Yet another monitor distance formula variant

[TheNoobPolice]

I thought I'd share a formula I have used that matches my own preferences pretty perfectly for a "one size fits all" scope zoom scaling, (an updated "uniform soldier aiming" if you will, for games that use many scope zoom levels).

As many of you agree focal length or "0% monitor match" is the mathematically principled way to scale, with arbitrary monitor distances effectively being just a hack to mitigate the natural slowdown effect that zooming-in creates when using focal length scaling. 

While playing games like Battlefield 4 / 1 or the newer Cod's, I always ended up with the coefficient set to 0% for low-zoom scopes, and then each scope's individual slider gradually increasing in sensitivity the higher the zoom level.

It was always fairly apparent to me that commonly used monitor distances like vertical 100%, 133% or especially 178%, are too fast at low-mid zooms of irons / red dots etc, whereas focal length scaling is always much too slow at high zooms / sniper scopes. I think this experience is also shared by many others.

So I have taken the monitor distance hack a step further to allow what is effectively a dynamic coefficient via a simple calculation based on the start and end FOVs. This is nothing new of course, but unlike other variable methods like Viewspeed or Jedi's trick that also do this, it scales much more broadly by comparison. Converging to focal length scaling for the lowest zooms, and approaching an asymptotic monitor distance limit at an "infinitely high zoom" (or a hard cap).

Here's a graph of the formula with regular 133% vertical monitor distance and focal length scaling for comparison. By replacing the monitor distance coefficient with simply Limit*(1-(ZoomFOV/HipFov)) the coefficient approaches a value of zero when the two FOV's are close together, and gradually approaches the limit the more they diverge.

https://www.desmos.com/calculator/rlrmeml65f

If you enter the hip and zoom vFOV's with the sliders, the graph will calculate a monitor distance based on the variables entered for any games ADS FOV level exposed on this site.

A limit of 2 would mean the maximum monitor distance is 2 for when "zooming to infinity" - the transitional shape would then be like a logit function with the midpoint of 0.5x zoom sensitivity multiplier occurring at exactly half of the base FOV (i.e coefficient of 1 at the midpoint). This value probably makes the most sense, but I personally prefer a limit of 1.5, as seems the most appropriate for the zoom amounts we tend to use in games. As an example, this results in the highest zoom scope I used in BF4 having roughly 130% mdv, and the red dot sights having around 14% mdv when scaled from hipfire. The power could be raised to stay closer to focal length scale before approaching the monitor distance limit, but probably best to leave at or around 1-2.

This is still just an arbitrary solution of course and I am not claiming it is objectively better than any established method, just an approach that very closely approximates my own preference formulaically - with pre-set limit / power of 2 I do believe it would be better for users as a "one click" option than the existing relative / USA with coefficient options.

Edited June 5, 2022 by TheNoobPolice

[MacSquirrel_Jedi]

Hi im working on standalone utility  "mouse sensitivity graph" and just today it starting to get a shape. It will allow you to compare all aims in one graph (the monitor distances). Everyone will be able to compare their ideas.

Can you provide me a 360° distances for each aim of your or any game here with your method?

[mlem]

Been using this and I like it.  Would be good if it could be integrated into this website to automatically calculate the figures as it a bit tedious calculating every scope value. 

Good stuff. 

[TheNoobPolice]

On 6/28/2022 at 7:57 PM, MacSquirrel_Jedi said:

Hi im working on standalone utility  "mouse sensitivity graph" and just today it starting to get a shape. It will allow you to compare all aims in one graph (the monitor distances). Everyone will be able to compare their ideas.

Can you provide me a 360° distances for each aim of your or any game here with your method?

You can just divide any base hipfire 360 distance by the graph calculated "zoom sens multi" to arrive at that for any target FOV and configured variables, if you wanted to calculate by 360 distance instead of monitor distance.

7 hours ago, lolngoway007 said:

Been using this and I like it.  Would be good if it could be integrated into this website to automatically calculate the figures as it a bit tedious calculating every scope value. 

Good stuff. 

afaik the calculator here doesn't support a method where the user could tune 3 variables for a scaling method (although perhaps only 2 are needed; cap could be omitted most likely), so it would be a case of hard-coding specific parameters that make sense (of which I would suggest both Limit and Power set to 2) but the intent is really for the user to find their own preferences by feel, and "map" those closely via the coefficient curve that they can then use again in the future as a shortcut, as it is clear you have done. My own preference of limit 1.5, power 2, just so happens to be extremely close to where I set all the BF4 / BF1 scopes by feel that I am extremely used to, so this then functions as a barometer for me with at least slightly more logic than just "set everything by feel", which is of course also a valid approach but hardly the target user of this website

[randomguy7]

I would love this to be added to the calculator, as I can't be bothered to do any of this myself. It seems like a lot of work.

[mlem]

By the way - does the hipfire vFOV entered change what values should be used.

In your default example, it uses hipfire 90 vFOV with 1.5 limit/2power (your personal preference). But say the hipfire vFOV is 55, would it be more ideal to use say higher limit/lower power etc.

I personally use hipfire 73.74 vFOV and the dynamic coefficient looks significantly flatter/not as pronounced at either ends of the hipfire vFOV (1.5 limit/2 power) compared to your hipfire 90 vFOV.

I tweaking the limit/power and trying to determine whether the power/limit have ideal ranges (closer to 1 or 2) depending on your base/hipfire vFOV being high/low, or is this really all just 'preference'?

[Scca]

Why is the max HipFOV 100?

[TheNoobPolice]

On 7/7/2022 at 7:16 PM, lolngoway007 said:

By the way - does the hipfire vFOV entered change what values should be used.

In your default example, it uses hipfire 90 vFOV with 1.5 limit/2power (your personal preference). But say the hipfire vFOV is 55, would it be more ideal to use say higher limit/lower power etc.

I personally use hipfire 73.74 vFOV and the dynamic coefficient looks significantly flatter/not as pronounced at either ends of the hipfire vFOV (1.5 limit/2 power) compared to your hipfire 90 vFOV.

I tweaking the limit/power and trying to determine whether the power/limit have ideal ranges (closer to 1 or 2) depending on your base/hipfire vFOV being high/low, or is this really all just 'preference'?

Well, yes and no. The starting hipfire value does not change how it scales when the target zoom FOV is the same ratio away from it.
zooming from 90 to 45, yields the same scaling as zooming from 70 to 35, or 60 to 30 etc for any values you select, because all FOV's in this example are being reduced by half.

You'll notice this is not the same as "zoom amount" though (which is focal length change). This is because reducing the starting hipfire vFOV reduces the change of zoom ratio when the numerical ratio of the target FOV is the same. 90 to 45 is 2.41x zoom, but 60 to 30 is 2.15x zoom. So you may indeed have a different preference.

Now I think about this, the calculation within the coefficient could change to the zoom ratio instead which would mean that the opposite occurs - the scaling would be consistent on zoom amount regardless of hipfire FOV, but not by the ratio of FOV change.

So instead of:
monitor distance coefficient = Limit * (1-(ZoomFOV/HipFov))^power

it would be:
monitor distance coefficient = Limit * (1-(tan(ZoomFOV/2)/tan(HipFov/2))^power

For what it's worth I always use a hip vFOV of about 84 where available. I would never use this as a way to scale hipfire between games, only for ADS / zoom changes within a game where I have set the base FOV I prefer.

Graphing like this is also slightly misleading visually since they all seem to converge to zero, when in fact the ratio between the calculated sensitivities of focal length vs any monitor distance is larger at the highest zooms, not smaller.

On 7/8/2022 at 1:55 PM, Scca said:

Why is the max HipFOV 100?

The values are just an example, you can enter whatever you want. 100 vertical FOV is pretty high though.

Edited July 10, 2022 by TheNoobPolice

[TheNoobPolice]

On 7/7/2022 at 7:16 PM, lolngoway007 said:

By the way - does the hipfire vFOV entered change what values should be used.

This was actually a really good point, so I went ahead and amended a version that uses the zoom ratio instead. As I mentioned this will maintain the same scaling as per actual zoom vs just the ratio of FOV change, which I guess may be more intuitive if you play games with different base hipfire FOV's.

https://www.desmos.com/calculator/yfn7lpyfbf

This would then scale slightly more aggressively towards the limit with the same parameters set, but you could increase the power to compensate to create similar results to what you had, whilst now maintaining that relationship for zoom amount on different hipfire FOVs.

Edited July 12, 2022 by TheNoobPolice

[mlem]

1 hour ago, TheNoobPolice said:

This was actually a really good point, so I went ahead and amended a version that uses the zoom ratio instead. As I mentioned this will maintain the same scaling as per actual zoom vs just the ratio of FOV change, which I guess may be more intuitive if you play games with different base hipfire FOV's.

https://www.desmos.com/calculator/alu7snosul

This would then scale slightly more aggressively towards the limit with the same parameters set, but you could increase the power to compensate to create similar results to what you had, whilst now maintaining that relationship for zoom amount on different hipfire FOVs.

nice i been enjoying your coefficient method - fiddly but worth it for me. Thanks for the updated version.

[Pyroxia]

Tried it with limit 1.5 power 2 pretty good.

[PressingForward]

Can't believe it took me this long to stumble across this thread. Liking the approach and the values it spits out seem sensible, can't wait to take it for a spin. Thanks, bud!

[Pyroxia]

well I want to keep this thread live. Because it's really usefull so I'm commenting. If really there is a way for this I really wan't to see this method integrated with m-s.com calculator.

[Magico.-]

I wish I could try out this method by having it integrated on this website. Unfortunately I'm a bit lost in all the theory, but would love an easy way to figure out how to try this method in my games.

[DPI Wizard]

Sorry for the long lost reply here, but this is being worked on to be integrated into the calculator

[DPI Wizard]

Should I fix the limit and power to e.g. 2, or try to make them configurable? Fixing them is more user-friendly, but some might prefer to customize it, idk.

Also, what should we call it?

[TheNoobPolice]

I think "Dynamic Monitor Distance" or "Dynamic Coefficient" probably makes the most sense as to what it is doing.

Also, are you going to add the linear scaler version or the zoom ratio scaler version? I think the latter is possibly more useful, but the limit 2 and power 2 was really defaults I suggested based on the former.

@PressingForward had a good suggestion to me of using the existing scale and percent parameters and having them a call a different function when selecting this aim method, so they could directly apply to Limit and Power instead (if the structure of the site allows for it). You could have an max of 3 and a min of 1 for Power, and scale those values from 0-100% in the scale field (perhaps inversely? So increasing it makes the sens scale faster), with the percent field simply setting the target maximum monitor distance i.e limit. This would of course remove the usual function of those parameters for this mode, but it saves any extensive GUI updating

[DPI Wizard]

1 minute ago, TheNoobPolice said:

I think "Dynamic Monitor Distance"

This is exactly what I was thinking too

2 minutes ago, TheNoobPolice said:

Also, are you going to add the linear scaler version or the zoom ratio scaler version?

Zoom ratio.

1 minute ago, TheNoobPolice said:

using the existing scale and percent parameters and having them a call a different function when selecting this aim method

This is also what I had in mind.

Also, for 2D conversions, it will use the limit as the coefficient since 2D essentially is infinite zoom.

[mlem]

This may/may not help but under the v2 zoom scale formula - using power 2.364 provides the same results as v1 fov scale formula at power 2 at the same limit.

 

[TheNoobPolice]

I can't check the math right now, but I'm pretty sure the match point between the two would have to vary when selecting different FOV ranges.

There would definitely be "some value" that was the same between the two though for any individual case, which is why I don't think it would be required to have both.

[mlem]

Yea i should have added, this was only for hipfire vFOV at 73.74 (this is wat i use).

I haven't tried another FOV so perhaps that 2.364 figure is purely for 73.74.

But i've tried limits of 1.5/1.78/2 and at vFOV hipfire 73.74, the power of 2.364 (zoom scaling) matches very closely to power of 2 (FOV scaling). This has been done x1, 1.25, 1.5, 2, 3.0, 6.0 zoom (Battlefield series, COD etc).

I will play around with another hipfire vFOV out of curiosity though. I just plugging numbers and observed that.  =/

[DPI Wizard]

20 minutes ago, TheNoobPolice said:

using the existing scale and percent parameters and having them a call a different function when selecting this aim method, so they could directly apply to Limit and Power instead (if the structure of the site allows for it). 

Actually, since there's no scale field for hipfire and desktop, I might have to add or somehow use another field as a global power or limit. I'll play around with it and see what makes sense.

[TheNoobPolice]

Alternatively, do you think it even requires an entry for desktop or hipfire?

I would personally only ever suggest this for someone wanting to scale all their scopes from one game to another (like for example, a BF player to their CoD scopes when they all use different zoom FOV's)

[DPI Wizard]

3 minutes ago, TheNoobPolice said:

Alternatively, do you think it even requires an entry for desktop or hipfire?

I would personally only ever suggest this for someone wanting to scale all their scopes from one game to another (like for example, a BF player to their CoD scopes when they all use different zoom FOV's)

For desktop, it's not really needed since it's not actually dynamic but fixed to the limit. So we can skip it there.

For hipfire, I think it can be useful though.

[mlem]

13 minutes ago, lolngoway007 said:

Yea i should have added, this was only for hipfire vFOV at 73.74 (this is wat i use).

I haven't tried another FOV so perhaps that 2.364 figure is purely for 73.74.

But i've tried limits of 1.5/1.78/2 and at vFOV hipfire 73.74, the power of 2.364 (zoom scaling) matches very closely to power of 2 (FOV scaling). This has been done x1, 1.25, 1.5, 2, 3.0, 6.0 zoom (Battlefield series, COD etc).

I will play around with another hipfire vFOV out of curiosity though. I just plugging numbers and observed that.  =/

Yep a quick test showed my suggestion is redundant. only applies for that specific hipfire FOV.