Correlation between mouse sensitivity and size of the targets ingame (focal length)

[Dribbler]

 Hey there. Recently i came up with the question if  the size of the picture/targets ingame (focal length) should be also considered when comparing sensitivities?

 As far as we allready know even same cm per 360 but on different FOV would give you completely different feeling. For example 20cm/360 on fov 80 would feel like much much faster sens then 20cm/360 on fov 120. For the same reason you dont want your cm/360 to be the same when in hipfire and zoomed modes and sens ratio scaling exists for that matter. Same goes why monitor distance is more superior method to get consistent mouse feel across different games then just raw copying cm/360 from game to game.(Even though its still arguable which one is better 0% monitor distance, 75% ,100% or whatever but we can clearly state that fov factor matters when we comparing sensitivities)

 Now lets think of an opposite factor. The higher the fov the smaller targets appear on your screen making them in theory harder to hit since you need to be more precise which leads to a question if sensitivity should be lowered accordingly to match the same feeling? For instance we compare settings of two players, both of them have same monitor size, use same screen resolution but they have different FOV which means their visual perspective of an objects on the screen would be different in game and we can calculate  how big they appear for them by using Focal Lenght calculation (that is rough and technically incorrect explonation of what focal length stand for but still  we get actual number of pixels as the result of that calc which kinda represents the size of objects) So knowing that focal length values, lets assume its 1000 pixels for player1 and 500pixels for player2 is it fair to say that if player2 wants to match player1's mouse feeling without changing his focal length he would need to lower his sens by 50%?

Any thoughts on this? Would be appreciated

[Drimzi]

Yes, sensitivity is tied to focal length.

You can measure the focal length with pixels, which is a physical measurement since they also have a physical size. So different monitors will need different field of views to end up with the same focal length and sensitivity.

The focal length is basically the radius for the spherical image. A high focal length will be a large radius, resulting in a large sphere, and since the monitor size is fixed, it will result in a smaller portion of that sphere fitting inside the monitor space, resulting in a lower fov and an image that has a lower curvature. A shorter focal length is the opposite. Curvature plays a huge role in how the sensitivity feels, which is why even a perfect conversion (0%) to a different focal length still feels different. 2D would be kind of equivalent to an infinite focal length, as it is an image with no curvature.

The ratio between the spherical representation of the sensitivity (measure as cm/360 degrees), and the spherical representation of the image, is the actual sensitivity, the 'Control-Display Ratio'. This is often expressed as 'Control-Display Gain', which is how much faster or slower the output is compared to the input. This actual sensitivity is a constant value as long as you convert using 0%.

You can find your actual sensitivity using this. The defaults in the calculation is a result of doing a desktop to csgo conversion using 0% for a 24.5" monitor at 1920x1080 and 400 CPI, which results in an identical 2D and 3D Control-Display Gain of ~4.45. Someone may think to themselves that a 1:1 Control-Display Ratio would be optimal, but it will feel incredibly slow, even for just 2D, which is probably due to the mouse mass, friction, etc.

 

Also here are some useful visuals and links:

 

Graphical FOV Converter

 

Spherical representation of sensitivity and image at high and low fov.

 

Small monitor, small fov, large monitor, large fov. Same focal length. Same cm/360°.

 

Same fov, different monitor size. Different focal length. Different cm/360°.

Edited January 17, 2019 by Drimzi

[Dribbler]

Thanks for detailed response and explanation! 

The fact that monitor diagonal also depends on the way mouse sensitivity feels was counter intuitive indeed, cause from my own experience it felt absolutely the same without any diviations to my regular aim accuracy either using 19", 24" or any other monitor size as long as aspect ratio is kept the same. The only thing changed was the visual perception of the picture on  display, like its being harder to keep edges of the screen in focus for eyesight on larger monitors so distance how far you sit from the monitor had to be adjusted accordingly.  But seems like techincally monitor size also plays sufficient role in those calculations 

Edited January 17, 2019 by Dribbler