iironiic's little experiment

[iironiic]

Hey guys! As you all know, I have been working on something secret (not so secret anymore haha) in the past few days. Because it seems pretty accurate, I think it is time to introduce what I am going to propose for FFR.

Essentially, my goal behind this experiment is to measure someone's skill level based on the number of AAAs the player have obtained throughout their stay on FFR. For example, an 11.5 according to my formula constitutes that the player's AAAing skill level is simply around the mid-FMOish level. Similarly, this applies for all values between 1-13. This generally comes in handy when it comes to tournament placements since there are some players that don't entirely max out their stats.

This formula assumes that you have played all of the public files on FFR to your best ability. Of course that doesn't mean that you can't apply this formula to yourself if you haven't played a few songs. If that was the case, all that will result from this formula is a less accurate rating of your AAAing skill level (most likely an underestimate).

So what is this formula? Well, there are actually a few formulas that will determine the AAAing rating and it will depend on how many AAAs of that difficulty a player have obtained. Here is a flowchart that determines the formula you will use:



Begin AAAing Rating Computation (determining the formula):

1) Check to see if the player have at least 20% of all FGOs AAA'd. If so, apply the FGO AAA formula. The result of this FGO formula is the final rating the player will receive. If not, move onto 2).

2) Check to see if the player have at least 20% of all FMOs AAA'd. If so, apply the FMO AAA formula**. If not, move onto 3).

**If the player scores anything above or equal to a 12, apply the FGO formula. Otherwise, this is the player's final rating.

3) Check to see if the player have at least 20% of all VCs AAA'd. If so, apply the VC AAA formula**. If not, move onto 4).

**If the player scores anything above or equal to a 11, apply the FMO formula. Otherwise, this is the player's final rating.

4) Check to see if the player have at least 20% of all 9s AAA'd. If so, apply the 9 AAA formula**. If not, move onto 5).

**If the player scores anything above or equal to a 10, apply the VC formula. Otherwise, this is the player's final rating.

etc.



Why 20%? When implementing my formulas onto a few people, it seems that those who score one level higher generally AAAs at least 20% of that level. I don't want a fixed number here since this will essentially lower the percentage of needed AAAs to be "confident" in that level.

Now onto the formula:



The FGO Formula:

With R is rating of the player, determines the players FGO Revised AAA Count, and Q(12) equals the number of FGO files in the game.

So how is determined?

First, compile a list of FGOs that you scored better than or equal to (2-0-0-0). Let's call A(x) the number of FGOs you scored x on.

There are weights assigned to each of the scores:

AAA = 1
(0-0-0-1) = 50/55
(0-0-0-2) = 45/55
(0-0-0-3) = 40/55
(0-0-0-4) = 35/55
(0-0-0-5) or (1-0-0-0) = 30/55
(0-0-0-6) or (1-0-0-1) = 25/55
(0-0-0-7) or (1-0-0-2) = 20/55
(0-0-0-8) or (1-0-0-3) = 15/55
(0-0-0-9) or (1-0-0-4) or (0-1-0-0) = 10/55
(0-0-0-10) or (1-0-0-5) or (0-1-0-1) or (2-0-0-0) = 5/55

Take the corresponding weight, multiply A(x), and add up everything. This is your .

For example. I'll take my jackbuddy's (alloyus) stats as of 10/29/2011. He AAA'd 11 FGOs, scored (1-0-0-0) on 3 FGOs, and scored (2-0-0-0) on another 3. Therefore,

Now, plug everything into the FGO formula. For jackbuddy's case, this is what it results down to:

This implies that alloyus have a AAAing skill level at around a low-FGO level.


The concept is similar for all other difficulties except different weights are assigned:

For difficulty p:

p AAA = 1
p (0-0-0-1) = 25/30
p (0-0-0-2) = 20/30
p (0-0-0-3) = 15/30
p (0-0-0-4) = 10/30
p (0-0-0-5) or p (1-0-0-0) = 5/30

p+1 AAA = 1.25
p+1 (0-0-0-1) = 27.5/30
p+1 (0-0-0-2) = 25/30
p+1 (0-0-0-3) = 22.5/30
p+1 (0-0-0-4) = 20/30
p+1 (0-0-0-5) or p+1 (1-0-0-0) = 17.5/30

So if p = FMO, this is what the table would look like:

FMO AAA = 1
FMO (0-0-0-1) = 25/30
FMO (0-0-0-2) = 20/30
FMO (0-0-0-3) = 15/30
FMO (0-0-0-4) = 10/30
FMO (0-0-0-5) or FMO (1-0-0-0) = 5/30

FGO AAA = 1.25
FGO (0-0-0-1) = 27.5/30
FGO (0-0-0-2) = 25/30
FGO (0-0-0-3) = 22.5/30
FGO (0-0-0-4) = 20/30
FGO (0-0-0-5) or FGO (1-0-0-0) = 17.5/30

A few things to mention:

The formula proposed here assumes that each FMO/FGO/VC w/e holds the same difficulty which is clearly not the case. An ideal formula would consider complex cases like this, but this is beyond way too much for me to handle.

Again, this formula assumes that the player plays all of the public songs to his/her best ability. An underestimate is most likely to yield from this formula if there are some unplayed songs.

There is a reason why those specific fractions are determined for weights. If you are interested in knowing why, let me know.

Lastly, I give big thanks to AJ (TC_Halogen), Justin (justin_ator), and all of you guys who posted on my earlier thread for making this possible.

EDIT: Thank you Enginuity for creating an excel program to make calculations much easier! Attached here is a program in a .zip file where you can download it and implement my algorithm on your public level ranks. Make sure to change all unrecorded scores (especially AAAs and flags) from (0-0-x-0-0) to (x-0-0-0-0). If more files are added in the game, Enginuity can easily fix the spreadsheet. The score to the left of the green box that doesn't say "NOT ENOUGH AAAs" is the score that determines your rating.

Any question? Comments? Critiques? Feel free to discuss about it here.

[Ksl33zy24]

Welp, I won't even be considered in any formula here. (: Pretty cool, though. Maybe they'll implement this...

[justin_ator]

Well if this gets implemented that'd be sick cause it could draw from stats and I wouldn't have to search people's ranks to get you data ;P

Hope this gets implemented, you should post a few rankings just so people can get an idea more of how the numbers come out for people. =]

[One Winged Angel]

Honestly, I used to think of players in terms of the numbers that would be achieved using these formulae, you just took it to a whole new level hahaha

Really sick stuff here, Wilson. Looks disturbingly accurate too, wow.

[iironiic]

Originally Posted by justin_ator

Well if this gets implemented that'd be sick cause it could draw from stats and I wouldn't have to search people's ranks to get you data ;P

Hope this gets implemented, you should post a few rankings just so people can get an idea more of how the numbers come out for people. =]

I can do that with some of the data I have haha:

DossarLX ODI - 12.9604
TC_Halogen - 12.55570248
Xayphon - 12.50023471
AlexDest - 12.33429421
Ziergdsx18 - 12.14857521
One Winged Angel - 12.0814843
star reaper - 12.0889124
smartdude1212 - 12.07438017
alloyus - 12.06665785
samurai7694 - 12.70865785
leonid - 12.19200331
xThai - 12.11683967

This is not under the 4 digit rating though. That can get implemented after this formula gets tweaked if needed.

[justin_ator]

Lol at Dossar being almost at the 13 level.

[SkRAWRk]

Originally Posted by iironiic

There is a reason why those specific fractions are determined for weights. If you are interested in knowing why, let me know.

I'm interested. I have a few ideas, but I'm not at as advanced a level of Maths as you are, so I'm not sure if they'd be right.

Despite that, I'm extremely interested in things like this and I like what you've done here, it looks really good. ^___^

[SkRAWRk]

I think the only thing that kinda sucks is the huge gaps at the upper end of the table, but they definitely represent the skill levels correctly and in an efficient way. I think the FGO's will always be kinda inaccurate, but it seems like it should work well with FMO and below.

[One Winged Angel]

I'm also extremely interested in knowing how you achieved those weights

edit: disregard what I wrote earlier if you saw it, didn't see the 1.25 for each FGO AAA, derp

[iironiic]

Originally Posted by SkRAWRk

I'm interested. I have a few ideas, but I'm not at as advanced a level of Maths as you are, so I'm not sure if they'd be right.

Despite that, I'm extremely interested in things like this and I like what you've done here, it looks really good. ^___^

Haha well I'll only discuss about the FMO case since they were all found in a similar fashion.

Anything less than or equal to a BF is arguably close to AAAing something (except for the case of FGOs since they are generally harder). So consider their raw scores.

Let's say we have a song with a perfect raw score of 10000. Then, a blackflag is 9975. Because raw scoring is based off on an increment of 5 points, anything above a 9970 is considered close to a AAA. The difference we are dealing with here is the 30 seen at the denominator of the weights. The numerators of the weights are the difference between the raw score you scored minus that threshold of 9970 for this example. This implies that if someone have a BF, then he would score 5 points over that threshold, which shows that a BF is 5/30. Same argument applies for all other scores less than a blackflag.

Originally Posted by SkRAWRk

I think the only thing that kinda sucks is the huge gaps at the upper end of the table, but they definitely represent the skill levels correctly and in an efficient way. I think the FGO's will always be kinda inaccurate, but it seems like it should work well with FMO and below.

I realized that too, and I wish I can do something about it. However, I think the only explanation explaining this is that most people generally AAA a few handfuls of FGOs before AAAing all of the FMOs. That can also be seen under the case of VCs and FMOs. I think that's why there is this somewhat huge gap between the two difficulties.

I'm glad that most people are supporting this too

EDIT: For the difficulties +1 higher than the scoring difficulty, I made them weigh just slightly more since they also have to be considered in the formula.

EDIT2: Another reason why I think there is this huge gap is that the remaining FGOs at the upper end of the scale are generally much much difficult and should be more rewarding. It may seem that way, but you get A LOT of points if you have something like 12.7 and AAA'd one of your remaining FGOs.

[i love you]

That is one sick idea you got there iironiic. I definitely support this idea wow.

[justin_ator]

See, now is when I really wish I knew enough coding/etc to set it up myself to draw data from the levelranks, cause I'm curious to see how this works on lower rank users as well.

I suppose if someone really wanted me to try and gather some lower level data from a user or two, I could, but I need someone who knows the general range of their skill so I know where to look through their stats (as well as having played most of the public songs of that difficulty and lower that way things aren't skewed).

[Enginuity]

Out of curiosity, I wrote an excel file that calculates my score. I'm willing to post it (so people can use it for their own scores), if it's okay with you iironiic.

In anycase, my score is 1609.53 (diff 7, not enough AAA's in diff 8) [Corresponded to 7.233].

[DossarLX ODI]

This is frickin amazing haha.

Originally Posted by justin_ator

Lol at Dossar being almost at the 13 level.

Crowdpleaser

[iironiic]

Originally Posted by justin_ator

See, now is when I really wish I knew enough coding/etc to set it up myself to draw data from the levelranks, cause I'm curious to see how this works on lower rank users as well.

I suppose if someone really wanted me to try and gather some lower level data from a user or two, I could, but I need someone who knows the general range of their skill so I know where to look through their stats (as well as having played most of the public songs of that difficulty and lower that way things aren't skewed).

It would work on everyone. For those that can't AAA anything song harder than Free Space, that person will have a rating of 1 since it's: 1+ (0/4) = 1.

That means his/her 4 digit rating is at 1000.

If someone have loads of FMO AAAs but for some magical reason, cannot AAA Free Space, he will still have that rating around that FMO level. Fortunately I don't have to consider rare cases like this xD.

EDIT:

Originally Posted by Enginuity

Out of curiosity, I wrote an excel file that calculates my score. I'm willing to post it (so people can use it for their own scores), if it's okay with you iironiic.

In anycase, my score is 1609.53 (diff 7, not enough AAA's in diff 8) [Corresponded to 7.233].

Yeah that's completely fine! In fact, I encourage you to do it since I'm sure there are many people out there that have no clue what I'm saying haha.

[justin_ator]

Lern 2 pleese crowds maang.

[One Winged Angel]

Also I'm going to go ahead and laugh at the fact that I'm pretty sure I had some sort of influence over 20% being chosen hahahaha

[Enginuity]

Oops, I implemented it incorrectly earlier (just implemented the scoring mechanism for Diff 12 for all difficulties). Score: 7.499.

To use this to calculate your score, you just have to replace my level ranks copied in with yours... [this shouldn't affect any of the formulas] this might take a little bit of effort unless you're familiar with excel...

I picked a random score (leonid's) and it came up with the same value as you did iironiic.

[Emithith]

lol the way this formula works.. impressive.
Though, lol I would be like low 2 or something due to my lack of AAAs
Either way though, good job.

[iironiic]

Originally Posted by Enginuity

Oops, I implemented it incorrectly earlier (just implemented the scoring mechanism for Diff 12 for all difficulties). Score: 7.499.

To use this to calculate your score, you just have to replace my level ranks copied in with yours... [this shouldn't affect any of the formulas] this might take a little bit of effort unless you're familiar with excel...

I picked a random score (leonid's) and it came up with the same value as you did iironiic.

For some reason, I got 15.07611628 from your spreadsheet for my own level ranks haha. Am I doing something wrong?