A "Formula" for Comparing Recoil Stats

[banana]

I hope we get those BO2 numbers soon

[RageHulkSmash]

I remember there was a discussion back in BO1 days about how some weapons might look like they have good recoil/centerspeed stats on paper but terrible in practice. The weapon mentioned was the mp5k. It fires the next round when the recoil is at its max amplitude, causing the gun to have larger recoil than indicated. Do these stats take that observation into account or no?

Also, let's say you are comparing weapons that have the same viewkick and centerspeed values but different firerates (BO1 HK21 vs Stoner for example). For you math/stats people, which of the two weapon would get the biggest accuracy boost, relative to its original values, from a stat like kick, decreasing viewkick by 10%? Which weapon would get the biggest accuracy boost, relative to its original values, from a stat like grip, increasing the centerspeed? Part of me is saying they would both increase the same degree because both stats increase the effectiveness by the same percent. However, another part of me is saying they wouldn't be equal because the firerates have a bigger effect to recoil than my understanding. Anyone care to help?

[RageHulkSmash]

Dec 3, 2012 15:16:47 GMT -5 Mousey said:

^We found out that we had the recoil formula wrong, so that whole business wasn't the case

Wait, which business are you talking about?

[asasa]

Dec 3, 2012 15:11:44 GMT -5 RageHulkSmash said:

I remember there was a discussion back in BO1 days about how some weapons might look like they have good recoil/centerspeed stats on paper but terrible in practice. The weapon mentioned was the mp5k. It fires the next round when the recoil is at its max amplitude, causing the gun to have larger recoil than indicated. Do these stats take that observation into account or no?

Also, let's say you are comparing weapons that have the same viewkick and centerspeed values but different firerates (BO1 HK21 vs Stoner for example). For you math/stats people, which of the two weapon would get the biggest accuracy boost, relative to its original values, from a stat like kick, decreasing viewkick by 10%? Which weapon would get the biggest accuracy boost, relative to its original values, from a stat like grip, increasing the centerspeed? Part of me is saying they would both increase the same degree because both stats increase the effectiveness by the same percent. However, another part of me is saying they wouldn't be equal because the firerates have a bigger effect to recoil than my understanding. Anyone care to help?

Not sure what you're speaking of in the first part, but as for kick and centerspeed on two weapons alike in everything but firerate, my understanding would be that both would help the slower firing one more.

But, depending on the original kick and CS values, the difference, percentage-wise could range from none to massive. And I dont just mean a gun with 5000 viewkick and 5000000cs vs 5 / 500.

[asasa]

Well see thats where things get iffy. While RF will never increase the number of shots recentered, it can eventually reduce the average deviation from the original aimpoint, and long before that, it can make the gun more consistent & controllable, like Galil vs Famas.

[asasa]

IDK if anyone has ever done the math on that, but you're probably right that no guns will ever hit that point.

[probaddie]

Dec 6, 2012 23:29:44 GMT -5 asasa said:

IDK if anyone has ever done the math on that, but you're probably right that no guns will ever hit that point.

Well, here you go:

Let

x = 0.5at^2 + vt,

where x is the angular displacement of the gun, t is the firetime, a is the (signed) centerspeed and v the velocity
(kick) of the weapon. It's easy to show that the gun reaches its peak at:

t_peak = -v/a.

Now, t_peak = 60/r_peak, where r is the is the firerate (in rpm). Solving for r:

r_peak = -60a/v.

Note that the acceleration does not change at all here, since the gun never moves back towards center.

As an example, take a gun that has a guaranteed kick upwards of 40 deg/s and a centerspeed of -1300 deg/s^2. The rate of fire that ensures that this gun receives its next kick at the top of its trajectory is:

r_peak = -60*(-1300)/40 = 1800 rpm.

[bigal093]

probaddie, will you be making a spreadsheet for BO2 recoil numbers?

[probaddie]

Feb 25, 2013 13:35:46 GMT -5 bigal093 said:

probaddie, will you be making a spreadsheet for BO2 recoil numbers?

Yeah, I'll try eventually. The guns with variable firerate are going to be a problem to account for though, and I'm bogged down in plot stuff. Don't expect them anytime soon.

[banana]

patiently waiting

[banana]

Yeah I know im just bored

[Usagi]

Feb 25, 2013 15:57:00 GMT -5 probaddie said:

Feb 25, 2013 13:35:46 GMT -5 bigal093 said:

probaddie, will you be making a spreadsheet for BO2 recoil numbers?

Yeah, I'll try eventually. The guns with variable firerate are going to be a problem to account for though, and I'm bogged down in plot stuff. Don't expect them anytime soon.

Don't forget that you'll have to account for ADS spread on the SMGs sans Peacekeeper and the pistols sans B23R.

[goosetard]

Nov 14, 2012 13:17:19 GMT -5 probaddie said:

I understand what you're getting at. I wouldn't want to be the guy counting thousands of dots on a screenie, though. And you would need thousands of shots to get reliable results that way.

Hey probaddie, I've been lurking these forums for a while but I've become so interested in a better comparison of weapon performance than the simple charts allow that I made an account to try to contribute. I'm particularly interested in your approach. I remember from some of your earlier threads that you use Mathematica (or mathcad? Maybe I don't remember...). I use a lot of Matlab and I know that doing some simple image processing and coupling it with the kind of analysis you're describing is easy to code. I'd be happy to contribute on that front if you decide to pursue that.

I'm a little weary of giving each gun an overall aggregate score, weighted or unweighted. I think when you're trying to fire accurately in-game there aren't a lot of times you just hold down the trigger (or maybe that's just me). When I consider undertaking a ranking system like this, I want to figure out how fast a gun can put damage into a target of a certain size, so a sort of "accuracy-weighted DPS," assuming the user is comfortable enough with the weapon to fire at the best rof for that range (letting off the trigger long enough per-round or few rounds to let the crosshair re-center). The trouble I ran into is that I don't know the unit sizes of models or quite how the game translates kick into an actual angle. (Please PM me if you think this approach is worth helping me out). The target size would, naturally, be a player model. Then I'd graph the "accuracy weighted DPS" vs range for each weapon on the same graph (except snipers, which clearly win in this approach) and see how they stack up.

I guess different graphs could be given based on how much of the player model is exposed. This would also be assuming that the player doesn't fight against vertical recoil with the controller. Another thing to consider would be guns that are too fast to feasibly fire in a semi-auto fashion; how many rounds per-trigger squeeze is realistic? That would be somewhat arbitrary to the player. Also, this would ignore headshot damage; I guess you'd have to consider a separate comparison based on number of shots on a smaller target... although at that point the number of variables is becoming cumbersome. I do appreciate the simplicity of having a single number ranking, like you do, and want to carry as much of that into my approach as I can, if it's worth pursuing.

*obligatory first-post junk*
I love this board. I'm so happy to find a community which cultivates an in-depth intellectual investigation of these game mechanics.
You are my bro, bro. <---- Not required in first reply, but given freely with much appreciation.

[banana]

That would actually be really cool

[probaddie]

Mar 18, 2013 17:15:05 GMT -5 goosetard said:

Nov 14, 2012 13:17:19 GMT -5 probaddie said:

I understand what you're getting at. I wouldn't want to be the guy counting thousands of dots on a screenie, though. And you would need thousands of shots to get reliable results that way.

Hey probaddie, I've been lurking these forums for a while but I've become so interested in a better comparison of weapon performance than the simple charts allow that I made an account to try to contribute. I'm particularly interested in your approach. I remember from some of your earlier threads that you use Mathematica (or mathcad? Maybe I don't remember...). I use a lot of Matlab and I know that doing some simple image processing and coupling it with the kind of analysis you're describing is easy to code. I'd be happy to contribute on that front if you decide to pursue that.

I'm a little weary of giving each gun an overall aggregate score, weighted or unweighted. I think when you're trying to fire accurately in-game there aren't a lot of times you just hold down the trigger (or maybe that's just me). When I consider undertaking a ranking system like this, I want to figure out how fast a gun can put damage into a target of a certain size, so a sort of "accuracy-weighted DPS," assuming the user is comfortable enough with the weapon to fire at the best rof for that range (letting off the trigger long enough per-round or few rounds to let the crosshair re-center). The trouble I ran into is that I don't know the unit sizes of models or quite how the game translates kick into an actual angle. (Please PM me if you think this approach is worth helping me out). The target size would, naturally, be a player model. Then I'd graph the "accuracy weighted DPS" vs range for each weapon on the same graph (except snipers, which clearly win in this approach) and see how they stack up.

I guess different graphs could be given based on how much of the player model is exposed. This would also be assuming that the player doesn't fight against vertical recoil with the controller. Another thing to consider would be guns that are too fast to feasibly fire in a semi-auto fashion; how many rounds per-trigger squeeze is realistic? That would be somewhat arbitrary to the player. Also, this would ignore headshot damage; I guess you'd have to consider a separate comparison based on number of shots on a smaller target... although at that point the number of variables is becoming cumbersome. I do appreciate the simplicity of having a single number ranking, like you do, and want to carry as much of that into my approach as I can, if it's worth pursuing.

*obligatory first-post junk*
I love this board. I'm so happy to find a community which cultivates an in-depth intellectual investigation of these game mechanics.
You are my bro, bro. <---- Not required in first reply, but given freely with much appreciation.

Welcome to the forums. I guess I'll respond to your points in turn.

1. These scores are meant to grade the recoil (i.e. dispersion of the shots) of the weapons only. I only mention a "grand formula" for scoring weapons as motivation for grading recoil, since this has been attempted in the past with -- in my opinion -- very poor results. I, too, would be interested in finding some way of measuring the raw killing power of a given weapon taking its recoil into account, but I think we're a far ways away from that. I've been working on something separately that attempts to measure killing power (without recoil taken into account) but with all this work I've been doing on recoil plots its been falling to the wayside a little bit.

2. For these statistics (and my plots) I assume the player can pull their trigger no faster than 625 RPM. Most players can't actually achieve this on any platform, but in my opinion it represents a realistic worst-case scenario.

If you want more technical details on how these work, how recoil works, etc. feel free to PM me or join us on the #Den_Kirson IRC

[roseflowers]

I am new to this forum....

[banana]

Welcome to these forums

[42]

May 11, 2013 14:40:17 GMT -5 banana said:

Welcome to these forums

It's a bot.

[banana]

arent you a bot

[banana]

Probaddie why not just give weapons with variable fire rates 2 different scores? One for the faster shots and the other for the slower ones. Since the units are directly comparable you could just add them to each other. For example say the an94's second shot has score of 5 and it's other shots have a score of 10 and the type 25 has a score of 9; If you want to find out which is better you could do 5+10+10+10+10=45 vs 9+9+9+9+9=45 so after the 6th shot the type is better (first shot doesn't count). Or does it not work like that?

[probaddie]

May 12, 2013 12:15:18 GMT -5 banana said:

Probaddie why not just give weapons with variable fire rates 2 different scores? One for the faster shots and the other for the slower ones. Since the units are directly comparable you could just add them to each other. For example say the an94's second shot has score of 5 and it's other shots have a score of 10 and the type 25 has a score of 9; If you want to find out which is better you could do 5+10+10+10+10=45 vs 9+9+9+9+9=45 so after the 6th shot the type is better (first shot doesn't count). Or does it not work like that?

Not quite. The problem is that they don't directly add together shot after shot.

I've been doing some work on this recently and it turns out that the way recoil accumulates over time is dependent on the recenter probability. Unfortunately, that's about all I can say at this point.

[banana]

I bet you the devs don't even fully understand recoil

[probaddie]

May 30, 2013 22:54:03 GMT -5 banana said:

I bet you the devs don't even fully understand recoil

In all fairness, I don't think anyone does:

mathoverflow.net/questions/94226/a-random-walk-with-uniformly-distributed-steps

Someone asked this as a research-level statistics problem just over a year ago. The question is basically asking (using a simplified version of Call of Duty's recoil model) what the probability of the point of aim is being back at the origin after the nth shot. The first and second answers provide an explicit solution, but only for the case when the recenter probability for the first shot is exactly 1/2. The second answer answers the question for the general case, but it involves an algorithm that directly computes what is an unsolved counting problem (i.e. no one knows of any generating function that represents the sequence that gives the number of ways of solving the counting problem, let alone a formula for that sequence directly).

All this for a simplified version of the problem. And this doesn't even begin to touch on the problem of measuring variance (recoil).

[probaddie]

Updated the OP with link to the tenth draft (Advanced Warfare statistics). The format should be self-evident.

Edit: Necromancy +100 for me.

[banana]

The nostalgia

[probaddie]

And I've updated the Advanced Warfare statistics. You can find them here.

There are two important changes:

1. There are two scores for each weapon: one is the unbiased inaccuracy and the other is a biased score with a horizontal-to-vertical bias of 2.77.

2. Every weapon was simulated using fifteen shots per trial - even those that cannot actually fire that number of rounds before expending their maximum capacity. This is to facilitate direct comparisons between weapons.

Edit: I know ninopettis is specifically interested in these results, so I am pinging him here.

[ninopettis]

Thank you!