Perceived sensitivity

[Cocyx Skeleton]

personally, out of everything i've tried, 0% feels the best to me. i play pretty low sens though (57.5 cm/360). i've never been able to do a full 360 in one swipe in about 5-ish years, so i'm very used to low sens + lifting mouse (even in quake/fast arena fps's). 0% feels especially good for "aimlocking" onto peoples heads across all games i play (even fortnite!)

[potato psoas]

16 hours ago, miaoliang said:

i think 0%mm is not good for controlling  auto mode akm

i think 56.25%mm(Vertical 100%),100%mm is better for game weapon has recoil,0%mm would be better for game weapon dont having recoil

that is why in call of duty,overwatch,people always use 0%mm for ads and zoom sens,and r6,bf1,csgo using 56.25%,75%,100%mm

This just isn't true, it's the opposite. Like MuntyYy said, 0% actually makes it easier to control your recoil. Recoil mechanics happen at the crosshair, and if you have muscle memory at the crosshair, then you can better control recoil at any FOV.

12 hours ago, Bryjoe said:

it's probably a little easier to move your mouse on a fast moving target with 75%, as it simply requires less 360/distance compared to 0% relatively speaking.

As you approach 100% monitor match, the deviation in sensitivity at the crosshair gets bigger. You do not have muscle memory at the crosshair with 75% monitor match. And if you don't have muscle memory, then it's not actually easier. What you may be finding is that with higher FOVs the sensitivity at the crosshair is slower, so you feel more in control. But at lower FOVs, the sensitivity is much faster. Then if you compared the desktop to 90 FOV, you would find that they feel completely different at the crosshair.

[miaoliang]

47 分钟前, potato psoas说:

This just isn't true, it's the opposite. Like MuntyYy said, 0% actually makes it easier to control your recoil. Recoil mechanics happen at the crosshair, and if you have muscle memory at the crosshair, then you can better control recoil at any FOV.

As you approach 100% monitor match, the deviation in sensitivity at the crosshair gets bigger. You do not have muscle memory at the crosshair with 75% monitor match. And if you don't have muscle memory, then it's not actually easier. What you may be finding is that with higher FOVs the sensitivity at the crosshair is slower, so you feel more in control. But at lower FOVs, the sensitivity is much faster. Then if you compared the desktop to 90 FOV, you would find that they feel completely different at the crosshair.

i play a lot of fps game from 70 fov borderland,80-90 fov BF1,WWII,103-106 fov overwatch,,csgo,120fov r6,130fov quake,what % MM do you recommand for matching sens between those games

according to my experience,if i use 0%mm make 70 FOV 45cm/360,and i play for a while ,then switch to 130 FOV game,i feel 130 FOV game sens to fast

100%mm just make the oppsite,70FOV fast,130FOV slow

I have not found the right proportion

what do you think about it

 

[potato psoas]

20 minutes ago, miaoliang said:

i play a lot of fps game from 70 fov borderland,80-90 fov BF1,WWII,103-106 fov overwatch,,csgo,120fov r6,130fov quake,what % MM do you recommand for matching sens between those games

according to my experience,if i use 0%mm make 70 FOV 45cm/360,and i play for a while ,then switch to 130 FOV game,i feel 130 FOV game sens to fast

100%mm just make the oppsite,70FOV fast,130FOV slow

I have not found the right proportion

what do you think about it

 

Yeah, with 0% monitor match, you really can't use too high a FOV. It just becomes too fast. But on the other end of the spectrum, 100% feels too slow at the crosshair. You could use a monitor match around 50% to find a good balance, but if you ask me, this is the wrong way to go around it. You pick the monitor match that helps your aim rather than works best with your settings. The best thing to do with any percentage is to just to cap your FOV. Stop playing Quake at extreme FOV if you care about transferring muscle memory to other games.

[MuntyYy]

How do we determine the distortion in relation to mm% ? Is it the same for let's say 20%mm as it is for 30  ?
#Potato psoas care to explain, why you think 100% mm will be perfect if no distortion is present ?
How about 133%, 200% ? 
And a last thing.. shouldn't we all get used to 100% ( in case its the best possible choice ) and hope for a distortion free virtual environment where a different type of projection is used ?

[miaoliang]

7 小时前, potato psoas说:

Yeah, with 0% monitor match, you really can't use too high a FOV. It just becomes too fast. But on the other end of the spectrum, 100% feels too slow at the crosshair. You could use a monitor match around 50% to find a good balance, but if you ask me, this is the wrong way to go around it. You pick the monitor match that helps your aim rather than works best with your settings. The best thing to do with any percentage is to just to cap your FOV. Stop playing Quake at extreme FOV if you care about transferring muscle memory to other games.

I tested for hours using 50% mm from 70FOV-130FOV

after geting used to the feeling in 80 FOV PUBG TPP,switching to 103 FOV overwatch is still make me feel my sens is to slow

Can you give another suggestion?

[MuntyYy]

36 minutes ago, miaoliang said:

I tested for hours using 50% mm from 70FOV-130FOV

after geting used to the feeling in 80 FOV PUBG TPP,switching to 103 FOV overwatch is still make me feel my sens is to slow

Can you give another suggestion?

You are comparing a 3rd person experience to a first person one, I don't think that's what you are supposed to do.
Try 0%, try 100%, try viewspeed v2  > choose the most comfortable

[miaoliang]

2 分钟前, MuntyYy说:

You are comparing a 3rd person experience to a first person one, I don't think that's what you are supposed to do.
Try 0%, try 100%, try viewspeed v2  > choose the most comfortable

what you say is very reasonable,i m going to test 0%,56.25%,100%,for a couple hours,and then share my feelings with you guys

a new question for you,do you have a method to make 80 fov tpp and 80 fov fpp sens feel same,is there a good formula for this?

[MuntyYy]

56.25%mm isn't viewspeed v2 but could be a good choice.
I never played 3rd person shooters to give you an adequate response. What I can say, is that FOV 80 in PUBG first person is significantly narrower than the same one in CS:GO/ COD.
 

[potato psoas]

5 hours ago, MuntyYy said:

How do we determine the distortion in relation to mm% ? Is it the same for let's say 20%mm as it is for 30  ?
#Potato psoas care to explain, why you think 100% mm will be perfect if no distortion is present ?
How about 133%, 200% ? 
And a last thing.. shouldn't we all get used to 100% ( in case its the best possible choice ) and hope for a distortion free virtual environment where a different type of projection is used ?

I explained earlier in the forum, but basically, if the distortion were corrected then all points of the monitor would be matched across all FOV. You'd do this by stretching the image on the screen to compensate for the difference between eye FOV and ingame FOV. But trying to do it would be messy, so there's really no point.

Also, don't think that 100% monitor match is special...

4 hours ago, miaoliang said:

what you say is very reasonable,i m going to test 0%,56.25%,100%,for a couple hours,and then share my feelings with you guys

a new question for you,do you have a method to make 80 fov tpp and 80 fov fpp sens feel same,is there a good formula for this?

I explain in this post how every percentage above 0% is arbitrary. What is "56.25%" and what is "100%" depends on the dimensions and aspect ratio of your monitor and the distance from your monitor. What matters most with picking a percentage above 0% is how much of the screen you actually want to use.

[Bryjoe]

13 hours ago, miaoliang said:

i play a lot of fps game from 70 fov borderland,80-90 fov BF1,WWII,103-106 fov overwatch,,csgo,120fov r6,130fov quake,what % MM do you recommand for matching sens between those games

according to my experience,if i use 0%mm make 70 FOV 45cm/360,and i play for a while ,then switch to 130 FOV game,i feel 130 FOV game sens to fast

100%mm just make the oppsite,70FOV fast,130FOV slow

I have not found the right proportion

what do you think about it

 

Yeah the best way to is to match FOVs in every game, 0% MM on Quake would probably feel fine for aiming, but the movement would be much faster than you are used to. Matching FOV is the way to go and for that purpose 106.26 FOV or 90 FOV is by most considered balanced and the "standard". In games with poor FOV calculations, but have a lot of scoping or aiming down the sights, I would just recommend matching on 360. Hipfire firing outside of CS and Quake precision usually isn't paramount.

[Drimzi]

So I have been away from home for a few days and have been using a laptop. First thing I did was convert my CPI to maintain distances, but it felt horribly slow. I then converted my CPI again, this time maintaining the same hand:cursor ratio, and it felt normal again.

Since this laptop has some crappy fake 16:9 aspect ratio with its 1366x768 resolution, I changed the resolution to 1280x720, and disabled display scaling so that it doesn't become a blurry mess. I then tested the cursor speed, and it felt completely fine, so I tested 800x600, and again, the perceived cursor speed was the exact same. I didn't even have to change my view distance (distance between eyes and screen) depending on the display size. This leads me to believe that you should not scale the dots moved per inch based on the resolution, unless the low resolution is getting stretched to fullscreen. You need to maintain the same hand:cursor ratio every time you switch resolution or monitor. If you disable display scaling, then the panel size will scale with the resolution, and no CPI change is required to maintain the same hand:cursor ratio.

You can see here that my gaming PC at 2400 CPI (300 DPI) is almost (due to CPI discrepancy) matched to the laptop at 2700 CPI (337.5 DPI). Typical DPI conversion would suggest that the laptop is matched with 1706.6666 CPI instead, which is very slow in comparison. That would only work if the laptop had the same panel size as the gaming PC.

Hand:Cursor Ratio = PanelSize/(sqrt(ResWidth^2 + ResHeight^2)/(CPI * WindowsPointerSpeed * DisplayScaling))

ScaledPanelSize = (PanelSize * (sqrt(ResWidth^2 + ResHeight^2) / sqrt(NativeResWidth^2 + NativeResHeight^2)))

Desktop = 24.5/(sqrt(1920^2 + 1080^2)/(2400 * 1/8)) = 3.3365
Laptop = 15.6/(sqrt(1366^2 + 768^2)/(2700 * 1/8)) = 3.3597
1280x720 = (15.6 * (sqrt(1280^2 + 720^2) / sqrt(1366^2 + 768^2)))/(sqrt(1280^2 + 720^2)/(2700 * 1/8)) = 3.3597
800x600 = (15.6 * (sqrt(800^2 + 600^2) / sqrt(1366^2 + 768^2)))/(sqrt(800^2 + 600^2)/(2700 * 1/8)) = 3.3597

 

You can test this yourself by lowering your resolution and disabling the resolution scaling (in Nvidia/AMD Control Panel, and for Intel set it to 'Center Image') and moving the cursor around. You may find the cursor speed does not change, it's just the resolution shrinking.

 

Since sensitivities are generated using the resolution only, and the 2d sensitivity depends on the physical size of the monitor, then different sized monitors with identical resolutions are going to have different cm/360s. This suggests that the current ideas are flawed, or cm/360 really doesn't matter.

Edited July 8, 2018 by Drimzi

[CaptaPraelium]

Hi guys.

I have been very sick and unable to really work on this recently. I hope to be able to get back to it in a week or so.

Might I ask that if you want to go offtopic, you could please create a new thread? There are a couple pages of 'muh feels' and 'how do I convert X to Y' in here and it's really quite far from the topic of this thread. Makes it hard for me to pick it back up when I recover.

Thanks in advance

[CaptaPraelium]

Life is hard but I'm not dead yet. Just for proof:
https://www.geogebra.org/m/hgbtnmqb

Pink line is monitor match
X axis is monitor height (so x=1 is full height of your monitor)
Purple line shows the slope of the pink line
Hidden stuff is just to confirm that cslculations work out the same if taking into account the distance from the monitor

Have a play with the fova and fovb sliders. Values are currently at 14.8 (BF 4x scope) and 80 (my hipfire) but most insight is gained from very distant values. Try 120 hipfire and 4 for a high zoom. You can see how far it gets from 0%MM, and how quickly.

This is a fun one because it serves as proof of several previous assertions made ITT:
100%(vertical) MM is just division of the FOV angles
Correct sensitivity divider approaches zoom ratio as we approach centre of screen
Correct sensitivity divider approaches 1 (1 meaning same sensitivity for all zoom levels) as we approach 180degrees from centre, regardless of the configured FOV
0%MM becomes increasingly incorrect as the target moves away from the centre of screen
We can quantify an average error in monitor match **
Minimal error for any target at any point including off screen is 100% (vertical) MM aka just divide the FOVs
Different zoom FOVs should be monitor matched to different % in order to minimise the error at any point on screen

** This will be the indefinite integral of f(x) = atan(tan(fova/2)x)/atan(tan(fovb/2)x) with limits 0 and 1. The inverse of that function will provide us with the MOST correct monitor match percentage for the given FOVs. 

Yes, I tried throwing it at wolfram and exceeded computation time. Damn. If some lovely person would like to find that formula, we've got our minimum error formula.... Otherwise I'll re-learn more math and let you know when I'm done

Edited July 22, 2018 by CaptaPraelium

[espe89]

So which conversion method is the most correct for you ?? Im exclusively playing 16/9

 

[CaptaPraelium]

Just now, espe89 said:

So which conversion method is the most correct for you ?? Im exclusively playing 16/9

Well, none of them yet.... The intention of this thread is to develop a new formula which results in the most correct sensitivity.

I don't want the thread to veer offtopic again, but... If I had to pick one right now: Either 0% or 100% vertical (aka in the calculator as 56.25% horizontal at 16:9) Monitor matching.
0%MM gives us the perfect match for the centre of the screen (and therefore perfect tracking if the target never leaves the exact centre of the screen) and if the 3D game were 2D that would be the end of it.
100%(aka 56.25%) gives us a division of the FOVs which results in the correct movement considered as angles, however the distortion on screen means that it is not always intuitive.
100% is also the most correct across the entirety of the game world, however we are usually most concerned with the part of the world which is projected onto our screen.

TL;DR
If you want good tracking go 0%MM
If you want good flicking go 56.25%MM
If you want some rough approximation of "most correct" go 28.125%MM
If you want actual "most correct" we don't actually know yet, and I would love help with the math

[espe89]

well I'm using 100% since long time now, It match at the edge of the screen for 16/9

 

56.25 matches at perfect square 1/1 ? exact ? so X = Y ?

[sidtai817]

I see a lot of members here asking about the optimality of MM%, but from their question I see them claiming that they play with different FOVs in different games. That shows they, and possibly a lot of the "layman" non-nerds, do not understand that the preface of using MM% is that FOV is setup correctly with respect to your monitor size and seating position. If one plays at different FOVs in different games, at the same MM% the sensitivity as well as perception of sensitivity is going to differ, and IMO there is no point in using any MM methods. I think they would be better off picking a sensitivity multiplier and have it divide the 360 distance, then converting it back to ADS sensitivity.

 

The point of this is to say that people need to stick to one FOV across all games in order for the MM method to be useful across them.

 

On the side note I play with 55VFOV across all games, with 0%MM and a 0.77 ADS multiplier on top of that.

Edited July 23, 2018 by sidtai817

[Bryjoe]

17 hours ago, sidtai817 said:

I see a lot of members here asking about the optimality of MM%, but from their question I see them claiming that they play with different FOVs in different games. That shows they, and possibly a lot of the "layman" non-nerds, do not understand that the preface of using MM% is that FOV is setup correctly with respect to your monitor size and seating position. If one plays at different FOVs in different games, at the same MM% the sensitivity as well as perception of sensitivity is going to differ, and IMO there is no point in using any MM methods. I think they would be better off picking a sensitivity multiplier and have it divide the 360 distance, then converting it back to ADS sensitivity.

 

The point of this is to say that people need to stick to one FOV across all games in order for the MM method to be useful across them.

 

On the side note I play with 55VFOV across all games, with 0%MM and a 0.77 ADS multiplier on top of that.

I feel 360 distance is best for  hipfire, third person games or vehicles (unless you are doing a lot of aiming in said vehicle). You should be matching FOV for consistency in both movement and aiming across all your games. On a side note, I am getting really good with the awp in CSGO using 0% matchmaking for about 4 months now. The flicks are amazingly consistent. IMO 0% MM is the "holy grail", but you should also be trying to match your FOV on hipfire if you can. 

[CaptaPraelium]

I need a break from the math so I'll explain the above in more depth.

As discussed previously ITT, there is no perfect way to convert sensitivity between FOVs, so the only way to have consistent sensitivity is to always use the same FOV. Since that's not possible for weapon zooms (every game zooms differently) setting the same hipfire FOV between games makes a lot of sense, since it's often the ONLY thing that can be perfectly matched. That being said, what is a useful FOV for one game may not be suitable for another, so as strongly as I would recommend setting the same hipfire FOV, I wouldn't judge anybody who chooses not to.

Also, and on a related note, there is a strong argument for using ~55FOV as your hipfire FOV because your peripheral vision extends from around this angle, and it is our natural inclination to position ourselves from our monitors so as to have the monitor fill our active vision and we achieve an actual FOV of around 55 degrees. That being said, while it may be optically superior to do this, it presents some limitation on our awareness in-game, not to mention, that there are advantages in such matters as recoil control, in using higher FOVs - because the higher mouse sensitivity requires smaller movements to correct a given deflection of our point of aim - So I certainly don't fault anyone for opting for higher FOVs.

Regarding the holiness of 0%MM, I will explain using the above linked geogebra demonstration; I recommend you open it up and play along, as it makes it easier to see the pros and cons of 0% when you can, well, see it.

First, consider that x=0 (the Y axis) is the centre of your screen. The edges of the screen are x=-1 and x=1. So, you can imagine that you have a target somewhere on your screen, as being somewhere between -1 and 1. There is a dashed white line labelled a(x), right at the top of the screen. That is the divider for 0%MM. Note that it crosses the Y axis at the same point as the pink line. The pink line represents monitor matching at any percentage.

So, let us consider targets at certain positions on screen.

For a target at the centre of the screen, we think of it being at x=0. If we follow X=0 (the Y axis) upward until we hit the pink line, we can see that the perfect match for a target at that position is where the pink and dashed white lines cross, and that's 0%MM.

So let's keep this related to reality, let's say we have a target and we turn to him in hipfire and we zoom in, aimed right on him at the centre of the screen because we are perfect players with perfect aim. Our FOV changes as we right-click, and 0%MM is applied, so our sensitivity is divided by the value at the dashed white line. Sweet. Except we don't control the target, and that sneaky sod strafed because he saw us too, and we do have a reaction time, so let's say we don't react to his movement until 100ms after we see it (because we are just THAT fast because we are perfect, remember?). Given that our target strafes at 5m/s, he has now moved 50cm to the right and we need to adjust our aim before we fire because we're not aimed at his head any more.

So, our target is now at, let's say 10%, which will be on the first grey grid line to the right. So we follow that line up and we cross the pink line, indicating the correct MM %age, before the 0% dashed line. What does this mean? Well, it means that our sensitivity, since we use 0%MM, is a little bit too low, because the 0% divider we have set up is greater than the 10% divider we need, to hit the target. But you know what, it's pretty darned close. 6.46 vs 6.4. There ain't much in it. 0.06*zoom is our error here.

OK well let's say we aren't perfect, maybe we had a late night, let's say we were a little off-centre when we zoomed in on our target, and we took a little longer to react to his movement. Let's say he's at 20%, the second grey line. We follow the line up, same as before, and we're now at about 6.25. OK now our error is 0.2*zoom. That jumped up a lot from last time.

What about if it's more of a flick shot? We're hardscoping a doorway and oh snap, the enemy came through the other door. Have to snap to 30%, the third grey line. We follow it up and now we're at about 6. That's getting EVEN FURTHER from our 0%MM settings. Now our error is 0.46*zoom.

Notice how, the further the target gets from the centre, the more wrong it is? We're accelerating away from 0% being correct. This is where the purple line down the bottom becomes important. It shows us the slope of the pink MM line. As long as that's going away from 0, things are getting worse, faster. The place where that purple line peaks, is the most correct/least wrong, considering the entirety of the game world.

So, as it's saved, that chart shows 80FOV hipfire and 14.8 for the zoom, which is my 4x scope. Let's not be too sensationalist here, let's grab that fova slider and slide it up to say 55, let's say we're using ironsights. Note now that the pink line stays quite close to the 0% dashed white line, for quite some distance out. The purple line is flatter. Things are less wrong at closer FOVs. But OK what about an 8x zoom? Grab that fova slider again and this time take it down to say 4.8. Well, dang. That's not good. The purple line is spikey as heck, and you have to scroll up just to see the top of the pink line and wow, it's a spike. It just touches the white dashed line and then takes a quick trip into wrongville. And what if we have a really wide hipfire FOV? Let's leave the fova slider at 4.8, and take the fovb slider up to 120 for tryhard hipfire. Well, that ain't good, is it? We can see clearly that the more distant our FOVs, the more wrong 0% becomes, faster.

Now we can just go for the least wrong thing, and that would be the place where the purple line peaks, which is insanely close to 100%MM (vertical. I don't know why the calculator uses horizontal. it's 56.25% in the calculator, assuming a 16:9 screen) for most of the time. But that's the least wrong across the ENTIRE game world, including everything behind you. And let's face it, that should be a problem you deal with in other ways (awareness, turning when hipfire, etc). We're much more concerned with what's actually on screen, especially since that is what's effecting our perception of the game world and requires a change in sensitivity at all. If we're adjusting for our sensitivity based on things behind us, it comes at the expense of accuracy to things in front of us, which would be of very questionable value.

So, what we need is a formula that works like the purple line, but only considers the on-screen game world - and returns the peak of that curve, to tell us what our sensitivity should be, to get the least amount of error aka the most accurate sensitivity. No, I don't have that formula YET, (Still taking volunteer help. Anyone? Anyone at all? feelsbadman) but we can make observations from what we have here that will give us some hints: At lower zoom levels, where the zoom is closer to hipfire FOV, the value will be quite close to 0%. As the zoom levels increase, and the difference between hip and zoom FOV increases, the value will depart further from 0%. This comes as no surprise given our intuition and experience with previous testing. Flickshots under high zoom have always felt better at higher MM%. Tracking at low zoom (or by increasing distance from the target as demonstrated in the Wizard's recent YT video) has always felt great at 0%.

So is 0% the holy grail? No. There is no doubt that it has its imperfections as all formula always will. But in certain scenarios, it's darned close, and we can expect my formula to result in values close to the values of 0% for low zoom FOVs. Likewise, while 0% is perfect for a 2D world and fails in 3D, 100% vertical aka 56.25% horizontal @16:9 is perfect for angular displacement, but ignores the 2D projection we are looking at, and angular distance is a thing (see links earlier in the thread), and our eyes will lie to us about the required rotation to a target, so it isn't the holy grail either. But at higher zooms, and when snapping not tracking, it has its temptations.
The holy grail is somewhere inbetween - and it's different for every scope.

Edited July 24, 2018 by CaptaPraelium

[Skwuruhl]

Alright I've been meaning to make a post about it for a while so:

I think it's better to look at 0% as zoom ratio. Like it's not "wrong" (well, mostly) to call it 0%, but imo it's not as accurate. Forget the whole 0% part of it for this post and just consider the zoom part of it.

First, if we ignore the 0%, where do we get the equation? Aside from "the apparent size change" the definition of zoom is the ratio of focal lengths. The equation for focal length is 

However we don't know the working distance only, that it's the same between FOVs. But remember that we only need the ratio of focal lengths to get the zoom ratio, therefore:

And then simplifying

And then you have the equation. You can observe this in-game:

In Overwatch when you ADS enemies appear to be 2.63 times "farther" away: https://imgur.com/a/szjlq

They also become 2.63 times larger: https://imgur.com/a/A0NQG

Scaling sensitivity by this is consistent to how your mouse movements change as an enemy is nearer/farther from you. For example, ignoring zoom entirely for a moment, consider an enemy 10m away moving at 1m/s around you. This means they'll have an angular velocity of 0.1 radians per second. This is the rate at which you'll have to rotate your camera in order to track them. Now consider the same enemy 5m away moving at the same speed: their angular velocity will now be 0.2 radians per second, 2x the mouse movement required to track them. Additionally since the enemy is half the distance from you, they'll appear to be 2x as large, same as the change in mouse movement.

@DPI Wizard demonstrated this in his video: https://youtu.be/00dhyUfcLSY

While scaling sensitivity by zoom ratio, if you stand x times farther away with the same x times zoom, then enemies will appear to be the same size and take the exact same mouse movement to track.

Edited July 24, 2018 by Skwuruhl

[CaptaPraelium]

I call it 0% just because that's what most people call it. I call it zoom ratio when I address you because that's what you call it Same same, different name! 56.25% aka 100% vertical could be "angle ratio" and explain its beneficial aspects much better. I've used the MM %ages above because I'm drawing comparisons between them all.

Have a read of my post above, or actually you're a math nerd you might just be able to construe it from the graphs. It's easy to find certain scenarios where certain formula might seem correct but we know that none of them ever will be. It just isn't mathematically possible. Using that video as an example it looks great. But we don't move when we ADS. If we went from a 120FOV hipfire to an 8x zoom in that example we'd have to move back some 400m before it seemed correct XD And then it would only be correct if we tracked the target perfectly (which is physically impossible), and once the target leaves the centre of the screen it gets to feel way too slow, and at that zoom ratio (>20) it does so very quickly. We've observed this experientially, and now I've shown mathematically why that feeling exists. And I've not even gotten into the perception of the size of and distance to the target resulting from the projection (discussed much earlier in this thread)

But what IS mathematically possible is to find the least incorrect among them all. Your assistance would be appreciated! If it helps any, these are the equations in a form that wolfram likes (I think you use that? I don't know):



Monitor match - C is first FOV, c is second FOV (not even sure how to place variables in there and most letters don't work is the only reason I used C and c), x is monitor height:

f(x) = (tan^(-1)(tan(c) x))/(tan^(-1)(tan(C) x))

d/(dx)(f(x) = (tan^(-1)(tan(c) x))/(tan^(-1)(tan(C) x))) = ((tan(c) tan^(-1)(x tan(C)))/(x^2 tan^2(c) + 1) - (tan(C) tan^(-1)(x tan(c)))/(x^2 tan^2(C) + 1))/tan^(-1)(x tan(C))^2


Just my luck, it won't integrate it for me (exceeded computation time) so I have to do it manually.

 

Edited July 25, 2018 by CaptaPraelium

[CaptaPraelium]

For reference for the non-skwuruhl-level nerds among us, and maybe to help what I'm saying make more sense to skwuruhl because I don't speak mathanese

What I'm talking about here is using this: https://en.wikipedia.org/wiki/Mean_value_theorem
This page has some nice pictures that help it make sense

We can specify the centre and the edges (vertical being 1 and horizontal being 1.7777 or whatever as determined by your aspect ratio) of the screen as a and b in that function, and get our f`(c). I just don't have a formula to get our value for c (and accordingly f(c)) from that. Once we have that formula, what we get is some math that does this:

"I only care about 'this' part of the screen. I want to convert between 'this FOV' and 'that FOV'. What is the sensitivity that will be the most correct, across the part of the screen I just said?" ... and it will spit out an answer.

Basically, we're taking the guesswork out of "Which monitor match percentage is best?". We already know that it's going to be close to 0%. It will just shift outward for high zoom scopes.** But we can quickly look at the graphs above and predict - it won't be much. 0% is darned close.

** Actually it shifts inward toward 0%, but the effect is that it is a number that moves away from the 0% line as zoom increases.

Edited July 25, 2018 by CaptaPraelium

[Drimzi]

People only refer to it as 0% because that is what you have to put into the calculator in order to use that formula.

I have come to the conclusion that chasing a formula that depends on any kind of screen distance is just a waste of time. It is a fundamentally flawed concept, and that geogebra shows that quite well.

0% preserves the differential sensitivity, scaling by the change in focal lengths. It doesn't care about screen distances, aspect ratios, where you measure the FOV, etc. It is the one solution that isn't pseudoscience. I have readjusted all my values to use this formula for a while now, and it is extremely effective. Making a game zoom in and out slowly over time, it becomes apparent how well the sensitivity scales. The mousing motions are linked to the scaling on screen, as the targets shrink and move further away, the motions diminish by the same rate.

I think a lot of us make huge mistakes when comparing sensitivity in different games. We test using identical mousing motions, 180 flicks, etc, at different FOVs, which is going to favour 360 distance, viewspeed, or a particular monitor match % that favours those particular mousing patterns used in the comparison. Shaking the mouse back and forward, doing figure eights, circles, etc, while switching between two completely different FOVs, using 0%, is always going to feel wrong if you expect that constant motion to result in an identical outcome, as that is going to rely on a specific monitor match % that correlates to those specific motions.

Monitor distance matching scales the sensitivity by an arbitrary amount, preserving a distance that we probably don't even need to preserve, if that isn't how we perceive sensitivity. I doubt very much that you judge a mousing distance to a 3d target by using the 2d distance that you see on the screen, and even then it would still be a flawed concept, as that distance will rely on pure vertical movement or a neutral pitch with pure horizontal movement. Monitor distance match only really preserves the pitch distance (valid in at least one direction under all circumstances). There could be an enemy occupying the same pixel in two different scenarios, the same distance away from the crosshair, and it would require dramatically different movements to reach that target if the pitch was neutral in one scenario and looking up in another, basing your flicks off a screen distance will result in incorrect flicks under pretty much all circumstances if this is how we perceive sensitivity.

[CaptaPraelium]

Right, and that's why I'm not using monitor matching. I refer to the results of the formula as a monitor matching percentage because, as you said, that's what people are familiar with, but if you read what I'm talking about, I'm just scaling the sensitivity to the value which produces the least error (ie it is the most correct, mathematically) in the projected view, so that it's not some arbitrary value. Since we're talking about the view projected onto the monitor we can translate that to a monitor match, but that's not what it is really. This same formula can be extended beyond the extents of the monitor or constrained to a portion of the monitor (and not necessarily the centre, either), not that there would be any reason to do that but the point is that it's not based on any pseudoscience or made up numbers and it does not ignore the flaws in any particular formula, instead it accepts that all formula are flawed (an unavoidable fact) and finds the optimal result. What I'm talking about does not care where you measure the FOV, screen aspect ratio, screen distance (well it does care about that but it makes no difference). It simply finds the least erroneous aka most correct sensitivity.

14 minutes ago, Drimzi said:

is always going to feel wrong if you expect that constant motion to result in an identical outcome, as that is going to rely on a specific monitor match % that correlates to those specific motions.

This is exactly the thing I am avoiding here. The fact is that no situation is ever going to be perfect. For example we all know that 0%/zoom ratio/focal length ratio/pick a name, gives perfect tracking. We all also know that perfect tracking is literally physically impossible. If we are to avoid pseudoscience, we must accept that there will always be an error, and then attempt to minimise it as best as possible. That's what this formula does.