Analysis: is "0.81893" really the best zoom sensitivity?

.818933 - Master Race?

I recently stumbled across this post, a mathematical analysis of the zoom_sensitivity_ratio_mouse command in CS:GO. The TL;DR of that post goes as follows:

Many people set their zoom sens to "1.0", since this should align with their rifle aim. However, if zoom_sensitivity_ratio_mouse is set to 1.0, it is not a true 1:1 ratio when you are scoped in, due to the FOV difference in weapons.
This means that your scope sensitivity with a scout is different than with the AWP, and each of those are different from scoped rifles, and none of those are the same as your rifle.
The "real" sensitivity that matches your un-scoped sensitivity is 0.818933027098955175 , but since CSGO only cares about so many digits, ".818933" is good enough.

So that's it, right? Set your zoom sens to ".81893", and forget about it?

Well...

It looks good at first...but there is one claim in this thread which raises some serious questions. That is the following:

Here is what a zoom sensitivity of 0.818933027098955175 does:

It does the opposite of 1.0, which lets you flick accurately over a huge distance for those sick MLG plays, while 0.818933027098955175 lets you flick accurately over smaller, more realistic distances.This is more important in most situations since the target tends to be closer to the crosshair than the edge of the screen.

In other words, if you aim at something close to your crosshair, then it mirrors your rifle (non-zoom) sensitivity perfectly. But if you aim at something further away, it will be less accurate.

Green is more accurate, Red is less accurate

If you were to use a ratio of 1.0, this thread argues that the the opposite would be true:

So your "short" flicks aren't the same as your non-zoom sens, but long-range ones are!

"Got it, so if I'm Woxic, use 1.0, and if I'm Device use the 8-point-whatever? tnx x0tek, ez global"

The Problem

Not quite. You see, what I just said can't possibly be true. Here's why:

Let's say you're using the .818933 sensitivity, and you peek out with your AWP scoped in. The bad guy outside of the "accurate" range of your scope!

AAAAAAAAAAAAAAAAAAAAAAAAAAAAAAHHHHHH

But, let's say instead of instantly flicking to the bad guy, you instead flick to the very edge of your "accurate" range; like so.

Whew

So now he's in your "accurate" range. You flick again - this one also perfectly accurate. Naturally, you get the shot, ez global elite major champion.

But hey, wait a second. What happens if you do these tiny flicks really, really fast? How can a long range shot be inaccurate, but if you take it step by step, it's accurate?

And that's exactly it.

You don't have to do these flicks slowly - in fact, you can do them so fast that it's basically one flick! And if at every step along the way you're perfectly accurate, how can the end result be inaccurate?

There's some weird math here involving infinite series that prove this point, but it's also intuitive.

In other words, the fact that an "inaccurate" long flick can be compartmentalized into a series of "accurate" short flicks means that long-range flicks must always be as accurate as short range!

Unless...mouse acceleration?

So what does this mean?

This means that either the assumptions of the original post were flawed, or there is mouse acceleration built into the scope sensitivity of CS:GO.

I don't have the technical prowess to test the latter, only the Microsoft Paint skills to consider the former.

However, given that this post was made 4 years ago, and I've seen no further discussion of it since, I figured it was important to address / clarify! I spent some time looking for answers on my own, but couldn't find any :)

TL;DR

Either some of the assumptions underlying the ".818933 master race" argument-thread are inherently flawed

CS:GO's zoom sensitivity ratio calculation adds in inescapable mouse acceleration.

In either case, further research by smarter people is needed.

Conclusion (after reading all the replies)

So, let's get down to the questions posed above!

0.81893 is NOT the zoom sensitivity closest to your rifle sensitivity.
The "actual" zoom sensitivity that replicates your rifle sensitivity is somewhere between 0.81893 and 1.00.
The closer you are to 1.00, the more accurate your long-range flicks will be.
However, since 1.00 is most accurate at ranges outside of your scope Field of View, it may make sense to lower the upper bound slightly, such as to 0.92, since this reduces the discrepancy at the edge of your scope rather than a projected 4:3 box.
The closer you are to 0.81893, the more accurate your micro-flicks will be.
However, since 0.81893 is only accurate at incredibly microscopic adjustments, it may make sense to raise the lower bound slightly, such as 0.83, since this increases accuracy at the mid range without introducing much error at the lower end.
If you want your mid-range flicks and fast tracking to feel closer to your rifle, a more "middle of the road" number is likely to be your fit: such as 0.85, 0.89, etc.
There is no zoom sensitivity that perfectly replicates rifle sensitivity!
There is no inherent mouse accel, the discrepancy of distance is accounted for by an accumulation of error as you change the angle you're looking at.