CaptaPraelium

The answer is: The distance your mouse travels when you rotate your arm through a 90 degree arc. More than this is bad for your body (over-rotates the shoulder), less than this is bad for your accuracy (lower sensitivity makes for higher accuracy) and your body (over-stresses the wrist).

I treat this as if we have one eye only, and that is our dominant eye. https://en.wikipedia.org/wiki/Ocular_dominance

It does, but here is the tricky part: It does if you use 100% VFOV, but for 100% HFOV it is still distorted - It is distorted by a factor of the aspect ratio (ie 1.77777~ for 16:9 monitors) at the greatest extent, ie, we are converting 180 FOV to 0FOV.. This is exactly the problem I'm trying to solve right now. I know that it's something to do with the tan function distortion and finding the 'middle ground' but I'm not quite sure how to handle the math behind it. I'm searching for a function that scales between zoom ratio, and zoom ratio*aspect ratio, with a tan curve, and 45 degrees along that curve will be the minimum error. I'm no @Skwuruhl

Sorry mate I'm honestly not too sure. I don't dabble in 2D to 3D conversion much yet. This thread is more about conversions between different FOVs in 3D. Once I'm really satisfied with that working, I'll branch out into 2D.

Right, I know what you mean. It didn't quite 'click' in my head until I was reading Valve's document and they mentioned it and I was like "hangon" *punch numbers into calculator* "Holy cow it works" Yeh, honestly I've been completely avoiding this largely for reasons of simplification.I did gloss over it, and I'm fairly confident that since we are viewing a flat, 2D image (even of a virtual 3D world), the binocular cues don't really apply. Which is good because it would make everything really really difficult. https://en.wikipedia.org/wiki/Depth_perception#Binocular_cues Speaking of reminders, you've reminded me of an important thing I've neglected to mention. It's unlikely that what we will get from the above concepts, is a single 'monitor distance' for which we will match all FOV's, as we have with the 'monitor match' method. Instead, what we will probably get is an 'angle match', where each FOV will match the other FOVs only at a given angle (probably 90 degrees as per the tan curve thing I mentioned above, but that will depend on the stuff with ***'s marked on them actually being calculated.) To put this in terms of monitor distance, in hipfire it's likely to be around 100+% (vertical), but in very high zoom it is likely to be entirely off-screen. Don't quote me on this This is the kind of thing which I usually keep to myself until I've formulated and tested and verified it but since I'm trying to be more communicative, there it is. By the way, 0% monitor match and 0° angle match, are the same thing..... 0%MM is still pretty much the basis for all of this.

Being an ex-console peasant, I have the same gift, and I've been very careful to maintain it. I don't have a 'muscle memory' of any significance, since my muscle memory is for sticks not a mouse, and I'm constantly changing my sensitivity in my search for a formula. You're right, there can be no perfect method, at least, not based on monitor distance matching. Because the distortion of the image is introduced by our stationary position relative to the monitor, while the focal point of the image shifts back and forth, the image on the monitor is not an accurate point of reference for rotation. This is well evidenced by the failure of 0% MM which is the perfect representation of the image on the monitor. Me too. The thing is that nobody has really tried before me so I am inventing the wheel here. I have a rare disease and am not able to work on this often, and I'm knowingly biting off more than I can chew, so I stand on the shoulders of giants, in medical/psychological fields as well as gamers here, but there is some leftover which I must do alone (unless others pitch in here as I've invited ) One of the really problematic parts I'm finding, is that I can come up with concepts, do working on paper, but to share my progress takes twice as long as making the progress, since I have to do fancy images and stuff. I'm a lot further along than the thread shows, but it's hard to share. I'll try and give some updates to what I've learned, today, in my replies to you. No. This is a common misconception and one which has led us (and I say "us" as in, me too!) astray. Our brain expects us to move a certain ANGLE from the crosshair, NOT a certain distance. Our brain uses the angle to determine the distance between two objects. The headshrinks refer to this as https://en.wikipedia.org/wiki/Visual_angle . Note in the image on that page, we need V and D to determine S. We cannot expect a movement in distance, because we do not know the distance. We can know the angle thanks to feedback from our eyes. Using 0%MM accounts for the shift in D (refer to the geogebra links above), however it does not account for the distortion introduced by 'faking' the shorter distance (read: zooming the image, rather than actually rendering what it would look like from a shorter distance, or moving your head to the focal point every time you ADS haha) And, that's where this comes in: The reason any sensitivity feels faster at the edges of the monitor is a result of the 'stretching' introduced by the distortion of the image. As we diverge from the centre, the image becomes more and more stretched, so the same angular movement causes a greater distance to be travelled on-screen. Everything starts off slow at the crosshair The reason it feels best at the edge is because the angle of rotation is perfectly matched to that monitor distance, but it will always feel 'off' anywhere else. As discussed above, by accounting for distance, we get 0% MM which is great except for the distortion; and as you'e covering here, the distortion can never be fully accounted for. What we're after here is the 'most correct'. And now we begin to touch on what I've been working on recently.... Now before I get into this I have to say, some of this is untested and unconfirmed. I'll mark those with a ***. Normally, I like to be REALLY fricken sure before I post something here, but I realise that my lack of communication is detrimental and probably moreso than posting a possible mistake....So, I'll post this possible mistake - but I'm sure you'll see where I'm going with this. As I'm sure is obvious by now (so I won't go in-depth explaining why) the distortion we see on-screen is a tangent function. If we consider the sensitivity "monitor matched" at 180 degrees (directly behind us, hence the quotes on "monitor match" because that's NOT on the monitor obviously....), we're looking at something which approaches having no divider for mouse sensitivity whatsoever, as in, the same cm/360 for every zoom level (*** pretty sure of this, haven't finished the math, but I'm very confident). If we consider the sensitivity at 0 degrees (the crosshair), we are looking at 0%MM. You can see this in the geogebra image in my posts above. I have to re-do that geogebra magic to allow for a target that is off-screen, but you can see where it's going. Using that image, I started to suspect that perhaps the formula was as simple as dividing the two FOVs. You can see that at vertical 100% (slide the 'Target' X in that image to the top of the 'screen'), that's exactly what we have. This seems to make a lot of sense, since we've learned that we're not dealing with distance, we're dealing with angles, so dividing the angles of the FOVs seems sensible. And then it clicked, hey this won't work in HFOV. Dividing the two HFOVs does NOT provide the same result as dividing the two VFOVs. A quick spot of experimentation showed me, that if we scale between 0 and 180FOV, we get the monitor's aspect ratio as the ratio between the divided results. No big surprise there, but as I alluded to in my previous post, this got me to thinking: Where is the best place to match? 100% VFOV seemed nice but 100% HFOV breaks that wide open. And then I got to thinking: 100% HFOV is the same thing as 177.77~% VFOV (on 16:9 monitors at least). Knowing the importance of aspect-ratio independent sensitivity (as per my previous discussion and the example of being in a plane or spaceship or whatever, and rolling it over...) This got me to thinking: WHY do we assume that the target is on screen? It's entirely common for me to be in-game, and hear footsteps behind me and have to spin and hit them. Sure, it's not as common as a target roughly in front of me and within FOV, but that has no bearing on what's correct for the formula, it's related to my own movement. The target might be at the right edge of a 16:9 monitor, that's the same thing as being entirely off-screen above me. And oh look, there goes a plane flying above me. Think about things like rocket jumping where you spin 180, fire, then spin back.... As soon as I started thinking about this, examples flooded my head. There has long been discussion about which monitor match percentage is correct, and I am now asking myself, who says it has to be on the monitor at all?! So, we have to find a place that scales correctly, given a minimum sensitivity, as provided by 0%MM, and a maximum, being identical cm/360(***). Which has the least amount of error involved? Well, this is easy if we think of it as a tangent function. At the asymptotes, we have a vertical line, representing maximum sensitivity (same cm/360 ***). that's 90degrees (tan(90degrees)). At 0, we have a horizontal line, representing minimum sensitivity, the 0%MM. annnnd hello 45 degrees. Keep in mind that I am referring to an angle from the centre of screen, so that's a 90FOV. If you consider the average kind of hipfire FOVs people use, this is going to be somewhere just a little greater than 100% VFOV. I'm reminded of the conversation about Battlefield's USA, where they started with what we call 0%MM, and everyone said it was too slow, then they tried 100%VFOV matching and it was almost there, then 100%HFOV but some people found it too fast, and then came to the conclusion that some people feel it differently, and settled on CSGO's 133% as a 'middle-ground'. Believe it, it's true You can see it for yourself, it's been proven, and not only by myself. One way to see it is with the geogebra image I posted above. If you move the 'eye' to the focal point for a given FOV, there is no distortion of the angle from the eye to the target on-screen and beyond. Another more tangible way to do it is by using the high-FOV images from the first page of this thread. Use the formula: opticallycorrectdistance=(heightcm/2)/(tan(hipfov/2)) and move your eye to that correct distance (you'll have your face right up in the monitor!) Look at the centre of the image and note the complete lack of distortion toward the edges. It's funny because I think I've been too easy on it. At first glance (and second and nth, lol) it appears to be perfect. I said early on here, that I expected this thread to validate a previous formula, and not so much to make something new, and to be honest, what I silently expected was to prove that 0%MM was correct. The more I look into it, the more I realise why it feels too slow for everything beyond 0% from the crosshair - because it is the MINIMUM sensitivity across a range of sensitivities which contain the most correct one. As our FOV decreases (we zoom in), so does our range and so does any error in our sensitivity, so it's quite hard to see any error in it. The greatest exposure of any error, is going to be in the way we treat our hipfire FOV.

You're doing it right!

Been busy and haven't had a lot of time to put into this.... Anyway here's the current situation I'm working with: We can see from the graphics above, that as our target deviates from the centre of the screen, the change in angle deviates from zoom ratio.... So, it seems a matter of finding a formula which provides the minimal error. But here's a spanner in the works: WHY DO WE ASSUME THE TARGET IS ON SCREEN Yeh, there's a can of worms. You can probably hear the gears turning in my head from where you are.

Another update to the graphics. As usual, you can grab the points and move them around to see how it changes things. https://www.geogebra.org/m/DyZprxpA Note the text in the orange box. As this grows above 1, movement to the target FEELS SLOW BY THAT MUCH. That number is pretty much the "Why zoom ratio feels bad" number.

Updated geogebra demonstration with a target on screen: https://ggbm.at/QQU5cTeY

Short answer to your question: Mostly because you are used to it. Like you said above, even if we gave KennyS a perfect formula which doesn't exist yet, he'd be better with 75% because that's what he has practised to use. I think it's time to do some pictures..... Sorry, I'm short on time right now so I know they suck but I hope these will do the job OK. If you visit this link, you can see a demonstration of how the usual Zoom Ratio aka 0%MM formula (=tan(fova/2)/tan(fovb/2)) compares to a simple division of the lengths of the focal points of those FOVs. You can grab the FOVA and FOVB points and slide them around to see the numbers change. But our head does not move when we zoom in and out, so we are not viewing the image from the focal point, so although we have perfectly accounted for the difference in image on screen, we have not accounted for the image which reaches our eyes. https://www.geogebra.org/m/ByAfGqzc

Well, that's kinda the point of this thread. 'muh feels' doesn't really have a place here, so muscle memory and such don't factor in.... Well, that's not entirely true. 'muh feels' has a place here, which is in the question "why does 'muh feels' disagree with 0%MM/ZoomRatio?". We pretty much have that answered now, all that's left is to find the mathematically optimal formula which accounts for perception - and when I say perception, I mean optical perception, as in, how our brains process the image which reaches our eye; this is in contrast with perception, as in, the above plus a bunch of subjective experiences like operating with suboptimal sensitivities or whatever. You're certainly right though, that pretty much any sensitivity will work just fine with sufficient experience. Our brains will, and do, make a 'formula' that works. It would be nice though, to put a formula such as that, into a computer, so we can use it across new games and FOVs.

I'm sorry I've been sparse with the updates to this thread. This is largely because it's very time-consuming to make illustrations which are really needed to explain the progress I'm making. I'm old.... I've been doing it with pen and paper and such I might just get a camera and put pics of some of that here, rather than just nothing. Theoretically, 0% is perfect. For the image, on the screen. But what we see, is not what is on the screen. What we see, is on the inside of our eye. This is why 0% feels 'slow'. It does not account for the last step in the game world being projected from the monitor to our eye. We do not have any formula which do so, and accordingly, 0% is the most correct theory we have as of right now. As per the science nerdery posted above, we know that we do not measure distance between two points, in the real world or the game world, directly - as we would with say, a ruler, or by pixels on screen. We measure it by means of deriving the distance from the angle between two points. This is a terrible thing to attempt to explain without pictures, but I'll try, because it offers us two interesting insights. Firstly, it offers some validity to 'monitor matching', and secondly, offers some hint as to why it is that we seem to prefer to monitor match at the kind of percentages which we do. If none of this makes any sense, I'll do some cruddy mspaint to explain it Firstly, let's picture our monitor from above or from the side (it doesn't really matter, but I do it from the side because the games use VFOV) so we have a straight line. Now we need to measure our monitor and our seating position (assuming that your eyes are directly in line with the centre of the screen, which for the purpose of FPS games, they should be). We can use the following formula to find our actual FOV of the monitor. I sit 32.5cm from a 1440p 27" monitor (I can hear my mother telling me that's unhealthy), so mine looks like this: widthpx = 2560 heightpx = 1440 diagcm = 27*2.54 viewdistance = 32.5 <-- ^--- Yep, centimetres because science. Also I'm Aussie You can use inches, just don't *2.54 in the line above. heightcm = (diagcm/sqrt(widthpx^2+heightpx^2))*heightpx actualfov = 2(arctan((heightcm/2)/viewdistance)) = 54.70173510519102597649 Unsurprisingly, valve know their stuff (see links above) and I have adjusted my workspace to bring my FOV close to the natural 55-60 degree FOV where our eyes and brain treat the image as important (beyond this is our peripheral vision where we do not see so much detail but mostly movement, again see links above) So, now we can envision that there is a triangle formed between our eyes (well, our eye. We don't need to worry about stereo for this, so we just use the dominant eye) and the edges of the screen, and the angle from the eyes is as calculated above. Cool. But, let's imagine that angle is increased to say 80degrees (my hipfire FOV). In order for the triangle to meet the edges of the screen, our eyes should be much closer.... and if they are (ie, we move our head closer to the monitor), we see NO distortion. The distortion of the image is NOT caused by the projection. It is caused by the fact that our head doesn't move, to match the focal point of the projection. Here, we start to uncover the real reason WHY we feel the need to change mouse sensitivity when zooming, at all. It's about the amount of angle our eyes need to move, to cover the same amount of angle in the game world. This is distinct from, the distance our eyes move, to cover the distance between two points. Our brain doesn't work that way. It thinks of all distances as angles, which makes sense really, since it's all a matter of feedback from our eyes telling our brain how much they rotated. Now, if we take a few FOVs (in my testing I've been using actual, hipfire, 4x and 8x zoom) and measure out the distances to the focal points, we will have one very close to the monitor (hipfire), one where we sit(actual), one some distance behind where we sit (4x), and one very far behind us (8x). Guess what the ratios between those distances are? zoom ratio. Great And we already know, that Zoom Ratio/0% gives us perfect movement in the centre of the screen. So, why does it fail? Let's say, that we see a target which is half-way to the edge of our monitor. Let us not make the mistakes of the past and think of this as pixels or cm or inches, it is an angle. Our brains all agree on this In my case (using the same formula above and dividing the screen by half again), that's angle= 2(arctan((heightcm/2/2)/viewdistance)) ~=29.00degrees from the centre of the screen. So, now let's put this into effect using our hipfire, 4x and 8x zoom. Our eyes move 29degrees, how far do we need to rotate in game, to aim at this target? (yes, it can be simplified mathematically, but for the purpose of conversation...) We can calulate the focal distance from our screen, for a given FOV, using the following formula: opticallycorrectdistance=(heightcm/2)/(tan(fov/2)) So, I'll do that for my 3 example FOVs: hipdistance=(heightcm/2)/(tan(80/2)) = 20.03463865597708287603 fourdistance=(heightcm/2)/(tan(14.8/2)) = 129.4379759752501060469 eightdistance=(heightcm/2)/(tan(7.45/2)) = 258.21347922131382533488 And now we can just use the same formula above, with these distances, to calculate how far that ~29 degrees of eye movement amounts to, in the game world: actualfov = 2(arctan((heightcm/2/2)/hipdistance)) = 45.52095254923326167504 actualfov = 2(arctan((heightcm/2/2)/fourdistance)) = 7.43098865714869079575 actualfov = 2(arctan((heightcm/2/2)/eightdistance)) = 3.72894033006548981691 Ok that's well and good, but why is it important? This quick example, when we compare the results to those of 0%MM/zoom ratio,demonstrates that as our FOV decreases, the effect of the distortion on angular displacement decreases. So what? well, this tell us that the most important adjustment to our mouse sensitivity, is that made between the widest FOV - which is going to be hipfire - and our actual FOV of the screen from our eyes. As the FOV becomes smaller (higher zoom in game) the distortion is lower and lower and less and less meaningful. So, since we can NEVER make a perfect adjustment of sensitivity for all parts of the screen, because the distortion is not constant across the screen; but we can make an adjustment which is perfect for one part of the screen (this is why there is a percentage in monitor matching and a coefficient in BF and a zoom sensitivity in OW etc)... Which part of the screen is most important? If we say, the centre, then we use zoom ratio. But almost all agree, that 0% feels 'slow', and we know that is because of the angles vs distance thing. If we are CSGO or BF1 defaults, we use 4/3 aka 75% because muh feels. If we're the average OW pro, we use 18%. Why does everyone disagree? Well, if you take the hipfire FOV of a player, and his actual FOV, and work out your ratio from there....suddenly it all begins to line up with what 'muh feels' has been telling us all along. Sure, ANY variation from the optically correct distance from screen, for a given FOV, will introduce distortion; and that distortion will ensure that our mouse sensitivity will never be correct to any given point on the screen..... but the lower our FOV gets, the more zoomed in we get, the less of a difference it makes. The big difference, is that between our wide hipfire FOV, and our actual FOV of the screen.

You're fast mate Thanks!

Little bump @DPI Wizard

tldr present scaling formula only worry about the image on screen and not the image that gets to your eye. New formula incoming.

deleted drimzi's posts

Went searching for some old gold on the forums. @Drimzi What happened mate?

USA uses two different formula, one for C > 0 and another for C = 0. It used to work in the calculator but something's changed.....

Apparently not at all, but that's kinda my point, it makes me ask, why? If I look at a kangaroo 100m away, then scope in on it, it still looks 100m away, just zoomed in. If I look at a bot on screen 30m away, then scope in on it, it looks a lot closer. Or, to be more precise about it... when I zoom out, it looks a lot further away than it really is. Especially when I run a higher FOV. The only real difference in what is happening, is that the image is distorted... and we know now that the only reason the image is distorted - when it hits our eyes, not when it's drawn on screen - is because of our distance to the monitor, and the fact that it never changes when the zoom does. Funny, that. Yeh, there's some swing to it, but there's no doubt those numbers are centred around zoom ratio. Man I would LOVE to see the monitor size and distance from the monitor for those guys. Have a funny feeling that no such stats exist I've done some fun experiments, regarding the whole 'it looks further' thing. If you move away from your monitor when you zoom, to the 'optically correct distance' as valve put it... it totally negates that effect. I've got some sketches here, but no formula as yet. I'm really close to something useful, so I'll probably post some math tonight.

So, I was trying to use the calculator today, and setting sensitivity for Battlefield 1. The Uniform Soldier Aiming Coefficient is set to the default 1.33, but if I try to set it to 0, it just uses 1.33. Works OK for other numbers, just 0 seems to be broken.

What I find interesting about this is that everyone says the same....Whether they be from a background of CSGO 75%, COD 0%, or in my case, thumbstick. There's surely more to it than bias alone... I've got some time to spare today so I might get a formula going and give it a try before I post it here to embarrass myself

Every individual is different. What is a comfortable sensitivity for any individual, comes down to the way their individual body is structured. Just because it's good for you, doesn't mean it's good for him. That's why we have adjustable chairs I'd definitely say there's logical reason to it. Once again it's a matter of body mechanics, mostly, the rotation of the shoulder and the length of the forearm. Once you roll your wrist inward, as when holding a mouse, it doesn't move very far horizontally, so there's but a handful of cm in that. Likewise, your shoulder has it's limits. If you sit up straight and have your arm out straight parallel to your upper leg, you can rotate it inward all the way to touch your belly pretty easily, but to rotate it outwards that same 90-ish degrees, you'll feel a stretch in your chest and/or a pull in the front of your shoulder if you don't move your shoulder blade with it. If you take a look at how far your hand moves during all of this, and limit that distance to where it feels comfortable and easy not like you're doing yoga, it's gonna be about 40ish.

It's not wise to just assume that it's simply fatigue. There's a big difference between 'feeling the burn' (as in, you're exercising muscles more than you normally would) and actual pain (as in, connective tissue damage resulting from an unnatural strain). OP really needs to elaborate here.... or like, see an actual doctor I wouldn't want to be responsible for OP suffering a rotator cuff injury because I told him he's just weak and needs to work on it more. It should be noted that, if OP has an appropriate sensitivity, the fatigue will be evenly spread throughout his entire arm, as in, his wrist will be just as tired as his shoulder, and the burn would be evenly spread throughout the entire arm.

I'm pretty well versed on this subject as I suffer from a disease which directly effects my ability to move, and which is directly effected by my movement. You're talking with a guy who literally tore both arms out of their sockets by using a computer. I'm sure that you'll never be in that situation, but as the guy at the wrong end of the scale, I've had to learn a few things along the way so that I can remain functional. There is no short answer to this. Too low a sensitivity is not good for you (as mentioned above), but nor is too high. There are so many other factors at play, such as your playstyle, diet, exercise, and I cannot sufficiently stress the vast importance of posture. Even with my illness, I can easily play for hours on end without any stress...but ONLY if I do it right. I run a fairly low sens (about 42cm/360), to balance the stress between my wrists and my shoulders, because if it's too high then your wrist is doing all the work and that's bad, but if it's too low, then your shoulders are, and that's bad too. But if I get lazy and slump in my chair, it causes my shoulders to lean forward, which means that my upper arm is elevated higher, and I will get muscle spasms in the back of my shoulder, and it's GG for me. If I get lazy and lean back too far, the reverse happens, the front of my shoulder goes mental, and again, GG. Your body is well designed for lots of movement, but most of it is only designed to move in a certain direction. A good example a physiotherapist once gave me, is in the hands. Take your outstretched hand, now move your index finger to touch the palm of your hand. Note how far it moves. Now, take your outstretched hand, and move your finger side-to-side to touch the fingers next to it. Note how far it moves now. Much less, right? That's because your fingers aren't meant to move far like that. If you're making your body move as it is designed to do, it'll do it very well, and a lot....but if you try to twist it in some direction it doesn't like to go, it's gonna hurt. Like I say, you aren't likely to suffer from these kind of mistakes, to the degree which I do, but they still have the same negative effect, and as any sports instructor will tell you, if it's hurting, YOU'RE DOING IT WRONG SO STOP. It may just be that your general fitness is not so great, and that your muscles just aren't up to the task, but even if this is the case, punishing small areas of your body is not the right way to build muscle strength. Muscles need to balance each other out, you can do dumbbell curls all day and get mad biceps, but if you don't work your chest and triceps and back and neck and hips and legs, somewhere along that chain of muscles you're going to develop problems. If you like, you can describe in more detail the arm pain your'e experiencing (what kind of pain, where exactly (be super-specific!), what movement makes it hurt more,etc) and I'll be able to take a pretty good guess as to why, and suggest some things you can do to mitigate it. If I were a gambling man, I'd take a bet with pretty good odds, that it's not your sensitivity, it's that you sit badly.