[Backer Build 1] Shot Circles and the Bell Curve

After playing a bit it felt like my shots tended towards the edge of the yellow circle more than being a truly random dispersion inside of the circles, though I thought it might just be confirmation bias. After coming here I’ve seen that the dispersion inside of the circles is actually based on a bell curve which causes the shots to gravitate towards the yellow circle with shots more towards the center or red circle both being far more rare. PLEASE don’t go with this type of a dispersion system as it is incredibly frustrating the more inaccurate your gun is.

World of Tanks used to use a system that likewise caused a large number of shots to land at the edge of the aiming circle and the players found it highly frustrating. Eventually they changed it to a truly random dispersion and the playerbase found it far more enjoyable (though if you go there the playerbase does still have complaints about accuracy but it’s different from the old complaints about shot spread).

Likewise I think players here would find it more enjoyable if it was a truly random shot dispersion. It isn’t really fun to aim at a target, have a large chunk of the target covered, but then have a disproportionate number of one’s shots go more towards the yellow line. It’s even worse with the Machine Gun which is already so inaccurate AND can’t move very far while still being able to fire.

This whole hidden Bell Curve system also can greatly affect how one would want to aim. A standard player is likely to try and maximize the interior of the circle being where they want their shots to go, while a player who actually understands this system is going to maximize the yellow line since that’s where the majority of shots actually gravitate towards instead of simply landing inside of. Which in turn puts the standard player at a disadvantage and is likely to make them feel as if the game is “rigged” against them as their shots aren’t really going where one would expect.

TLDR, please consider implementing a truly random shot dispersion system as opposed to a bell curve system.

EDIT: As I’m off to bed now I’ll try to grab some SSes tomorrow (if I have time) of different aiming shots to illustrate what I’m talking about in regards to maximizing aiming for the bell curve vs random dispersion.

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TBH, the need to deprioritize the center or crosshair as a highly unlikely spot to be hit, and prioritize a ring around it as more likely feels weird. I guess it does provide some interesting gameplay moments at times - to choose the perfect aiming position by aligning the center of crosshair to where you don’t want your shots to go, but… it feels wrong.

On the other hand the 50%/100% hit chance ring is a wonderful idea. Considering many enemies are usually a long distance off and you rarely get a guaranteed shot, then it does not make the game too easy, but it does seem to solve the dreaded “99% hit chance shots missing” known from firaxis series.

More intuitive would be if the chosen distribution would be based on a strict rule like:

Any shot is more likely to land where the player aimed and increasingly less likely to land farther from it.

It may be quite close to equal distibution within the 100% ring to not make aiming too simple but a player should still aim where they want to hit. I believe it would be a lot more intuitive and cause less player frustration compared to the bell curve ring-model.

Indeed it feels counter-intuitive to prioritize the yellow circle and deprioitize the actual center when aiming. One should be aiming at what they want to hit, not aiming off to the side to maximize the middle ring.

And yes I very much like the rings. My complaint is just how shots are distributed inside of them.

Going to A:IW in a bit and just got off work so I’m unsure if I’ll get to those SS today.

I have a bit of time to work on this feedback so here goes. Below is a comparison of the old vs new WoT aiming system after 3,000 shots in each.


While this isn’t a bell curve system we can clearly see how the shots had a strong showing along the ring (in this game that was the outer-most accuracy ring and yes even then shots would occasionally be outside of it somehow). This in turn wasn’t fun for the players as that red ring is ~20% of all shots taken, so the system was changed. In the new system we can see that while there is still a mild ring at ~75% of the max radius, the shots are a lot more evenly spaced out.

Now this isn’t to say that the system illustrated here isn’t without flaws. Rather than having an equal chance of shots landing anywhere we can see that they gravitate towards the middle and then at the ~75% spot. This in turn means that guns which are supposed to be inaccurate were far more accurate than intended.

Without a graphic like this for PP accuracy it’s hard to say exactly how bad it is, but with a bell curve we know that the middle should be far more sparse than this, with the shots getting thicker towards that solid line (which would be akin to the yellow line or the top of the bell curve) and then becoming sparse again as we move away from it (so towards the red aiming circle).

Off to the movies now, next time I should be able to get SSes from the actual game to show how this affects how one “should” aim to account for the bell curve vs how someone would naturally aim if not trying to game the bell curve.

Movie over and screenshots taken (A:IW is a good movie for any who haven’t already seen it). Below are the two screenshots of me aiming at a crabman.

The first screenshot “looks” like the better target. I’m aiming at what I want to hit, the shield eats up maybe 25% of the yellow, and the target mostly fills in the yellow. That said, because of the bell curve the second screenshot is likely the better shot even though I’m aiming at the shield and the shield covers up roughly half of the yellow.

So what’s the difference? The unseen shot distribution. With fewer shots landing in the middle that means that fewer are actually going to land on the crab in the first shot or the shield of the second. Likewise the second screenshot is placed to try and optimize the top of the bell curve, which is just to the left and right of the yellow ring. This compared to the first screenshot which, while filling in more of the inner “50%” circle has actually pushed out the band where the majority of shots actually land. To better illustrate this below is the same two screenshots but with two circles drawn on to represent the “band” where the majority of shots would land (note that these were drawn in paint, I’m not an artist, and it is merely for visual representation as I have no clue what the bell curve that is being used actually looks like).


And it is these screenshots that probably best show my concern with using a bell curve system as opposed to actually having it be random dispersion. The top one makes the most sense for naturally aiming at the target. But when we evaluate it we see that we lose a lot of the target due to it being “too close” to the center while a good chunk of the “band” has been pushed off of the target (I should have used a color besides black for this). In the second shot we can see that it doesn’t matter that we’re aiming at the shield and that we’ve managed to keep more of the crabman inside of the shot band.

Now all of this might be moot depending on the curve used but with knowing that a curve is used this is my concern. The curve’s shot band isn’t adequately displayed, the fact that such a thing is used is hidden from the player, and once a player knows of this it promotes counter-intuitive aiming in order to best optimize one’s shots. The curve might be fine for guns like the mini-gun which are inherently supposed to be less accurate (at which point its accuracy should be “improved” a bit to make up for this shot band) but in general I think it will be a source of consternation for many of those that know of it and a source of “the game’s rigged” complaints for those that don’t.

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Please kill this discussion. It’s based on misguided speculation.

If your so dreaded approach of having the densest hit distribution along the yellow circle, or indeed at any other point that the centre, has been implemented, this is indeed horendous, but as of now there is absolutely no evidence of this.

This is all rampant misunderstanding based on a statement from @UnstabledVoltage saying there is “a bell curve”, and that “hits close to the yellow circle are the most likely” – yes, of course they are, as there are many more points along the yellow circle than in the centre, and so the statement is easily true even though the most likely point to hit, i.e. the point where the probability distribution is denser, is the centre. This is exactly how it is for your “dispersion case” above, too, and this is probably what they’re already using. Anything else would be plain stupid, and I have no evidence these developers are just that – rather the opposite!

Do you think it’s more likely to hit exactly one point, which it is very likely to hit, or any one of thousands of points which are each slightly less likely to hit? The answer is obivous.
The one very likely point is, of course, the centre, while the thousands of slightly less likely points lie along the yellow circle.
The bell curve determines the likelihood of hitting each point. It can be at its highest in the centre, but still allowing the yellow circle to the most common place to hit, because it is a much larger target.

A bell curve is the result of (random) dispersion.

No, a bell curve is NOT the result of random dispersion. Random dispersion means that the shots would be just that. A bell curve dispersion means that while shots “can” land at the center/edge of the aiming circle, they’re most likely to land at the crest of the curve. In one of the other discussions on this board it has already been confirmed that a bell curve dispersion model is used.

The bell curve dispersion means that there’s going to be a band away from the center but not at the edge that has the majority of shots land in this area. By dividing this band in half it means that 50% of your shots would land inside of it while 50% would land outside it (aka the yellow and red aiming circles we see in the game), though realistically the majority of you shots would land inside of a small band to the left/right of the 50% line. How small or large this band is depends on the slopes of the curve and how long it holds the plateau for.

Likewise you yourself are speculating that what @UnstableVoltage said isn’t what he meant and isn’t how the game works. If an actual dev wants to chime in and state this is all wrong then great! But based off of what it seemed my shots were doing in game, what others have stated, and even another discussion on this very forum about this subject, this is my feedback on the matter. Feel free to disagree but please provide information/data actually backing it up.

I imagine this is what it feels like to fight hordes of zombies in any of those post-apocalyptic settings which are so trendy these days.

Anyway: dispersion itself is imprecise. I assumed you meant dispersion by diffusion from a central position, since that’s what you showed in your plots. So let me rephrase: A bell curve is the result of dispersion by diffusion. Actually, let me put it much more succintly: what you showed in your right-most scatter plot is precisely a bell curve, albeit a crude one, centered at the centre of the circle. If you know anything you statistics, you know this.

As for evidence, I’m saying just this: you have no evidence for this discussion, so let it cease. I’m not jumping to any conclusion, and for exactly the same reason: no evidence.

JMPicard, sorry but you are not right. I also thought that bell curve is speculation of one gamer but Snapshot patently write this in the pfd-guide:
"Red circle : All your shots will be randomly distributed in this circle (with a bell curve distribution where extremes of inaccuracy and accuracy are less likely)."

Still question remains is curve of bell. It’s calculated from red circle to red circle or from center to red circle and it need analysis in the game.


Then…why are you even bothering to post? You have done NOTHING to refute anything I’ve said or to back up your statements. There are statements from UV stating that a bell curve is used and you have done nothing to refute his statement (at most you have said other people have misunderstood him, but again you provide no proof). You are by all means free to leave this thread, though if you expect me to “let it cease” then you need to actually back up your statements.

Likewise had you of read my posts you would know that the scatter-plots are from World of Tanks and that I used them in reference to my feedback that such a system that leads to shots being so concentrated away from where one is aiming generally aren’t well received by the community (the WoT community hated having so many of their shots going to that outer-most band in the left plotting while they found the right plotting far more enjoyable as you didn’t have a band that was likely to miss when not at point-blank ranges).

Again those scatter-plots were NOT from PP. They are simply used as a reference to help illustrate the system and talk about how such a system with an “accuracy band” was received. The larger your shot circles the less well such a thing is received.

As it says in the Game Guide PDF (which by the way was written by @JulianG ) clearly states that a bell curve is used to avoid extreme cases of accuracy and inaccuracy. The bell curve is from the centre to the red circle (if it were red circle to red circle then the peak would be on the crosshairs meaning extreme accuracy would be likely). As for the argument that it’s better to aim with the yellow circle, that just doesn’t make practical sense. Let’s assume for the moment that 100% of shots land exactly on the yellow circle. You’re aiming at the crabman’s head. You’re close enough that his head fully covers the yellow circle - guaranteed hit. Now let’s say he’s further away, and only partially fills the circle. Which way do you aim? Let’s say you aim high so that the bottom of the yellow circle is on his head. The shots could all hit the top edge. Trying to use the edge of the yellow circle as the crosshair is impractical because you have no way to know or influence where along the circumstance the shots will land.

It makes perfect practical sense. If I don’t have a 100% hit chance then I want to work to maximize my hit chance. So lets go back to your example now and 100% of shots hit along the yellow line. I want to move the yellow line so that as much of it as possible is on the enemy. While sure the shots “could” go to the top, if putting the bottom edge on the enemy results in 25% of the line touching the enemy but putting the top of the line on the enemy results in less than 25% of the line touching (due to how the curve intersects with the model of the enemy) then my best chance of hitting is with putting it on the bottom. Of course one might wonder why you’re taking a 25% (or less) shot as opposed to repositioning, but that’s irrelevant for this discussion.

And this is what my last screenshot is showing. Even though I’m aiming at the shield, which I DON’T want to actually shoot, I have optimized the theoretical band for the maximum chance of hitting the enemy (I say theoretical because I don’t know the size of the band and thus just drew one on to illustrate the point; not saying that the band theoretically exists as it literally does exist). This compared to the screenshot before it where I’ve maximized filling in the inner 50% circle (which would make logical sense if not using a bell curve).

It isn’t about reaching 100% hit rate (once you hit that all of this becomes moot…unless trying to hit a specific body part in order to neutralize or reduce the threat of a target), but rather about maximizing one’s chance to hit. And in order to maximize your chance to hit you have to put as much of the band as possible on the enemy, which is different from actually aiming at the enemy since you’re less likely to hit what you’re directly aiming at. This aiming away from your target in order to maximize the hit band feels counter-intuitive while also making all guns inherently less accurate than their circles would initially indicate.

I finished 3 fights with about 200 shots just now. By results I can say confidently that about 20% of shots fall into center of yellow circle. Other shots are distributed around yellow and red circle. Unfortunately visual of shots does not coincide with their practical hits so it is difficult say how shots are proportioned at border. But rifle and pistol fall under the rule “center 20%”. Ironically the machine gun has a more even propotioned (perhaps this is a statistical error, heavy soldier shoots less but spent more ammo).