Stuck on you... Also statistics...
Posted on: August 3, 2014, at 12:26:17am

I've been playing a lot of the "Unplayed" playlist on R3, trying to get my rank up. I've got it down to about 34 hours of unplayed songs... clearly making strides. It's really fun though, grinding an hour every night. I'm not sure if it should be though, I remember not too long ago the idea of grinding in a rhythm game seemed repulsive to me, but I can see it has some merits. I kind of impress myself with my sight-reading abilities, if that's what you call it. It is also surprising how rarely I have to mash. If I had the setup for it, I'd start streaming this. I think there's something to be said for just pure sight-reading, maybe it would be interesting to watch.

Another thing, suddenly today I became interested in the mass of data that is "level ranks". If only I had some way of determining the quality of my best score, besides looking up each max score individually. Hmmm... Maybe if I had the score formula, I could sum all my perfs, goods, etc. and determine the max score that way... Hell yeah, I found it: http://www.flashflashrevolution.com/vbz/showthread.php?t=120994

So, I wanna use this to calculate what my approximate skill level is by weighting each level difficulty with the percentage of max. I'll try it both ways with raw score and combo, see what happens.

Okay, I weighted it three different ways and got three interesting numbers:

Difficulty x Times Played: 35.99
Difficulty x Average Percentage (combo score): 34.80
Difficulty x Average Percentage (raw score): 40.13

Of course the raw score is more favorable, but I like that the combo score also seems to align with the "Times Played" average. The the logic of Difficulty x Times Played is that one prefers something on or slightly above his/her own skill level.

Also interesting is the fact that if you take all of the songs on the site and take an average of the difficulty you get an average skill level of 48.26, with a median of 51. Assuming it is valid, the combo score would put me in the 28th percentile, and the raw score would put me in the 35th percentile.

BUT, the two weighting methods with which I used average percentage may not be as valid as using a sum of the percentage, which would more effectively account for having played multiple songs of a particular difficulty (rather than taking an average per difficulty). Using that method I get:

Difficulty x Sum of Percentage (combo score): 32.54 (26th Percentile)
Difficulty x Sum of Percentage (raw score): 35.90 (30th Percentile)

I find that this sits with me a little better.
BUT, then, using either of these methods with an empirical percentile would do little to account for an individual who has AAA's on all songs, perhaps there is a theoretical maximum that one could compare this to? Full AAA's would likely just give someone a rank of 48.26 (the average rank for all songs).

I could find the maximum possible weighted sum of having 100% in all songs, and compare my weight to that to find a more meaningful percentile. However, to avoid the conundrum of taking in to account songs I've never played (like average rank does), I should only acknowledge songs I have scores for. This seems very similar to the effect of just taking an average of my percentages, but perhaps it will yield significant results.

Ah yes, much different than taking an average of my percentages, I find that my max possible weight is 24723 (difficulty x #of Songs x 100%). The max possible weight of the entirety of songs available is 75580, and the weights of my combo score and raw score respectively are 14459 and 20803. Using my personal max possible weight would give me percentiles of 58 and 84 respectively (massively different). This (theoretically) is an indication of my skill as compared to someone who has played the same songs as I have. Using the max weight of all public songs, I would have percentiles of 19 (combo score) and 28 (raw score).

I'm still not comfortable picking either combo or raw score as a preferred indication of skill. The combo method seems more skill-oriented, to counteract the effects of scores that reflect mashing, but then again, if I do nothing but sight-read a bunch of songs, there's no way I'll be getting FCs. Also I'm pretty sure the whole combo score vs raw score is still hotly debated by some, so I'll just put that issue to rest for another time.