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ModDestroyer_1

Exact Formula for Richocet/Penetration chance.

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I have wondered this for a awhile but what is the exact formula for ricochet chances?

I have studied the global wiki but it doesn't give a fomrula; http://wiki.wargaming.net/en/Ship:Gunnery_%26_Armor_Penetration#Armor-Piercing_Internal_Ricochets

We know shells have penerative values and their chance to pen or bounce depends on the angle, speed, and thickness of the armor they strike.

We are given angles at which 'richoet angles start' for certain ships. Like 30 degree for the Americans heavy cruisers and 45 degree for everyone else. It says on the wiki shells hitting above those angles " 45-90 degrees -> ricochet doesn't occur " Clearly that isn't universally true because a DD AP bounces on a BB hull regardless of the angle. At the other end of the spectrum there are the over match mechanics.

Now getting to the part where my question really lies, on the wiki says, ' 30-45 degrees -> chance to ricochet." This is the zone in between auto bounce and zero bounce angles. This is the fomrula I want; that takes the penetrative value of the shells, speed, angle etc to find the CHANCE of a ricochet at those in between angles. That formula should also be what determines if a shell bounces/shatters like a DD shell on a BB hull at non richochet angles. The guns fired will determine the shells penetrative power in this game, as well as their angles and speeds of impact at various ranges. The only other input then is the angle and thickness of the armor being hit. With this formula I could draw up with very specific ranges & angles at which I would want to fire AP vs HE. The exact distance/angles at which AP would be more effective to fire vs HE would vary depending on which cruiser you fire from vs which you fire at. It would allow for vastly more precise ammo selection.

Thank you for the help!

 

Edited by ModDestroyer_1

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1 minute ago, ModDestroyer_1 said:

Clearly that isn't universally true because a DD AP bounces on a BB hull regard less of the angle.

Shatter =/= ricochet

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21 minutes ago, Lert said:

Shatter =/= ricochet

Even so there must still be a formula that takes into account that shells particular effective pen at that particular range/angle/speed of impact and compares it to the effective armor to determine whether a shatter or a *chance* to ricochet occurs?

Where is this elusive formula that is so key to game play?

Edited by ModDestroyer_1

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Hidden. WG isn't going to release that formula.

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5 minutes ago, Lert said:

Hidden. WG isn't going to release that formula.

Too useful huh? Hmmm, with enough data it could be deduced.

Would need an insane amount of data though admittedly. From all gun types hitting all the different armor thickness to be found at all the different angles possible without a large enough sample size of all of the different combos. What a pet project! Real issue would be recording/collecting the data. It would make LWM dispersion charts look easy. Once you have it deduction should be easy via regression.

Edited by ModDestroyer_1
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11 minutes ago, Hanger_18 said:

Thank you. Useful for getting preventative value and angles at all distances. But it doesn't inform us how this effective penetration vs effective armor actually effects this *chance* to ricochet at the angles between auto bounce and zero bounce. We are missing the formula that would inform that.

Which was what would have allowed us to actually determine how big of a deal a value of 50 more penetrative power actually means at those angles in terms of better chance to pen and thus resolve our other discussion.

:Smile_sceptic: I'm pretty nixed something this fundamental and important is hidden from us tbh. It's gotta be out there somewhere or I'll find a way to the collect the data to deduce it myself. Just a question of data collection that is the issue.

Edited by ModDestroyer_1

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6 minutes ago, ModDestroyer_1 said:

50 more penetrative power actually means at those angles

autobounce is calculated before penetration as a seperate thing. you can have infinite penetration and still bounce.

I've actually asked this question before to one of the editors and iirc they do not know either.

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19 minutes ago, ModDestroyer_1 said:

But it doesn't inform us how this effective penetration vs effective armor actually effects this *chance* to ricochet at the angles between auto bounce and zero bounce.

Because it doesn't.

11 minutes ago, Hanger_18 said:

autobounce is calculated before penetration as a seperate thing. you can have infinite penetration and still bounce.

And this is why.

Assuming overmatch is not in play, each AP shell has a ricochet range. For example, a 45 ~ 65 degree range. The chance to ricochet goes from 1% to 100% over that range. Since it's 20 degrees different it goes in 5% steps in this example.

Only after this check is made, is there a check for penetration. Not enough pen? The shell shatters.

It's not a single formula that checks for everything, it's a sequential series of simpler checks.

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21 minutes ago, Lert said:

Because it doesn't.

And this is why.

Assuming overmatch is not in play, each AP shell has a ricochet range. For example, a 45 ~ 65 degree range. The chance to ricochet goes from 1% to 100% over that range. Since it's 20 degrees different it goes in 5% steps in this example.

Only after this check is made, is there a check for penetration. Not enough pen? The shell shatters.

It's not a single formula that checks for everything, it's a sequential series of simpler checks.

Wait, so what is the fomrula you said WG does not release then?

Quote

Hidden. WG isn't going to release that formula.

If ricochet chance is linear or a function based on angle of impact alone when overmatch or shatter doesn't occur and it is just penetrative value compared to effective armor is there any unknown element then? If it isn't the exact formula for effective pen value, amour , or maybe some exact non linear function by which ricochet chance occurs (which you made it sound linear) that is unknown then nothing seems to be.

Edited by ModDestroyer_1

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1 minute ago, ModDestroyer_1 said:

Wait, so what is the fomrula you said WG does not release then?

Penetration. The formula that occurs after the ricochet check.

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11 minutes ago, Lert said:

Penetration. The formula that occurs after the ricochet check.

Sorry for all the Qs. I'm learning a lot about these obtuse non-obvious mechanics.

If penetration is hidden where does the graphs that show pen values for various ships Hanger_18 gave come from? https://mustanghx.github.io/ship_ap_calculator/

*edit* reading that website actually it says the info is data mined... so we don't have the formula but the output info but is apparently all there anyway and was given to me at the start. xD Circle complete.

Since that also gives you the angles of impact also all you'd need is to input the armor to get effective armor and then it is just a question of which number is bigger.

Second question, because I'm a sucker for details, do you know if ricochet chance is as linear as you made it sound with 5% increments or was that a simplified example?

 

 

Edited by ModDestroyer_1

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6 minutes ago, ModDestroyer_1 said:

If penetration is hidden where does the graphs that show pen values for various ships Hanger_18 gave come from? https://mustanghx.github.io/ship_ap_calculator/

Shells having a certain penetration value at a certain range is just one factor in the penetration calculation. A shell with, say, enough energy for 420mm of penetration as it reaches Yamato's 410mm belt will shatter if it hits at sufficient angle to increase the relative thickness of the plate without triggering a ricochet. Plus, there's Krupp - shell hardness - to take into account. The harder a shell, the more it penetrates and the softer a shell, the quicker it shatters.

Since almost all armor plates are inclined outwards to some degree, plus the ballistic flights of shells mean they impact at a downwards angle means that basically all armor plates in this game are functionally thicker than their values suggest.

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17 minutes ago, Lert said:

Penetration. The formula that occurs after the ricochet check.

they start at historical values from what I've seen. Most values match nav weps. From there they add in Krupp, which applies some spoopy black magic.

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14 minutes ago, ModDestroyer_1 said:

do you know if ricochet chance is as linear as you made it sound with 5% increments or was that a simplified example?

I am not quite certain. However, @LittleWhiteMouse might.

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10 minutes ago, Hanger_18 said:

 From there they add in Krupp, which applies some spoopy black magic.

Every time i think I finally understand the mechanics another obtuse element comes in. Where do you find the Krupp value for these different shells?

So now the variables we have that we know are penetrative value, Krupp, anlge of impact, and thickness of armor. With Krupps relationships being the least clear. Where as without it it would have been relatively simple to use angle  provided in the graphs to find effective armor and compare to pen value. I guess Krupp must do something along the lines of just add more pen value? Or maybe something more complicated?

Edited by ModDestroyer_1

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10 minutes ago, ModDestroyer_1 said:

Where do you find the Krupp value for these different shells?

Datamining.

10 minutes ago, ModDestroyer_1 said:

I guess Krupp must do something along the lines of just add more pen value? Or maybe something more complicated?

The best we know is that Krupp is shell hardness. 2400 is the base line average value. Higher than that means harder shells, means less chance to shatter. Lower than that means softer shells, means more shatters. So, yes, Krupp roughly equates to pen, though not quite exactly. After all, an Abrams' DU long rod penetrator will go through more concrete than a half filled sandbag at the same velocity, because of its hardness.

10 minutes ago, ModDestroyer_1 said:

So now the variables we have that we know are penetrative value, Krupp, anlge of impact, and thickness of armor.

Then there is also normalization.

And that's just for checking if a shell makes it through an armor plate. With spaced armor multiple checks are required, from ricochet check onwards. Then we get into fuse thresholds, fuse timings, etc ...

IIRC this video has some good info:

 

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5 minutes ago, ModDestroyer_1 said:

Every time i think I finally understand the mechanics another obtuse element comes in. Where do you find the Krupp value for these different shells?

So now the variables we have that we know are penetrative value, Krupp, anlge of impact, and thickness of armor. With Krupps relationships being the least clear. Where as without it it would have been relatively simple to use angle  provided in the graphs to find effective armor and compare to pen value. I guess Krupp must do something along the lines of just add more pen value? Or maybe something more complicated.

Data mine sites. Krupp is not on the wiki or in the game. But it doesn't need to be. It's just a small balance parameter built into penetration. Penetration is important and it helps to know what each ship can do. But knowing what ships Krupp value is, is absolutely pointless.

Knowing Krupp would be like writing out 1+1+1+1+1 instead of just saying 5

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2 minutes ago, Hanger_18 said:

Data mine sites. Krupp is not on the wiki or in the game. But it doesn't need to be. It's just a small balance parameter built into penetration. Penetration is important and it helps to know what each ship can do. But knowing what ships Krupp value is, is absolutely pointless.

Knowing Krupp would be like writing out 1+1+1+1+1 instead of just saying 5

Bingo.  Krupp is just a coefficient that Wargaming uses to artificially tweak penetration values of given ships.  All things being equal, a ship with 10% more Krupp will have 10% more penetration across all ranges. 

32 minutes ago, ModDestroyer_1 said:

Second question, because I'm a sucker for details, do you know if ricochet chance is as linear as you made it sound with 5% increments or was that a simplified example?

To the best of my knowledge, it's linear.

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WG doesn't want to reveal too much of their inner mechanics as that could be used by competitors for one reason.

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6 hours ago, Hanger_18 said:

Data mine sites. Krupp is not on the wiki or in the game. But it doesn't need to be. It's just a small balance parameter built into penetration. Penetration is important and it helps to know what each ship can do. But knowing what ships Krupp value is, is absolutely pointless.

Knowing Krupp would be like writing out 1+1+1+1+1 instead of just saying 5

I'm just trying to find out where this 'unknown' element lies if it exists.

So Krupp is baked into the penetrative value in the graphs from  https://mustanghx.github.io/ship_ap_calculator/ ? At least that is what you wrote suggests to me since you claim Krupp is pointless. If it isn't backed into those pen values then it augments them and isn't pointless.

Along the same lines, does the angle of impact in the graphs take into account normalization? If it does then we have a much more simple list of variables and no unknowns for angles with no ricochet or where shots pass the linear ricochet test. Pen value, armor thickness, and angle of incidence (made up of shell angle, armor/ship angle, and normalization) are the variables then to figure out if the shell simply pens or does not pen. Which is a pretty manageable list if all those more obtuse elements are baked into those data mined values.

Edited by ModDestroyer_1

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8 hours ago, ModDestroyer_1 said:

I have wondered this for a awhile but what is the exact formula for ricochet chances?

I have studied the global wiki but it doesn't give a fomrula; http://wiki.wargaming.net/en/Ship:Gunnery_%26_Armor_Penetration#Armor-Piercing_Internal_Ricochets

We know shells have penerative values and their chance to pen or bounce depends on the angle, speed, and thickness of the armor they strike.

We are given angles at which 'richoet angles start' for certain ships. Like 30 degree for the Americans heavy cruisers and 45 degree for everyone else. It says on the wiki shells hitting above those angles " 45-90 degrees -> ricochet doesn't occur " Clearly that isn't universally true because a DD AP bounces on a BB hull regardless of the angle. At the other end of the spectrum there are the over match mechanics.

Now getting to the part where my question really lies, on the wiki says, ' 30-45 degrees -> chance to ricochet." This is the zone in between auto bounce and zero bounce angles. This is the fomrula I want; that takes the penetrative value of the shells, speed, angle etc to find the CHANCE of a ricochet at those in between angles. That formula should also be what determines if a shell bounces/shatters like a DD shell on a BB hull at non richochet angles. The guns fired will determine the shells penetrative power in this game, as well as their angles and speeds of impact at various ranges. The only other input then is the angle and thickness of the armor being hit. With this formula I could draw up with very specific ranges & angles at which I would want to fire AP vs HE. The exact distance/angles at which AP would be more effective to fire vs HE would vary depending on which cruiser you fire from vs which you fire at. It would allow for vastly more precise ammo selection.

Thank you for the help!

 

Some DDs AP can pen even BBs like Khab for instance.

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20 minutes ago, ModDestroyer_1 said:

I'm just trying to find out where this 'unknown' element lies if it exists.

So Krupp is baked into the penetrative value in the graphs from  https://mustanghx.github.io/ship_ap_calculator/ ? At least that is what you wrote suggests to me since you claim Krupp is pointless. If it isn't backed into those pen values then it augments them and isn't pointless.

Along the same lines, does the angle of impact in the graphs take into account normalization? If it does then we have a much more simple list of variables and no unknowns for angles with no ricochet or where shots pass the linear ricochet test. Pen value, armor thickness, and angle of incidence (made up of shell angle, armor/ship angle, and normalization) are the variables then to figure out if the shell simply pens or does not pen. Which is a pretty manageable list if all those more obtuse elements are baked into those data mined values.

Yes, the graph takes into account angle of impact. It works by simulating the game's ballistic formula, and then at the same time as reporting the relevant data (velocity at impact, angle of fall, time of flight in-game) creates the penetration formula.

 

As far as the raw penetration formula goes, it's actually very simple, multiply (with various coefficients applied) the velocity at impact, the mass of the shell, and a constant, and then divides this by the shell diameter (the coefficient attached). 

How Krupp factors into this is as a modifier to the constant, as the constant first multiplied by a value derived by dividing the Krupp value by 2400, which is a 'neutral' value. Any Krupp value lower than this will reduce the penetration compared to what the formula gives, and anything more serves to increase it. 2400 alters nothing. This value is extremely useful for the massaging of penetration curves without altering the ballistics of a shell (asana change to shell mass, muzzle velocity, or drag coefficient would).

 

Once raw penetration occurs, this is of course checked against the overall angle of impact (due to the fact many armor sections have inclined, either intentional or merely because of hull shape), including the affect of normalization. Since the shell has already passed the auto bounce check, one of two things happens;

  1. The penetration is greater than the armor thickness, and the shell penetrates
  2. The penetration is less than the armor thickness, and the shell shatters

Unlike what the video above suggest, penetration reduction after punching through an armor plate is not a clean subtraction, but rather a reduction of velocity that further reduces the penetrative ability of the shell, by virtue of slowing it down.

 

The values in the graphs above utilize the penetration formula, and list the values against a perfectly vertical plate. I don't know, however, if normalization is taken into account for the above graphs - the code regarding angles of impact for the linked penetration graphs is here, but I don't know if the coder is using their own name for normalization or not.

 

The affect of Krupp can be pretty major. For example - Bretagne's 340mm APC in-game has about 340mm of penetration at 11 km in-game (sheer coincidence, actually). IRL, depending on the armor being shot at, it could vary from 233mm (Terni Cemented) to 317mm (Japanese Vickers Hardened).

The Krupp value in-game is 2350. Without changing the ballistics, if we wanted to make Bretagne's penetration more realistic without altering ballistics, would could do this by lowering the Krupp. Let's say we want ~275mm, which is about halfway inbetween the two values.

If we drop to a value of about 1935 Krupp, we get to just about 275mm of penetration against a vertical plate at the same range.

Now, of course, that's terrible penetration, but that's because French AP Caps in WWI were hot garbage, which gave their guns extremely poor penetrative characteristics. Their modern 1930s weapons are the polar opposite of this -but WG, for balance reasons, increased their penetration greatly over irl values, which does happen occasionally for balance reasons (Japanese Type 91 APC for 35.6cm, 41cm, and 46cm guns, USN 8" APC, French 305mm & 340mm APC). A relatively recent example of such balance cam early last year, which a major difference between the performance of Henri IV's 240mm APC pre and post buff - this was purely down to Krupp, turning it from a very 'meh' gun to the most powerful cruiser gun at tier X (until the Stalingrad's 305mm guns appeared).

 

 

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Penetration mechanic itself is actually very clear and there's no ambiguity to it.

Forumula is W^0.55 * V^1.1 / D^0.65, multiplied by a dimensional scaling factor. This is actually the USN Empirical formula, for those of you wondering. For W in kg, V in m/s, and D in mm, the scaling factor is 0.55616. This gives penetration relative to a reference Krupp value of 2400. The effective thickness of a plate is its absolute thickness multiplied by 1/cos(obliquity-normalization). If the shell checks penetration(i.e. it doesn't ricochet) and its penetration exceeds the effective thickness, it penetrates. No chances involved. After that, velocity is reduced by a factor of e^((armor-pen)/armor). So a shell with 600mm of pen impacting a plate with an effective thickness of 400mm will retain e^((400-600)/400)=0.606 of its initial velocity.

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