error I could have done.

Also, if you find any flaw in my proof, that's even more welcome!

I've uploaded it as a PDF file, you can download it from the following link:
http://www.flyupload.com/?fid=593416216

Hope you enjoy it
... and that I made it understandable for most people!
Deleted User
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05:21 Sat 13 Dec 08 (GMT)  [Link]  
I don't think many will understand it martin

Nice work there, can't see anything wrong with it, took a few min to read through though lol.

blutch
blutch
Posts: 1,089
05:24 Sat 13 Dec 08 (GMT)  [Link]  
damee said:
I don't think many will understand it martin

Well all maths used in the proof are only of secondary school level, so I suppose most people above 15-16 should be able to understand it.

Edited at 13:24 Sat 13/12/08 (GMT)
Deleted User
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05:30 Sat 13 Dec 08 (GMT)  [Link]  
The quadratic yeah but some of the sign's are of A level work, but people should get the jist of it.
Deleted User
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05:37 Sat 13 Dec 08 (GMT)  [Link]  
i get it nice work must of taken some time
ste_efc
ste_efc
Posts: 2,535
06:48 Sat 13 Dec 08 (GMT)  [Link]  
Nice work Martin
Deleted User
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08:14 Sat 13 Dec 08 (GMT)  [Link]  
Great work blutch! As to finding any errors in your prof, I have spotted a slight one - but not by you by me . I'll be off to fix my Ranking Calculater to inprove its accuracy ahem.

blutch
blutch
Posts: 1,089
03:01 Mon 15 Dec 08 (GMT)  [Link]  
Thanks for the feedback.

Dave, just out of curiosity, what had you forgotten?
Deleted User
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02:57 Tue 16 Dec 08 (GMT)  [Link]  
blutch said:
Thanks for the feedback.

Dave, just out of curiosity, what had you forgotten?


Not so much forgotton, more of a case of misinterpretation:

From Edge Modification Explanation said:

...
The actual amount is linear, at 900 points you lose 0%; at 950 points you lose 25%. If you get past 950 points it becomes even more severe, eventually resulting in a 100% loss of points at 1000.
...


Taking the highlighted phrase literally, I implemented a linear edge modifcation system as opposed to the quadratic implementation implied in your proof (I assume that you have spoken to Nick and this is the way its actually implemented - seems reasonable as it is just a straight simple calculation)

The following graph illustrates the difference in the two implementations:

Posted Image

From the graph, it is interesting to note that since the quadratic method is proven, the linear method is also proven since for all ranks the amount of reduction is less than or equal to the linear reduction.

The actual difference is at most 6.25% and considering the small numbers involved and other factors (such as inaccuracy of starting rank display, etc.), the error probably won't be noticable
blutch
blutch
Posts: 1,089
04:56 Tue 16 Dec 08 (GMT)  [Link]  
I have to recognize you are absolutely right. I have just checked this with some recent results of some virtuosos.

Until now, I had supposed it was an error in the help, and that the edge modification was actually quadratic. I didn't understand how it can be linear but be only 25% at 950, and it seemed natural to me that it then has to be quadratic... I just didn't think about the edge modification having a non-continuous derivative.
(sorry I can't reformulate these 2 words into a less technical way, in less than 10 lines )

Don't modify anything in your rank calculator! I'll update my proof instead, adding a few lines explaining that the quadratic proof also proves the linear one.

Thanks Dave!

Edited at 12:58 Tue 16/12/08 (GMT)
Deleted User
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05:11 Tue 16 Dec 08 (GMT)  [Link]  
Lol - good job I hadn't got around to making the changes (been too busy playing ). Glad to be of help mate - perhaps Nick could confirm that my original assumption was correct (if he has time) but in the meantime I'll hold fire.

(by the way, shouldn't this thread be on 'Game Queries' instead - wondered why I couldn't find it before)
Deleted User
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05:26 Tue 16 Dec 08 (GMT)  [Link]  
on 2.1 Conventions

you have typed funkys-nooker
luckypot
luckypot
Admin
Posts: 2,211
05:42 Tue 16 Dec 08 (GMT)  [Link]  
At first it was a game shout... But could probably provide some pretty in depth answers regarding the ranking system.

Therefore, moved to game queries.

Deleted User
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08:42 Tue 16 Dec 08 (GMT)  [Link]  
Err right that is Headblagging. I am in year 11 and am on a A*
Deleted User
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09:35 Sun 21 Dec 08 (GMT)  [Link]  
what would hapen if say a 996 rank (which we know is possible) plays a 995 rank ?? if 2 people got that far
Deleted User
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10:14 Sun 21 Dec 08 (GMT)  [Link]  
i think the winner would gain something like 1 point whilst the loser would lose a usually amount for two players with a very similar rank.
blutch
blutch
Posts: 1,089
11:50 Sun 21 Dec 08 (GMT)  [Link]  
snooker_andy said:
what would hapen if say a 996 rank (which we know is possible) plays a 995 rank ?? if 2 people got that far

The base points you gain for beating a player with the same ranking as you is 7 for original and 4 for arcade. But because the winner is 996, he would suffer an edge modification of 94%, so the real points won would be 0.42 for original, and 0.24 points for arcade.

All details here: http://www.funkysnooker.com/help.do?section=rankings

(edit) I forgot to count the winner bonus but the idea is still the same.

Edited at 19:55 Sun 21/12/08 (GMT)
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Mathematical proof that ranks cannot reach 1000

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