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:
 \right )^2})
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:
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,
+3\left(\frac{5}{55}\right)} = 12.9091)
Now, plug everything into the FGO formula. For jackbuddy's case, this is what it results down to:
^2= 12.066658)
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:
 \right )^2})
So if p = FMO, this is what the table would look like:
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.
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,
So how is
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:
Code:
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
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:
Code:
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
Code:
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.
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.
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