How to (Properly) Balance the Grip

[probaddie]

No, this is not another "well, I think blah blah blah" thread -- I promise you this belongs in "Hey, Den" -- where we randomly throw out numbers as to what the Grip attachment should do to be worth a CaC point, where everyone pretends to know what doing anything to any recoil statistic does to any gun at all without having any way of testing or simulating the proposed effect those changes would have (no offense). I'm going to tell you exactly how to balance the Grip; in other words, I'm going to provide a formula that prescribes exactly what the grip has to do to guarantee an x% reduction in recoil. (Yes, I can measure recoil; see this. Eventually I'm going to publish results for Black Ops II, but this result is short, sweet and pertinent given the current state the grip is in.)

Here goes: to multiply the recoil of a weapon by a factor of r, you multiply the CenterSpeed and all kick values of that weapon by the square root of r. This applies to weapons with ViewKick only. Now, rather than prove this with a wall of LaTeX, I'm just going to show you some plots of how this works. If some of you are really interested in an outline of the proof I can oblige by providing some details.

For example, let's take the SCAR-H. If we want to half its recoil, then we are trying to multiply its recoil by a factor of r = 0.5. To do this, we start by taking the square root or r, which gives 0.7071. We therefore must multiply the CenterSpeed and Kick values by that factor. Note that, in spite of intuition and common sense, we will be reducing the CenterSpeed here, even as we are trying to reduce recoil. For the SCAR-H, applying this multipler gives the following recoil statistics:

• adsViewKickPitchMin = 15 * 0.7071 = 10.61
  
• adsViewKickPitchMax = 60 * 0.7071 = 42.43
  
• adsViewKickMinMagnitude = 20 * 0.7071 = 14.13
  
• adsViewKickYawMin = 20 * 0.7071 = 17.68
  
• adsViewKickYawMax = -57.5 * 0.7071 = -40.66
  
• adsViewKickCenterSpeed = 1500 * 0.7071 = 1060.65

As evidence that this works, here is a plot of the real SCAR-H alongside the SCAR-H with the modified parameters:



To drive home the point, we'll try some other, more intuitive things that we might expect to work but fail in some respect. The first plot below shows the SCAR-H with reduced kick values (by a factor of of 0.7071, or by 29%) but with CenterSpeed left intact:



I think it can be easily agreed upon that this much more than a 50% reduction in recoil, whatever your measure of it is. Of course, reducing kick by 50% would only make the plot smaller, so we needn't check that possibility.

Next, we'll try increasing CenterSpeed by itself. It's a favorite line of one YouTuber who frequents this site to phrase an x% increase in CenterSpeed as an "x% reduction in recoil." Whether strictly true or not, I don't blame him for doing this: recoil is very technical after all and these things need to be simplified for a wide audience. Nonetheless, let's see what truth there is to this simplification by increasing the CenterSpeed of the SCAR-H by 29% (i.e. by a factor of 1.29) and examining the results:



Again -- though it is not a drastic this time around -- the reduction in recoil is likely to be considered greater than 50%. And again, we need not examine the case when CenterSpeed is increased by 50%, as the benefit will obviously be greater than this.

The significance of all this is that it guarantees a way to ensure that the grip (or any proficiency) decreases the recoil of any weapon consistently, rather than the mixed bag it tends to produce from weapon to weapon in almost every title in which it has been an attachment option. So, if you were, say, a developer, you could program the grip to work this way and not be concerned with how it interacts with every other weapon/attachment combination as though the grip might, for some apparently inexplicable reason, give a much greater benefit to some weapons over others. (Kick with MW3 ACR, anyone?) If anyone wants me to do a few more examples of this I can oblige using their favorite weapon and whatever reduction/increase they want -- or I can explicate my reasoning behind why this works if people want to know.

Cheers!

[Brick2urface]

First off how are you defining the recoil reduction in this scenario? What I mean is when you say reduce recoil by 50% are you reducing the area that the spread plot covers by 50%? Or are you reducing the max spread of the plot by 50%? Or what?

Second how does this formula hold up on fast firing weapons like the blops 2 scorpion?

[asasa]

I like this, although a 50% reduc is waaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaay too much.

[probaddie]

Mar 21, 2013 23:15:57 GMT -5 Brick2urface said:

First off how are you defining the recoil reduction in this scenario? What I mean is when you say reduce recoil by 50% are you reducing the area that the spread plot covers by 50%? Or are you reducing the max spread of the plot by 50%? Or what?

Second how does this formula hold up on fast firing weapons like the blops 2 scorpion?

1. I measure recoil as the origin-centered variance of the shots. In layman's terms, you can think of it as the area covered by the plot. (Technically not right, but it's close enough).

2. Just the same. fireTime does not figure into this method at all, though obviously it plays a role in determining the initial recoil of the stock weapon before the grip is applied. For your consideration:



Note that I took out the spread and idle in that plot.

That question got me thinking a little bit: is there a way to guarantee an increase in recoil by modifying fireTime in some way? As it turns out, it is. In fact, I can write a new formula here now: to multiply the recoil of a weapon by a factor of r while decreasing the fireTime by a factor of 1/r, multiply the CenterSpeed by the fifth power of the square root of r and multiply all Kick values by the cube of the square root of r. (I kid you not!)

This has interesting implications for balancing Rapid Fire: if I decrease a weapon's fireTime by a factor of 1/r (i.e. increase its rate of fire by a factor of r), then that formula will tell me what I need to do to the Kick and CenterSpeed values to guarantee that recoil increases by a factor of r. I don't know if this guarantees a perfect way to balance Rapid fire though, since we're now talking about time-to-kill stats and killing power balance, something I'm not at all qualified to comment on.

[Blurred Wolf]

You are truly the smartest dog on the internet.

Very interesting to see that the intuitive change won't necessarily obtain the result one desires.

[-3055-]

Oh yeah, that SCAR is looking reaaaaaaaaaaaaaaaal good in that second set.

I say make it -5% kick. I always thought it was weird to change the centerspeed value and not the kick value for foregrips.

[probaddie]

Mar 22, 2013 7:30:48 GMT -5 -3055- said:

Oh yeah, that SCAR is looking reaaaaaaaaaaaaaaaal good in that second set.

I say make it -5% kick. I always thought it was weird to change the centerspeed value and not the kick value for foregrips.

Um... you mean -5% kick AND -5% CS, right? The whole point of this was to show that you can't get consistent results by changing just the kick values or CS values by themselves.

Mar 21, 2013 22:08:50 GMT -5 probaddie said:

Here goes: to multiply the recoil of a weapon by a factor of r, you multiply the CenterSpeed and all kick values of that weapon by the square root of r. This applies to weapons with ViewKick only.

[Zero IX]

Bravo. If all "theorycraft" threads employed this level of insight, this board would be a much, much better place.

It's too bad Vonderhaar and 3arc refuse to revisit the Grip. I wouldn't doubt that it's a combination of seeing enough Grips being used (due to ignorance) in the global stats and the fact that they pay such close attention to the competitive community, where Grip hasn't fallen completely out of favor even though by now its effects are widely recognized to be statistically negligible. (Not sure if it's been posted before, but here's a snip from Clayster, one of the most dominant players at Dallas: imgur.com/423wCsp )

[Marvel4]

Mar 22, 2013 8:25:59 GMT -5 Zero IX said:

(Not sure if it's been posted before, but here's a snip from Clayster, one of the most dominant players at Dallas: imgur.com/423wCsp )

[markopolo]

As an Pure LMG user, I fully support this idea.

Make it so!

[banana]

Probaddie you're too smart ;D
I just wish the devs would read this

[-3055-]

Mar 22, 2013 8:05:30 GMT -5 probaddie said:

Mar 22, 2013 7:30:48 GMT -5 -3055- said:

Oh yeah, that SCAR is looking reaaaaaaaaaaaaaaaal good in that second set.

I say make it -5% kick. I always thought it was weird to change the centerspeed value and not the kick value for foregrips.

Um... you mean -5% kick AND -5% CS, right? The whole point of this was to show that you can't get consistent results by changing just the kick values or CS values by themselves.

Mar 21, 2013 22:08:50 GMT -5 probaddie said:

Here goes: to multiply the recoil of a weapon by a factor of r, you multiply the CenterSpeed and all kick values of that weapon by the square root of r. This applies to weapons with ViewKick only.

I'm aware that's what you're proving in the original post, but like I said, I personally think it's just crazy to change centerspeed values, even though that's the easier method.

I say +10% kick and +10% CS to all guns except for the Chicom and SVU, and make all guns with grip how they are now. Chicom and SVU gets a -10% kick and -10% CS with grip.

[probaddie]

Mar 22, 2013 13:09:57 GMT -5 -3055- said:

Mar 22, 2013 8:05:30 GMT -5 probaddie said:

Um... you mean -5% kick AND -5% CS, right? The whole point of this was to show that you can't get consistent results by changing just the kick values or CS values by themselves.

I'm aware that's what you're proving in the original post, but like I said, I personally think it's just crazy to change centerspeed values, even though that's the easier method.

I say +10% kick and +10% CS to all guns except for the Chicom and SVU, and make all guns with grip how they are now. Chicom and SVU gets a -10% kick and -10% CS with grip.

Okay, fair enough. (By the way, the grip isn't an available option for the SVU (regrettably )).

For anyone whose interested in an application of the second formula, I'm going to see what would happen if it were applied to the Skorpion EVO. Since Rapid Fire decreases fireTime by a factor of 0.66 on SMGs, we want to increase recoil by a factor of r = 1/0.66 = 1.5 (i.e. by 50%). The fifth power of the square root of r is r^5/2 = 2.76, so we'll increase CenterSpeed by a factor of 2.76, or by +176%. The cube of the square root of r is r^3/2 = 1.84, so we'll increase the kick values by a factor of 1.84, or by +84%. These are the results (I bumped up the number of simulations to 100 000):

[mmacola]

To properly balance the grip, one needs to buff the Select Fire attachment. If the Grip does more to reduce recoil on a weapon than the Select Fire, it becomes op. Or maybe they could do different things.

Select Fire reduces recoil by 15% (or multiply all it's values by ~0.921..) while the Grip reduces it 5%(~0.974..)//5.5%(~0.972..)//10%(~0.948..) for SMGs, ARs and LMGs respectively. Since LMGs don't get select fire, they deserve a bigger Grip bonus, but since their bonus is only worth one point versus SMGs and ARs two, it can't be too good though. Those number though are just an idea, not really sure how they would come out in the game since I don't have a super cool program like probaddie's which generate recoil plots for me.

[probaddie]

Mar 22, 2013 14:16:48 GMT -5 mmacola said:

To properly balance the grip, one needs to buff the Select Fire attachment. If the Grip does more to reduce recoil on a weapon than the Select Fire, it becomes op. Or maybe they could do different things.

Select Fire reduces recoil by 15% (or multiply all it's values by ~0.894..) while the Grip reduces it 5%(~0.974..)//5.5%(~0.972..)//10%(~0.948..) for SMGs, ARs and LMGs respectively. Since LMGs don't get select fire, they deserve a bigger Grip bonus, but since their bonus is only worth one point versus SMGs and ARs two, it can't be too good though. Those number though are just an idea, not really sure how they would come out in the game since I don't have a super cool program like probaddie's which generate recoil plots for me.

Yeah, I've always regretted the fact that I don't have the ability to convert this program into an .exe that people can download. (If anyone knows any good programmers, let me know .

[I Am Hollywood5]

this is the best idea for the foregrip i've ever heard.

[mw2baller]

Just make the grip do the same thing to recoil as laser sight, quick draw, and stock do to their respective stats. Qualitatively not quantitatively.

[banana]

reducing recoil by 50% seems equal to me

[-3055-]

NOOOO I DON'T WANT MW3 SCAR BACK

[goosetard]

So to recap, what the grip does NOW is simply increase centerspeed, and you're describing a better, more comprehensive way that grip SHOULD alter the mechanics to achieve a reduction in recoil measured relative to a gun's 'naked' stats. Right?

[-3055-]

Basically yes. But it's a bit more than that since grip right now might increase the centerspeed value, but only by 2% (negligible).
In my opinion, 29% cs reduction and 29% kick reduction is overcompensating. 15/15 seems fine. Even maybe 10/10.

[kirbyderby]

What's so bad about having an attachment that's actually useful? When that one CaC point has to compete with literally everything else in CaC, it better damn well be worth it.

[Dumien]

Probaddie you so smart.

I got a question. And its similar to Mr. Cola.

What would you do to Select Fire?

[goosetard]

Your way is also more complicated than simply increasing the center speed. If I'm reading between the lines correctly, one of the advantages to your method is that it would have an equal effect for each weapon (relative to their 'naked' spread, so every gun gets the same x% recoil reduction from grip) This leads me to a question that could probably be answered by staring at recoil plots for hours but would be a lot easier to answer using the formulas you derived:

Which gun(s) do(es) the current grip mechanic improve the most? And which the least?

(edit: internet only just acknowledged that my previous reply happened)

[probaddie]

Mar 26, 2013 9:15:18 GMT -5 Dumien said:

Probaddie you so smart.

I got a question. And its similar to Mr. Cola.

What would you do to Select Fire?

Not a clue.

The problem is this: when you start changing a weapon's fireTime and burst delay (if any), you start changing its killing power. I don't think its possible (yet) to adequately quantify killing power for me to be able to say just how much of a recoil reduction/increase is appropriate for a weapon with Select Fire, given what changes Select Fire makes to killing power. But supposing you could measure killing power effectively, I would simply ensure that the increase/decrease in killing power is exactly offset by a corresponding decrease/increase in recoil.

[probaddie]

Mar 26, 2013 11:14:58 GMT -5 goosetard said:

Your way is also more complicated than simply increasing the center speed. If I'm reading between the lines correctly, one of the advantages to your method is that it would have an equal effect for each weapon (relative to their 'naked' spread, so every gun gets the same x% recoil reduction from grip) This leads me to a question that could probably be answered by staring at recoil plots for hours but would be a lot easier to answer using the formulas you derived:

Which gun(s) do(es) the current grip mechanic improve the most? And which the least?

(edit: internet only just acknowledged that my previous reply happened)

Eh, you'll have to give me some time with that. I know how to figure it out but I'd have to write some code to calculate it out for every gun.

[goosetard]

Now that I think about it, perhaps it was a silly question... If your stat for comparing recoils has both gripped ungripped guns, we could just see which score improves the most.

[probaddie]

Mar 26, 2013 16:13:28 GMT -5 goosetard said:

Now that I think about it, perhaps it was a silly question... If your stat for comparing recoils has both gripped ungripped guns, we could just see which score improves the most.

Well, I don't have results posted for BO2 yet, so no dice there .

[banana]

Mar 26, 2013 16:13:28 GMT -5 goosetard said:

Now that I think about it, perhaps it was a silly question... If your stat for comparing recoils has both gripped ungripped guns, we could just see which score improves the most.

Well you also got to think that the bo2 grip is only a 2% increase in centerspeed, which like probaddie said turns out to be less than a 2% reduction in total recoil. Bottom line is that the grip in bo2 sucks so badly that it's not worth even half a CaC point.

[goosetard]

I think there might be some guns that are right on the cusp of being viable that the grip pushes over that line... that's why I'm curious to see which weapons it's most effective with.