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Extended ratings system: 6-stars and up!
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Kinitawowi  
 




Joined: 18 Sep 2007
Posts: 1074
Location: Newham, London, UK

PostPosted: Thu Jan 10, 2008 3:39 pm    Post subject: Reply with quote

Venge wrote:
If the 5* multiplier is 2.8x (40% more than 4*) instead of 3x (50% more) then shouldn't 6* be 3.92x, 7* = 5.488x, 8* = 7.6832x, 9* = 10.75648x? Or working off the GH1:GH2 ratio: 5* = 3.0:2.8 = 15:14 = 93 1/3%. Which would make 6* = 3.72x, 7* = 4.65x, 8* = 5.58x, 9* = 6.51x.

Well, the ratio system is right out, because it gets the 4* wrong - that's fixed at 2x, and your calculation (GH1:GH2 = 15:14 -> 2:x) results in x = 1.86666x - and the game knows that that should be 2x as well. As for the exponential approach...



Just no.
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pk217doc  
 




Joined: 08 Nov 2006
Posts: 145

PostPosted: Thu Jan 10, 2008 3:43 pm    Post subject: Reply with quote

Venge wrote:
JCirri wrote:
Code:

|                   |   Avg. Mult.     | SH Decimal Rating |
|   In-game Rating  |   GH1  |   GH2   |   GH1   |   GH2   |
------------------------------------------------------------
|      4-stars      |  2.0x  |  2.0x   |   4.0   |   4.0   |
|      5-stars      |  3.0x  |  2.8x   |   5.0   |   5.0   |
|      6-stars      |  4.0x  |  3.6x   |   6.0   |   6.0   |
|      7-stars      |  5.0x  |  4.4x   |   7.0   |   7.0   |
|      8-stars      |  6.0x  |  5.2x   |   8.0   |   8.0   |
|      9-stars      |  7.0x  |  6.0x   |   9.0   |   9.0   |

After reading the 1/8/08 updates in tma's Song Scores, Extended Star Ratings and Cut-Offs FAQ 20080108 it struck me that the math on the GH2/GH3 extended ratings might be faulty. I searched that thread and this one (the only logic places) to see if this has been brought up, so if there's an errant post out there, sorry, but it really should be addressed, either way, in this post.

If the 5* multiplier is 2.8x (40% more than 4*) instead of 3x (50% more) then shouldn't 6* be 3.92x, 7* = 5.488x, 8* = 7.6832x, 9* = 10.75648x? Or working off the GH1:GH2 ratio: 5* = 3.0:2.8 = 15:14 = 93 1/3%. Which would make 6* = 3.72x, 7* = 4.65x, 8* = 5.58x, 9* = 6.51x.

I understand the extended scoring is an arbitrary system we made up ("we" = the "royal" we = JCirri) and that logic doesn't necessarily apply. I understand this is the way it's been done for quite a while now and changing it would upset those that are opposed to change, not matter the reason. I understand this makes the extended scores more difficult and changing it would upset those that are above the old cutoffs, but below the "logical" ones; especially the 8*'s, since the first set of calculations put the 8* higher than the old 9*, which has yet to be achieved (?). I'm not even proposing that we actually change it, I was just curious if this was considered and if there was a reason it was rejected.


First off, I think you've put too much thought into all of this, since the extended star ratings is very simple. For GH1, they figured that since the difference between the multipliers of 4-star and 5-star was simply 1x, that a 6-star rating would simply be 1x higher that 5-star, 7-star would be 1x higher than 6-star and so on.

Same goes for GH2 and beyond, since the difference this time between 4 and 5-star was 0.8x, they added 0.8x to each extended rating to get the next (i.e. 2.0x, 2.8x, 3.6x, 4.4x, 5.2x, 6.0x). Or basically the formula could be 2+(a-4)*0.8, where "a" is the star rating you're trying to get.

Now, if you applied the logic that you did on GH2 to get the 3.92x, 5,488x, 7.6832x, and 10.75648x multipliers (adding 40% in other words) for extended ratings, and did the same thing for GH1, you would have to add 50% to each higher rating, giving a series of multipliers to be 2.0x, 3.0x, 4.5x, 6.75x, 10.125x, and 15.1875x. This would obviously make extended ratings for GH1 suck, since the highest rating anyone would probably ever get using these multipliers would be 6-star.

As far as trying to create a GH1 to GH2 ratio (the 15/14 that you mentioned), you really can't do that since the scoring mechanisms are different for those games. And you wouldn't end up getting the 2x multiplier for a 4-star on both games that way.
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pk217doc  
 




Joined: 08 Nov 2006
Posts: 145

PostPosted: Thu Jan 10, 2008 3:49 pm    Post subject: Reply with quote

Kinitawowi wrote:
Venge wrote:
If the 5* multiplier is 2.8x (40% more than 4*) instead of 3x (50% more) then shouldn't 6* be 3.92x, 7* = 5.488x, 8* = 7.6832x, 9* = 10.75648x? Or working off the GH1:GH2 ratio: 5* = 3.0:2.8 = 15:14 = 93 1/3%. Which would make 6* = 3.72x, 7* = 4.65x, 8* = 5.58x, 9* = 6.51x.

Well, the ratio system is right out, because it gets the 4* wrong - that's fixed at 2x, and your calculation (GH1:GH2 = 15:14 -> 2:x) results in x = 1.86666x - and the game knows that that should be 2x as well. As for the exponential approach...



Just no.


Ninja'd on the 2x multiplier not being the same, but Venge never mentioned anything about an exponential increase in the multiplier. The 40% increase is strictly multiplication and/or addition (depending on how you do it). So I'm not entirely sure how you were able to get an exponential graph, unless I have totally forgotten some of my math.
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Kinitawowi  
 




Joined: 18 Sep 2007
Posts: 1074
Location: Newham, London, UK

PostPosted: Thu Jan 10, 2008 3:56 pm    Post subject: Reply with quote

pk217doc wrote:
Ninja'd on the 2x multiplier not being the same, but Venge never mentioned anything about an exponential increase in the multiplier. The 40% increase is strictly multiplication and/or addition (depending on how you do it). So I'm not entirely sure how you were able to get an exponential graph, unless I have totally forgotten some of my math.

multiplier = 2 * [ 1.4 ^ (rating - 4) ]. Go back and re-read the bit in your maths textbooks about compound interest.

EDIT: relabelled equation
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pk217doc  
 




Joined: 08 Nov 2006
Posts: 145

PostPosted: Thu Jan 10, 2008 4:17 pm    Post subject: Reply with quote

Kinitawowi wrote:
pk217doc wrote:
Ninja'd on the 2x multiplier not being the same, but Venge never mentioned anything about an exponential increase in the multiplier. The 40% increase is strictly multiplication and/or addition (depending on how you do it). So I'm not entirely sure how you were able to get an exponential graph, unless I have totally forgotten some of my math.

multiplier = 2 * [ 1.4 ^ (rating - 4) ]. Go back and re-read the bit in your maths textbooks about compound interest.

EDIT: relabelled equation


Oh, I see where I went wrong on that thought. My bad on that part of it. I was just thinking of it the wrong way when I looked at your graph I guess. It's been a while since I've even had to think about any kind of math problems like this, but that's not much of an excuse to forget something as simple as compound interest.

But yeah, adding the 40% to each successive multiplier would give you the formula Kinitawowi mentioned, and in turn that would kill the usefulness of the extended star ratings.
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Venge  
 




Joined: 09 Aug 2007
Posts: 254
Location: Yuma, Arizona

PostPosted: Thu Jan 10, 2008 4:34 pm    Post subject: Reply with quote

pk217doc wrote:
First off, I think you've put too much thought into all of this, since the extended star ratings is very simple.

Problem is, I didn't put hardly any thought into it. As I said, I was reading tma's faq and it occured to me that just adding .8 to each sequential star ignores the fact that if the rating were reversed 3* would be 1.2x base score, which implies just adding .8 isn't 100% accurate. The two examples I could think of off the top of my head suffer the same problem (3- and 4- stars don't match up), but I didn't think about it that far -- which now makes me feel really stupid because they're flawed in exactly the same way I was pointing out .

The extended star ratings is very simple because we've made it that way; we just made some shit up and said that's the way it is. The math behind it is not very simple. I'm am not a math professor, but I know there are some very learned "mathies" here and wanted to make sure it was considered. JCirri's graph pretty much put it in perspective though: it might not be 100% accurate, but it's close enough.

EDIT1: Why the Hell was there a "[/i]" at the end of my post?!?
EDIT2: ^^ Rhetorical question ^^
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Kinitawowi  
 




Joined: 18 Sep 2007
Posts: 1074
Location: Newham, London, UK

PostPosted: Thu Jan 10, 2008 4:45 pm    Post subject: Reply with quote

Venge wrote:
Problem is, I didn't put hardly any thought into it. As I said, I was reading tma's faq and it occured to me that just adding .8 to each sequential star ignores the fact that if the rating were reversed 3* would be 1.2x base score, which implies just adding .8 isn't 100% accurate. The two examples I could think of off the top of my head suffer the same problem (3- and 4- stars don't match up), but I didn't think about it that far -- which now makes me feel really stupid because they're flawed in exactly the same way I was pointing out .

Oh, I've realised that myself a long time ago - the spreadsheet I use on my own computer has some special case fudging to fix 3-stars at 1.0x and then automatically works out 4-stars at 2.0x, 5-stars at 2.8x, 6-stars at 3.6x etc. Hypothetically, as far as the game's concerned it's irrelevant. The game says "if you get 2.8x you get 5-stars, otherwise if you get 2.0x you get 4-stars, otherwise you get 3-stars". That's why the 3-star calculations can be "wrong" under any model (because the game doesn't hold a value for them), but the 4-star and 5-star ones have to be right.
Quote:
The extended star ratings is very simple because we've made it that way; we just made some shit up and said that's the way it is.

Probably the most accurate thing said in this thread.
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bulletformyjew  
  
  



Joined: 13 Feb 2008
Posts: 223
Location: Manchester UK

PostPosted: Mon Mar 10, 2008 2:29 pm    Post subject: Reply with quote

on co-op Gh3 we got a times multiplyer on 2.710 but it was 5*????

Why?
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tma  
 




Joined: 03 May 2007
Posts: 1414
Location: Australia

PostPosted: Mon Mar 10, 2008 8:41 pm    Post subject: Reply with quote

bulletformyjew wrote:
on co-op Gh3 we got a times multiplyer on 2.710 but it was 5*????

Why?


We'd all like to know that.
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CovyKiller  
 




Joined: 10 May 2008
Posts: 127

PostPosted: Thu May 29, 2008 7:32 pm    Post subject: Reply with quote

Let me just understand one thing, it is completely impossible to achieve a nine-star rating on any song, correct?

PS: didn't really sift through all the pages, should've.
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blob  
 




Joined: 11 May 2007
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PostPosted: Thu May 29, 2008 7:35 pm    Post subject: Reply with quote

Its not impossible in the world of GH. But no song at this moment in any game can get 9*.
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thecaptainof  
 




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PostPosted: Thu May 29, 2008 7:43 pm    Post subject: Reply with quote

blob wrote:
Its not impossible in the world of GH. But no song at this moment in any game can get 9*.


...except The Seeker X/X co-op.
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zsjostrom35  
 




Joined: 17 Feb 2008
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PostPosted: Sat May 31, 2008 4:03 am    Post subject: Reply with quote

thecaptainof wrote:
blob wrote:
Its not impossible in the world of GH. But no song at this moment in any game can get 9*.


...except The Seeker X/X co-op.


Well, nobody knows exactly how the co-op star ratings work, so you can't really say that they got nine stars. Their average multiplier was indeed over 6.0, however, which is why most people refer to it as a nine-star run.
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galvao1090  
 




Joined: 09 Apr 2007
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PostPosted: Sun Sep 07, 2008 1:37 pm    Post subject: Reply with quote

Just a suggestion to the site:

Why don't you extend the concept of number of stars to the total score in each game? Then the users can be compared by their "Star Rating" too... (For example, a gamer that achieved an average multiplier of 3,6 across all songs a 6-star player)
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liljj93  
 




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PostPosted: Thu Sep 18, 2008 1:11 am    Post subject: Reply with quote

i didnt know a 6.0 avg. multiplier was possibly
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