Are you a math guru?

[Guest]

Welcome, Guest. Please login or register.
Did you miss your activation email?

1 Hour 1 Day 1 Week 1 Month Forever

Login with username, password and session length

[pqumsieh]

Something I've been looking to figure out, so far no luck.

If a weapon does 10 damage per second and another weapon does 20 damage per second then the second weapon is twice as good.

If the first weapon, that deals 10 damage per second, also has splash damage, lets say it has a radius of 5 splash equivalent to COH units, than what is the relative value of the first weapon to the second?

If you can come up with a method to solve this problem I will reward you in some way.

[Spartan_Marine88]

The answer is still the same, the dps would only increase if you specified the amount of targets that the splash was actually hitting.

Now assuming that the splash is the same as the full damage then one could presume that the dps would equal (10*x) dps where x is the number of units that the splash touches.

[nikomas]

Like he said, as far as my math goes...

(x = targets splashed)

Value of weapon A: 10*x
Value of weapon B: 20

You can't really put a direct mathematical value to A as it's situational depending on targets.

[Baine]

Are we talking about the Ostwind or Scoutcar upgrade in CoH2?

[nikomas]

Right, I'm no math guru but the way I'd think about it is, if both weapons are of the same stats aside from splash then I'd do this. Again, I ain't no math guru but what you seem to be looking isn't something set in stone either.

Weapon A, 20D = 100% Efficiency
Weapon b, 10D*s = xx% Efficiency

If s = 1 then b is 50%
If s = 2 then b is 100%
If s = 3 then b is 150%
If s = 4 then b is 200%
If s = 5 then b is 250%
If s = 6 then b is 300%



So, if it is a Russian weapon it will be fighting primarily 4 man squads. You'll want to take the chance of it splashing the entire squad into account but let's assume it catches 2-3/4 on most shots. This is how you'll have to judge what weapon is stronger. If against 6 man squads that the russians roll with, the splash weapon will be stronger than when going against the smaller german teams due to the greater number of targets.

I'd base the likelihood of how many members splashed by formation distance, out of curiosity how far is the spacing between each man in a standard formation?

Another thing to keep in mind is damage focusing, if splashing 2 men then it will kill them at the same rate the 20 damage weapon does. However 1 man will go down in half the time and this cuts the opposing squads (if 4 men) firepower sooner, this would also have a value in the number you're trying to get to.


Still, at the end of the day all you can do is assign your own "Value" to splash based on these parameters, as far as I know you can't really get a hard mathematical value for this given it depends entirely on how it behaves within the game system. All I can do anyway is make a best guess with the info above. Then again, I ain't no maths wizz.

[Spartan_Marine88]

How i would do it to be more precise would be.

Dps = (b+(x*(b/d)

b would be base damage.

x would be number of units caught in blast

d would be distance from target

So lets say we add a stuh into the mix and its firing upon 5 rifle man. Say the stuhs base damage is 25. and the rifle men are standing about 5 meters away. We will set x to be 4 because 1 rifle is hit head on

(25+ (4*(25/4) = 50

[nikomas]

However that would only apply to an optimal scenario were you are splashing an entire squad dead on and counting on this variable to be a constant will lead to an unrealistic performance value. One would have to take other factors into account as well when comparing it to a weapon with no splash but twice the damage.

[rolcsika0128]

Well Spartan and Niko are right, but the problem is unfortunately not so simple IMO. You can't really determine a weapon's value after its DPS, even if you consider all other circumstances ( accuracy, etc) the same.
Just a brief example so you know what I mean: let's say two particular weapons have the same DPS (100 for instance), and they are supposed to fight infantry (which have relatively low hp value). One of the weapons fires only once per minute, and it deals 6000 dmg, the other one fires every 6 seconds dealing 600 dmg per shot. Now since they are supposed to fight infantry which have relatively low hp, the 2nd weapon's value is bigger in this case, since a 600 dmg-shot will kill an infantry just as much as an 6000 dmg-shot will, but the second one takes 1 minute to reload. Probably the easiest way to determine their value is what Niko said, but it's not exactly correct.

[Ahnungsloser]

By default you can't compare them since both wapeons have in physical term to different dimension. The dimension of the first value would be [dmg*s^-1*m^-2] (spoken "damage per area and time") and the dimension of the second wapeon would be [dmg*s^-1] (just "damage per second)

It might be useful to introduce a new dimension like averaged damage per area since even bullets have a certain area of effect. But for that wapeons new introduced value would be really huge for projectils, since the damage is concentrated in a small area. Additionally you need to understand the difference between the integrated damage over time, weighted average/root mean square/arithmetic average -value to be able to compare different wapeons.

But there much more interesting values which are more useful to compare wapeons. In mathematical terms, the first time derivative of damage per second could is much more interesting - it could be interpreted as something like "damage different per time intervall". If you analyze a HMG with this, the deveriate value would be close to zero, since the damage output is really constant (which mean there is only a low difference over time) while a tank maingun whil have a big value for the first time diverate because it shots really slow and therefore there are big timely differences.


Maybe you don't even understood what I wrote but overall you can't compare this two values - and when you do it it's not meaningful and has no technical content.

[nikomas]

Hang on, give me a minute

[Ahnungsloser]

Hang on, give me a minute

For example: It's the same when you would compare pressure with force. Both have something to do with force (transversal accelerated mass := force, angular accelerated moment of inertia := torque) but the second (pressure) is defined with force per area.

Now you can adapt this example of the opening question.

[Ahnungsloser]

[pqumsieh]

More information for you to work with:

Both weapons are identical in how they function. Same ROF, accuracy, etc. The only difference is the damage and splash. For arguments sake, lets assume there is no overkill on the damage and each shot divides evenly into the units health.

The splash for the first weapon function as follows.

Distance = 4; this is the max radius of the splash area.

The AOE applies differing damage values depending on distance. At 0-1 the splash deals full damage; at 1-2 the damage scales from 100% to 25%; from 2-4 the damage deals 25% of the base amount. Accuracy is 100% at all distances.

I realize there is other contextual data to take into consideration such as the proximity of other units to the target; lets assume there are 2 units in proximity at all times - you can use any scenario duration you wish.

Given those variables, what formula would you use?

[rolcsika0128]

Well you are basically claiming the same as I am, no need to derivate tbh, just use common sense. But the question is still open: how to overcome this problem and give the best estimate for weapon's value?

[Ahnungsloser]

More information for you to work with:

Both weapons are identical in how they function. Same ROF, accuracy, etc. The only difference is the damage and splash. For arguments sake, lets assume there is no overkill on the damage and each shot divides evenly into the units health.

The splash for the first weapon function as follows.

Distance = 4; this is the max radius of the splash area.

The AOE applies differing damage values depending on distance. At 0-1 the splash deals full damage; at 1-2 the damage scales from 100% to 25%; from 2-4 the damage deals 25% of the base amount. Accuracy is 100% at all distances.

I realize there is other contextual data to take into consideration such as the proximity of other units to the target; lets assume there are 2 units in proximity at all times - you can use any scenario duration you wish.

Given those variables, what formula would you use?

That special szenario can be easily solved if.. the two targets are significant smaller in space then the inner splash radius.
Since you have 100% accuracy you will always hit the target directly and with the second condition you can always say that the second target will always stay in the inner splash radius. Which overall means that you will always deal the same amount of damage.

The first gun can only hit (lets say member of a of squad) at the time and dealing 20 damage, while the second gun deals 10 damage per shot, but will still be able to hit two member which sums up to 20 damage per shot. But this is just a ideal scenario - If you start to throw area accuracy, scatter, the different AOE damage modifier, squad movements... etc. into this mix it's really hard to build a formula for that. You need a complicated distinction of many different cases which will make you got nuts. And even if you have that formula, it will only works if you do a infinite time of analysis of this "experiment" because otherwise the statistic elements behind this will act as the variance component in this calculation.

To be honest: What is the real deal behind your question?

[pqumsieh]

Figure out how to value splash into a weapons value.

[rolcsika0128]

More information for you to work with:

Both weapons are identical in how they function. Same ROF, accuracy, etc. The only difference is the damage and splash. For arguments sake, lets assume there is no overkill on the damage and each shot divides evenly into the units health.

The splash for the first weapon function as follows.

Distance = 4; this is the max radius of the splash area.

The AOE applies differing damage values depending on distance. At 0-1 the splash deals full damage; at 1-2 the damage scales from 100% to 25%; from 2-4 the damage deals 25% of the base amount. Accuracy is 100% at all distances.

I realize there is other contextual data to take into consideration such as the proximity of other units to the target; lets assume there are 2 units in proximity at all times - you can use any scenario duration you wish.

Given those variables, what formula would you use?

According to these assumptions I calculated the following:

First weapon deals 20 DPS, no problem with that.

The second weapon will do the following DPS, assuming that there are 2 units in proximity:
1, both units are in close range : damage dealt per second: 2x10=20
2,both units are in medium splash range: dmg dealt per second: 2x10x0.625= 12,5   ( 0.625 comes from the average of 100%-25% dmg output, (100-25)/2 + 25%, assuming that its totally random)
3, both units are in long range radius: 5  (im just gonna write the number of DPS from now on)
4, first unit close range, second medium: 16,25
5, first close, second long: 12,5
6, first medium, second long: 8,75

If you add these number up you get 75, divide it with 6 ( number of different possible outcomes) you get 12,5 avg DPS.

Now you compare it with first weapon's 20 DPS you can see, that CP (cateris paribus- all other circumstances left untouched) the first weapon is more effective if they are facing 2 man squads.

I calculated the avg DPS for the 2nd weapon with the same method if there are 3 units in proximity, and I got 18,75 DPS. This clearly shows what common sense already knows: by increasing the number of units affacted by splash radius, the better avg DPS the second weapon will get, and therefore the 2nd weapon is getting more and more advantage over the first one.

Conclusion: it's important to determine the average squad size of infantry the weapon is facing + the space between the individual units. ( since if the squad size and the space between units is too large the splash wont affect all of them) Can you give these information aswell?

[Mysthalin]

From the get-go - there is no absolute way to derive the real constant value of a weapon in this kind of scenario. Weapons that deal splash damage will forever be subject to a floating value that depends on which enemy unit is being hit (that unit's position relative to other units around it), how many units are within range of splash and other factors. However, we can simplify some of these values to get an estimated value.

The fundamental problem is figuring out how many units will be splashed upon with each shot. Although there is no absolute way of knowing this (one could simply try and observe a hundred shots and see what happens each time to get a resonable estimate - but that will still be a chance-based occasion) let's try and decide upon a basic formula for this. I would propose the following one:

Effective splashed units = number of units splashable * (1+Splash Radius - Formation spread) / Formation spread.

0<=(1+Splash Radius - Formation spread)/Formation spread<=1

Why this formula? Well, it is a fairly simple that can give a reasonable insight onto what is going to happen. Units do not maintain constant formation spread - they are subject to a bound that they try to maintain, but they pretty much never do it perfectly. Hence certainty over splashing over them (or not splashing over them at all) can not be claimed. However, if the squad tends to have a spread that is more or less equal to the splash - some of the units will probably be hit, while most won't. That's why the number 1 is entered into the equation. The reason why the simple formula is bound between 0 and 1 is because you can never splash less than 0 units, and never more than there are which are splashable in the first place.
Let's give an example:

There are 5 units in a squad. We have a splash radius of 5 and a formation spread of 3.

Only 4 units are splashable (one is targeted directly), so substituting in the values we get :

ESU= 4*((1+5-3)/3)=4*1=4

Effectively, you can expect that all 4 units out of the 4 will be splashed.

Assuming that there is no splash drop-off in damage, the unit is enjoying the value of 50 DPS with a base damage of just 10 DPS.

If you know that the splash has periodic drop-off, all you need to do is simply calculate the ESU's for each bound, and adjust each ESU beyond the short-range one by subtracting the previous one to obtain the realistic ESU at each range.

E.g.:

Base ESUs:

Short - 1
Medium - 2
Long - 4

Real ESUs:

Short = 1
Medium = 2-1=1
Long = 4-2=2

(1 person will be expected to be hit in the short-range splash, 1 in the medium-range blast, and 2 in the long-range blast).

And then you simply multiply each Real ESU by the appropriate damage modifier.

If you are going to implement a continuously scaling function (I.E. Damage continuously drops from 100% to 25% as range goes from 1 to 4) then you can still use this sort of function, but you will need to define it as an integral - and frankly put I'm not really that interested in doing that, as it's kind of tedious without really giving much benefit. It simply makes more sense to define it as a single bracket with a damage modifier of 62.5% - the difference will be absolutely negligible except in very, very precisely defined cases.

[rolcsika0128]

ESU= 4*((1+5-3)/3)=4*0.5=2

That equation equals 4 ? 4*1

[Mysthalin]

Taking the second scenario that you gave with different info - no proximity, but guaranteed number of units always being SOMEWHERE in proximity.

This is much simpler to calculate.

10 DPS base (the target itself) - ignore for now, it's simplistic.

We know that 2 units will be in proximity of the target at all times. They are perfectly randomly distributed in the splash radius and have an equal possibility of landing at any continuous point (0;4)

Hence it all becomes about probability. 0-1 is 25% of the distance, so there's a 25% chance to land there and be dealt full damage.

2*0.25*10=5

1-2 is another 25% of the distance, with an average damage within this distance of 62.5% Units can be dealt 100%, or 25%, or 33.4559% - it doesn't matter. On average, due to the perfectly random nature of the distribution it will always be 62.5%. So:

2*0.25*6.25=3.125

2-4 is 50% of the distance, 25% damage taken in this bound. Ergo:

2*0.5*2.5=2.5

Total splash damage effective = 5+3.125+2.5=10.625

Total DPS = 20.625

You could also draft up a damage-probability table that would simply write out the joint probability of each event happening to each soldier and multiplied by total damage taken by both soldiers, giving Expected damage for each possibility. Writing out just the possible outcomes is simple:

(Legend - 1,2 denotes soldier, L,M,S denotes which range he was hit at).

1. 1S 2S - 20DMG 0.25^2 probability = 1.25
2. 1S 2M - 16.25 DMG 0.25^2 probability = 1.015625
3. 1S 2L - 12.5 DMG 0.25*0.5 probability = 1.5625
4. 1M 2S - 16.25 DMG 0.25^2 probability = 1.015625
5. 1M 2M - 12.5 DMG 0.25^2 probability = 0.78125
6. 1M 2L - 8.75 DMG 0.25*0.5 probability = 1.09375
7. 1L 2S - 12.5 DMG 0.25*0.5 probability = 1.5625
8. 1L 2M - 8.75 DMG 0.25*0.5 probability = 1.09375
9. 1L 2L - 5 DMG, 0.5^2 probability = 1.25

Added up = 10.625 EDPS from splash

So a total of 20.625 DPS for the weapon.