Vertex BETA vrofl Difficulty Level (hypothetical)

[URL]

Introduction

Vertex BETA vrofl is classified as a Lv. 255, the hardest file in the game by far. However, when looking at the statistics, something looked odd. It seemed as if its actual rating should be much lower.

Now, I do understand why the 255 figure is there: That shit's insane! I can't imagine any human actually AAA-ing this ever (hopefully more experienced players will agree). But the thing is, if we plug the MAGIC AAA Equivalency formula into some of its top scores, things go quite wrong.

Of course, before I can even talk about plugging in the MAGIC AAA Equivalency formula, we need to make something clear:

This is all purely hypothetical.

Simply put, vrofl is a way different beast than what the formula was made for. So any final result should be taken with a whole bottle of salt. Without further ado, let's dive right in!

The MAGIC AAA Equivalency formula

AAA Equivalency is meant as a way of measuring the skill of a given player. The process is simple enough. You play a level of difficulty D, you get a number R of raw goods, and your final AAA equivalency, E, is given by

,

where 𝛿 is a quartic polynomial in D and α, β, λ are constants. Your top 15 equivalencies are then added with given weights to give your Skill Rating. Easy enough, right?

However, let's say you know your Skill Rating already. If you are able to get a number R of raw goods in a song, you can use it to calculate the difficulty of the song. In theory.

In reality, when playing a song too high above my Skill Rating, the AAA Equivalency I get is always underestimated. And when I play a song too below it, I usually AAA it easily, capping the AAA Equivalency at the difficulty of the song.

So, if we want to get anything useful out of this, we need to make some unrealistic assumptions. The ones we'll use are the following:

• The AAA Equivalency formula is perfect.
• Players' Skill Rating when their top score at vrofl was achieved is the same as its current value.
• vrofl can be realistically rated.

We can now actually get to work. We'll first realize that getting D explicitly via our formula is impossible. Those exponential functions and the quartic polynomial just make it too hard. So instead, we'll settle for something else.

We'll first take the Raw Goods for the best scores on the song. We'll then substitute values of D from 1 to 1000 (it's quite reasonable to assume this isn't a Lv. 1000+) to see which gives the closest value to the actual Skill Rating of the person who got that score. Rinse and repeat.

Results

After plugging in the Top 25 scores (excluding users that had been closed their accounts because that's sketchy), we get a difficulty level anywhere between 169 and 185. Definitely not 255.

If you want to see the results yourself or try something similar, here's the link to my Excel file: https://mega.nz/#!nslhgYza!QXEhuW6eS...Els4iknwfLiNbo. I used macros to implement the Best Fit Difficulty function, I won't hijack your computer or anything.

Note: Plugging in the stats to any other level will give analogous results. Although, levels with more than, say, 10 AAAs will probably not work very well.

So yeah, this was my experiment. I had fun. You can comment down below.