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top 100 list Redux?


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Douche McCallister
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Title: DOO-SHAY
Joined: Jan 26 2007
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PostPosted: Nov 22 2008 05:15 pm Reply with quote Back to top

jprime wrote:
Not all guys are walking erections, you know.

Just the normal ones BURN!


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Lottel
Title: of the Eternal BWOG
Joined: Sep 02 2008
PostPosted: Nov 22 2008 05:18 pm Reply with quote Back to top

...
The candian chicks are the hottest ones on there.


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Valdronius
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Title: SydLexia COO
Joined: Aug 22 2005
Location: The Great White North
PostPosted: Nov 22 2008 06:11 pm Reply with quote Back to top

Those of you who have read through the Top 100 SNES list, and possibly the Top 100 NES list, might be wondering how we came to the final ordering for these games. Well, each game received a score from 1 to 1000 based on it's position on each individual list, and was then ranked against all other games with the highest scoring game getting the top spot.


Now you may be wondering how each games score was calculated. Well, to put it simply:



Where n is the number of individual lists the game appeared on,


x is the game's position on an individual list,


and l is the total number of individual lists.


For those of you who haven't taken university mathematics, I shall go into a more detailed explaination of each step along the way. (For those of you who have, I apologize for using 1.n, it just looks nicer than 1 + n/10).


Alright, let's start from the inside and work our way out. For clarity, from here out when I use the term 'rank', I'm refering to a games rank on an indivdual list.



The first thing we do is take the reciprocal of the games rank. If I rated one game 15th on my list, and another game 30th, it wouldn't make sense to give them 15 points and 30 points respectively, as we wanted the 15th ranked game to be higher on the final list. So we take the reciprocal of each number to achieve the desired result. 1/15 = 0.067, 1/30 = 0.033.



Before we take the reciprocal, we want to add what I call a 'limiter' to the games rank. The limiter is the total number of individual lists, less 1. It might not be immediately clear why this is necessary, so let's move forward.



The next step is to add up all those reciprocals from the individual lists. The more lists a game appears on, and the higher its rank, the higher this number will be. This is also where the limiter becomes important. Let's say there were 5 lists, and everybody voted a certain game #1. Then we'd have this happening:



So the highest possible total a game can have a this point is 1. Without the limiter, a game could have a score higher than 1 at this point, which would cause some wonky things in the next step.



Finally we have a booster. When a game appears on multiple lists, it gets a boost for the number of lists it appears on. So again, if there are 5 lists, a game could receive a low boost of 1.1 for being on 1 list, up to 1.5 for appearing on 5 lists. If you want to see why I had to use the limiters, take the 1.5th root of 2, and the 1.1th root of 2. For this system we would want the former to be higher, but you'll see that this is not the case. When the numbers are between 0 and 1, this achieves the desired effect.


Well, that was fairly long-winded. Let's walk through an example to see how A Link to the Past scored. There were 7 lists in total, and it was ranked 6, 1, 1, 4, 2, 2, and 4. Then we'll get this:



Multiplying the number at the end by 1000 is purely for aesthetic reasons. It is easier to rank numbers that range from 1 to 1000 than it is to rank numbers ranging from 0 to 1. To show that the booster does indeed work the way it is supposed to, let's take the 1.1th root of 0.8190476. This results in 0.834 or a score of 834.


So that's how the ranking system was designed. I hope someone out there enjoyed reading this.



Klimbatize wrote:
A Hispanic dude living in Arizona knows a lot of Latinas? That's fucking odd.

 
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JRA
Joined: Sep 17 2007
Location: The Opium Trail
PostPosted: Nov 22 2008 06:30 pm Reply with quote Back to top

wouldn't just 1 to 100 have been easier? Since it is a top 100 list?


There are a lot of what if's in life Donny. What if I hit you really hard in the face, knocked yo shit to the back of yo skull? What if I....had you girl gargle my nuts? The fact remains, you are a fuckin mutant.
 
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GPFontaine
Joined: Dec 06 2007
Location: Connecticut
PostPosted: Nov 22 2008 06:31 pm Reply with quote Back to top

Holy crap Val. That seems like it was a lot of work.

I think I just don't like mathematical symbols. They scare me. Not because they are complicated, but rather because I fear that they might be conspiring against me.



 
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Valdronius
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Title: SydLexia COO
Joined: Aug 22 2005
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PostPosted: Nov 22 2008 06:40 pm Reply with quote Back to top

GPFontaine wrote:
Holy crap Val. That seems like it was a lot of work.

I figured I should put my degree to work somewhere.

JRA wrote:
wouldn't just 1 to 100 have been easier? Since it is a top 100 list?

Do you mean 1 point for 1st place, 100 points for 100th place, or the other way around? Either way poses serious problems. The first way, a game with less points should be ranked higher in the end, but if a game appears on only one individual list, it will have less points.

If you say 100 points for a 1st place game and 1 point for being ranked 100, this also poses problems. Let's everyone listed a game at 100; it would only get 5 points if there were 5 people, and would be beat out by a game that one person ranked 95. For the purposes of these lists, a game that we all agreed was in the top 100 games for the system should definitely beat out a game that one person put at 95. That's why I developed this system.


Klimbatize wrote:
A Hispanic dude living in Arizona knows a lot of Latinas? That's fucking odd.

 
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Syd Lexia
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Title: Pop Culture Junkie
Joined: Jul 30 2005
Location: Wakefield, MA
PostPosted: Nov 22 2008 07:12 pm Reply with quote Back to top

I was supposed to put this explanation up on the site awhile ago. I suck. Crying
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Tebor
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Title: Master of the Universe
Joined: Aug 22 2005
Location: Gotham City
PostPosted: Nov 22 2008 07:13 pm Reply with quote Back to top

That looks way more complicated than it needed to be. Why couldn't you just score averages again? And ties would be decided by rock, paper, scissors.


"If you will not tell me, I will hurt people!!!" -Nuclear Man

"Do you hear? The alpha and the omega. Death and rebirth. And as you die, so will I be reborn!" - Skeletor

8341 unread forum updates since I left (2/7/14)... Uh-oh.
 
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JRA
Joined: Sep 17 2007
Location: The Opium Trail
PostPosted: Nov 22 2008 07:15 pm Reply with quote Back to top

Valdronius wrote:
GPFontaine wrote:
Holy crap Val. That seems like it was a lot of work.

I figured I should put my degree to work somewhere.

JRA wrote:
wouldn't just 1 to 100 have been easier? Since it is a top 100 list?

Do you mean 1 point for 1st place, 100 points for 100th place, or the other way around? Either way poses serious problems. The first way, a game with less points should be ranked higher in the end, but if a game appears on only one individual list, it will have less points.

If you say 100 points for a 1st place game and 1 point for being ranked 100, this also poses problems. Let's everyone listed a game at 100; it would only get 5 points if there were 5 people, and would be beat out by a game that one person ranked 95. For the purposes of these lists, a game that we all agreed was in the top 100 games for the system should definitely beat out a game that one person put at 95. That's why I developed this system.

A system that's more complicated than the pathways of Oxygen to Pat Robertson's brain.


There are a lot of what if's in life Donny. What if I hit you really hard in the face, knocked yo shit to the back of yo skull? What if I....had you girl gargle my nuts? The fact remains, you are a fuckin mutant.
 
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Valdronius
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Title: SydLexia COO
Joined: Aug 22 2005
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PostPosted: Nov 22 2008 07:27 pm Reply with quote Back to top

Tebor wrote:
That looks way more complicated than it needed to be. Why couldn't you just score averages again? And ties would be decided by rock, paper, scissors.

Because then I could put Shaq Fu as my #1 and because no one else would vote for it, it's average would be #1.


Klimbatize wrote:
A Hispanic dude living in Arizona knows a lot of Latinas? That's fucking odd.

 
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Tebor
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Title: Master of the Universe
Joined: Aug 22 2005
Location: Gotham City
PostPosted: Nov 22 2008 07:32 pm Reply with quote Back to top

Valdronius wrote:
Tebor wrote:
That looks way more complicated than it needed to be. Why couldn't you just score averages again? And ties would be decided by rock, paper, scissors.

Because then I could put Shaq Fu as my #1 and because no one else would vote for it, it's average would be #1.

If no one else voted for it, then divided by the number of other judges. So if there were four of you, it would get .25. Probably still too high, but it'd go down some. That system probably doesn't work in the long run as I'm not really thinking about this. And why couldn't you all rate every game as a score instead of position?

I am so out of the loop. Both those articles were excruciating long to read and I don't think I even finished the SNES one. Embarrassed


"If you will not tell me, I will hurt people!!!" -Nuclear Man

"Do you hear? The alpha and the omega. Death and rebirth. And as you die, so will I be reborn!" - Skeletor

8341 unread forum updates since I left (2/7/14)... Uh-oh.
 
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Syd Lexia
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Title: Pop Culture Junkie
Joined: Jul 30 2005
Location: Wakefield, MA
PostPosted: Nov 22 2008 08:15 pm Reply with quote Back to top

Another part of it was that one person didn't vote for Legend of Zelda at all, so the algorithm was intentionally tailored to take that into account and make sure that LoZ got a reasonable place on the list.
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Tebor
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Title: Master of the Universe
Joined: Aug 22 2005
Location: Gotham City
PostPosted: Nov 22 2008 08:20 pm Reply with quote Back to top

Syd Lexia wrote:
Another part of it was that one person didn't vote for Legend of Zelda at all, so the algorithm was intentionally tailored to take that into account and make sure that LoZ got a reasonable place on the list.

Then we shall call Val's wacky equation the "Legend of Zelda" factor! ... Or just Val's Wacky Equation.


"If you will not tell me, I will hurt people!!!" -Nuclear Man

"Do you hear? The alpha and the omega. Death and rebirth. And as you die, so will I be reborn!" - Skeletor

8341 unread forum updates since I left (2/7/14)... Uh-oh.
 
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JRA
Joined: Sep 17 2007
Location: The Opium Trail
PostPosted: Nov 22 2008 08:56 pm Reply with quote Back to top

Tebor wrote:
I am so out of the loop. Both those articles were excruciating long to read and I don't think I even finished the SNES one. Embarrassed

I just skipped to the games I cares about. Very Happy


There are a lot of what if's in life Donny. What if I hit you really hard in the face, knocked yo shit to the back of yo skull? What if I....had you girl gargle my nuts? The fact remains, you are a fuckin mutant.
 
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GPFontaine
Joined: Dec 06 2007
Location: Connecticut
PostPosted: Nov 23 2008 12:13 pm Reply with quote Back to top

I am converting Val's post into a Wiki article. I ran out of time for now though, I'll get back on it when I get back a little later.



 
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GPFontaine
Joined: Dec 06 2007
Location: Connecticut
PostPosted: Nov 24 2008 10:33 am Reply with quote Back to top

The Wiki version is complete.

Hey Val, when you get a chance can you just look at it and make sure I got everything correctly moved over?

http://history.sydlexia.com/index.php?title=Val%27s_Wacky_Equation



 
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