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LaurenBacall

Demolition Expert Math

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I'm not claiming to be an expert, just a long-time player that decided to run the numbers. Demolition Expert - when should it be chosen as a commander skill? Using the information found on the wiki and the forums, I concluded that the formula for probability (not the chance) of starting a fire over time looks like this:

X1 = 1 - (1 - H) ^ ((G * 60 sec / R) / 60 sec), where...

  • X = the probability of setting a fire every second (what we're solving for)
  • H = chance of HE shells causing fire on target (ship stat)
  • G = number of main battery guns that can realistically be brought to bear, port or starboard
  • R = main battery gun reload time (ship stat)

This formula is based on determining the cumulative probability of not starting a fire broadside salvo, over the course of a minute (# shells/salvo * 60 seconds / reload rate), divided by 60 seconds (to get a probability/second).

To tell whether the Demolition Expert skill is "worth it", we need to compare the difference in probabilities both with and without the Demolition Expert's 2% bonus to "chance of HE shells causing fire on target". Here's the above formula, modified to account for the Demolition Expert commander skill:

X2 = 1 - (1 - H + 0.02) ^ ((G * 60 sec / R) / 60 sec)

If the difference between these two probabilities (X1 and X2)is greater than 2%, then HE is "worth taking". Questions:

  • Is the formula and method above accurate? (Check my work!)
  • Should we be looking at DPS vs. DPM?
  • Is the 2% difference a good enough assumption?
  • Should Demolition Expert ever be paired with IFHE? Assuming the difference even with IFHE taken is about the same as without IFHE, it still makes sense to take Demolition Expert, no?

Using the above, here's a list of cruisers where taking the Demolition Expert commander skill "makes sense":

  • Atlanta, Bayard, Bogatyr, Budyonny, Buffalo, Chapayev, Colbert, Dallas, Danae, De Grasse, Des Moines,  Dresden, Duca Degli Abruzzi, Duguay-Trouin, Emden, Flint, Hindenburg, Irian, Kolberg, Königsberg, Kuma, La Galissonnière, Lazo, Marblehead, Marakov, Mikhail Kutuzov, Murmansk, Novik,  Nürnberg, Omaha, Perth, Salem, Seattle, Shchors, Smolensk, Worcester

Looking forward to analysis, comments, and questions. Thanks!

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Do you run that formula through your head as your'e playing the game? If you you do you are way better than me. I use the Kentucky long rifle method. Shoot at them and turn.

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I think you are over thinking this. A ship with a low single digit fire chance gets a huge boost to fire chance. A ship with a much higher chance such as a BB gains a much smaller percentage benefit. Plus most people take it as an offset for the penalty to fire chance for taking IFHE which I think is at least part of the idea with the increased penalty that the proposed IFHE change, it is far to easy for CL's to offset the current penalty.

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If you want to do the math I think you would be better off looking at the time to a given chance of setting a fire:

Baltimore with both fire flags (to pick something that's pretty average) has 16% fire chance. A tier 8 ship with fire prevention and the anti fire module reduces that to 57%, so your real fire chance per hit is 9%.

If you solve your equation for the number of shells instead of the fire chance, that's a 75% chance of setting at least one fire after 15 hits. DE reduces that to 13 hits. If you hit about half your shells, both of those are about three volleys.

 

The same math for a Cleveland gives you about 24 hits without DE, 20 with it. Akizuki goes from 48 to 34.

 

I think the main thing you get from doing the fire chance math is that the skill doesn't really do much on heavy cruisers, but heavy cruisers also don't have any pressing need for three more commander points so you end up taking DE anyway.

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56 minutes ago, LaurenBacall said:

H = chance of HE shells causing fire on target (ship stat)

If you're looking at the published per-shell fire chance, you're already doing it wrong.  The actual fire chance is a function of the shell, the target, and a list of modifiers.  For instance, a published per-shell chance of 6% is more like 3-4% in battle.  The amount of change from DE is probably a similar fraction of the published value.  Once you figure out what the actual per-shell change is, the rest falls out on the ground.

@WernerHerzdoghas a good illustration.

Edited by iDuckman

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41 minutes ago, BrushWolf said:

A ship with a low single digit fire chance gets a huge boost to fire chance.

Not true. I used to think that also. The effectiveness of DE is mainly determined by the ships rate of fire and the increased probability of a fire - which is the whole point, right? Why spend 3 points on a skill that doesn't give you much of an advantage over the course of the entire battle?

22 minutes ago, WernerHerzdog said:

Baltimore with both fire flags (to pick something that's pretty average) has 16% fire chance.

Again, see above. The increase in the chance to get a fire on a single shell (increased by fire-increasing buffs) isn't the same as the probability of setting fires over time. Yes, the modified chance to start fires is the base, but the main influence is over rate of fire and probability.

24 minutes ago, WernerHerzdog said:

If you solve your equation for the number of shells instead of the fire chance, that's a 75% chance of setting at least one fire after 15 hits.

Supporting math? And how long does it take to get those 15 hits, compared to say, a Smolensk or a Colbert? That makes all the difference in dishing out fires and that makes Demolition Expert that much more effective

22 minutes ago, iDuckman said:

The actual fire chance is a function of the shell, the target, and a list of modifiers.

Agreed, but I can't control what's happening at the pointy end of the shell arc. I'm just saying that if you take DE at face value, the above math appears to be how it's bonus gets applied in practice, based on probability math. Therefore, even if I take all other factors into account, the probability difference calculated above is "significant" independent of other factors. That helps me (just speaking for myself) to answer the question, "Should I spend 3 points on DE or not? Am I wasting those points?" 

Just thought my list of cruisers where the biggest improvements in HE fire starting % occur would be useful to folks.

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27 minutes ago, LaurenBacall said:

Not true. I used to think that also. The effectiveness of DE is mainly determined by the ships rate of fire and the increased probability of a fire - which is the whole point, right? Why spend 3 points on a skill that doesn't give you much of an advantage over the course of the entire battle?

Yep, the one thing you're neglecting here is that you have 0% fire chance if you hit a part of the ship that's already burning.

(like your math would say DE is a good skill on a ship with 5 second reload, 10 guns, and 50% fire chance, but in reality that ship is going to set fires so quickly it doesn't matter)

27 minutes ago, LaurenBacall said:

Again, see above. The increase in the chance to get a fire on a single shell (increased by fire-increasing buffs) isn't the same as the probability of setting fires over time. Yes, the modified chance to start fires is the base, but the main influence is over rate of fire and probability.

 Supporting math? And how long does it take to get those 15 hits, compared to say, a Smolensk or a Colbert? That makes all the difference in dishing out fires and that makes Demolition Expert that much more effective.

You have the right idea with your equation X = 1 - (1 - H) ^ ((G * 60 sec / R) / 60 sec) but there are a couple things missing.

The displayed fire chance is higher than the real fire chance, but that doesn't actually matter too much for whether DE is useful. You have half the fire chance against a tier 10 ship, but that also halves the effect of DE. Adding 2% to a base 10% fire chance isn't too different from adding 1% to a base 5%.

You're also dividing by the reload time in the exponent, but it doesn't make sense to have a per second fire chance. I don't think that's changing your results much though.

 

The way you get 15 hits is by taking the same equation 75% = 1 - (1 - 9%)^x and solving for x, the number of shells you have to hit for a 75% chance of at least one fire. A lot of the time you're shooting the same ship over and over, so your fire chance drops off dramatically once you get one fire and what matters the most is how long it takes to get that one fire. Obviously a Baltimore takes longer to set one fire than a Smolensk, but that doesn't matter if you're trying to figure out whether or not to take DE on the Baltimore.

Edited by WernerHerzdog

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2 hours ago, LaurenBacall said:

I'm not claiming to be an expert, just a long-time player that decided to run the numbers. Demolition Expert - when should it be chosen as a commander skill? Using the information found on the wiki and the forums, I concluded that the formula for probability (not the chance) of starting a fire over time looks like this:

X1 = 1 - (1 - H) ^ ((G * 60 sec / R) / 60 sec), where...

  • X = the probability of setting a fire every second (what we're solving for)
  • H = chance of HE shells causing fire on target (ship stat)
  • G = number of main battery guns that can realistically be brought to bear, port or starboard
  • R = main battery gun reload time (ship stat)

This formula is based on determining the cumulative probability of not starting a fire broadside salvo, over the course of a minute (# shells/salvo * 60 seconds / reload rate), divided by 60 seconds (to get a probability/second).

To tell whether the Demolition Expert skill is "worth it", we need to compare the difference in probabilities both with and without the Demolition Expert's 2% bonus to "chance of HE shells causing fire on target". Here's the above formula, modified to account for the Demolition Expert commander skill:

X2 = 1 - (1 - H + 0.02) ^ ((G * 60 sec / R) / 60 sec)

If the difference between these two probabilities (X1 and X2)is greater than 2%, then HE is "worth taking". Questions:

  • Is the formula and method above accurate? (Check my work!)
  • Should we be looking at DPS vs. DPM?
  • Is the 2% difference a good enough assumption?
  • Should Demolition Expert ever be paired with IFHE? Assuming the difference even with IFHE taken is about the same as without IFHE, it still makes sense to take Demolition Expert, no?

Using the above, here's a list of cruisers where taking the Demolition Expert commander skill "makes sense":

  • Atlanta, Bayard, Bogatyr, Budyonny, Buffalo, Chapayev, Colbert, Dallas, Danae, De Grasse, Des Moines,  Dresden, Duca Degli Abruzzi, Duguay-Trouin, Emden, Flint, Hindenburg, Irian, Kolberg, Königsberg, Kuma, La Galissonnière, Lazo, Marblehead, Marakov, Mikhail Kutuzov, Murmansk, Novik,  Nürnberg, Omaha, Perth, Salem, Seattle, Shchors, Smolensk, Worcester

Looking forward to analysis, comments, and questions. Thanks!

Wow! Awesome post. 
 

I dont have time to run the numbers.

would Atlanta benefit more from RoF(bft)than DE? My build has CE, IHFE, and AFT. 
 

None of the IJN cruisers benefit from DE?

Can you walk me thought Cleveland not benefit from DE?

what about DDs? Russians and RN? 

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1 hour ago, LaurenBacall said:

Just thought my list of cruisers where the biggest improvements in HE fire starting % occur would be useful to folks.

It could.  If you figure a standard target (e.g. same-tier cruiser/BB average) and standard modifier set (again, BB/CR average) with IFHE applied as appropriate (to CLs, not CAs), then the effect of DE per hit could be graded and extrapolated per minute.  A spreadsheet calls...

Personally, I pretty much use it to offset the effects of IFHE, only. 

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15 minutes ago, iDuckman said:

It could.  If you figure a standard target (e.g. same-tier cruiser/BB average) and standard modifier set (again, BB/CR average) with IFHE applied as appropriate (to CLs, not CAs), then the effect of DE per hit could be graded and extrapolated per minute.  A spreadsheet calls...

Personally, I pretty much use it to offset the effects of IFHE, only. 

To me DE is exponential more effective the more shells landed on target. For example Conq I’m a superb game I have landed 100 shells but mostly around 50. Or say Worcester, smoli or virtually any rapid fire ship where you typically land 100+ shells DE significantly raises the fire chance. Of course there are other modifiers like if the red ship used dmg con, FP etc. I tend to use DE on cruisers and some dd lines. 

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21 hours ago, wstugamd said:

None of the IJN cruisers benefit from DE?

Can you walk me thought Cleveland not benefit from DE?

what about DDs? Russians and RN?

All ships can benefit from DE, but some more than others. My assumption of what is "good enough" is at least a 2% increased probability of setting a fire every second (which is, obviously, theoretical, since ship reload times are longer than that.)  That makes it a better investment of 3 commander skill points on those cruisers listed above in my initial post.

(P.S. So far, none of the BBs I've analyzed "qualify" for DE. I'm sure most DDs will.)

21 hours ago, WernerHerzdog said:

You're also dividing by the reload time in the exponent, but it doesn't make sense to have a per second fire chance.

What I was trying to do is normalize the exponent to "# of shells fired per minute", instead of "# of shell fired per salvo". As you say, that shouldn't adversely affect the match, but thanks for pointing it out.

21 hours ago, WernerHerzdog said:

A lot of the time you're shooting the same ship over and over, so your fire chance drops off dramatically once you get one fire

So true. This makes a good case for spreading the HE around the map more if you have the kind of ship that can unload the rounds fast enough!

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On 2/17/2020 at 6:32 PM, LaurenBacall said:

I'm not claiming to be an expert, just a long-time player that decided to run the numbers. Demolition Expert - when should it be chosen as a commander skill? Using the information found on the wiki and the forums, I concluded that the formula for probability (not the chance) of starting a fire over time looks like this:

X1 = 1 - (1 - H) ^ ((G * 60 sec / R) / 60 sec), where...

  • X = the probability of setting a fire every second (what we're solving for)
  • H = chance of HE shells causing fire on target (ship stat)
  • G = number of main battery guns that can realistically be brought to bear, port or starboard
  • R = main battery gun reload time (ship stat)

This formula is based on determining the cumulative probability of not starting a fire broadside salvo, over the course of a minute (# shells/salvo * 60 seconds / reload rate), divided by 60 seconds (to get a probability/second).

To tell whether the Demolition Expert skill is "worth it", we need to compare the difference in probabilities both with and without the Demolition Expert's 2% bonus to "chance of HE shells causing fire on target". Here's the above formula, modified to account for the Demolition Expert commander skill:

X2 = 1 - (1 - H + 0.02) ^ ((G * 60 sec / R) / 60 sec)

If the difference between these two probabilities (X1 and X2)is greater than 2%, then HE is "worth taking". Questions:

  • Is the formula and method above accurate? (Check my work!)
  • Should we be looking at DPS vs. DPM?
  • Is the 2% difference a good enough assumption?
  • Should Demolition Expert ever be paired with IFHE? Assuming the difference even with IFHE taken is about the same as without IFHE, it still makes sense to take Demolition Expert, no?

Using the above, here's a list of cruisers where taking the Demolition Expert commander skill "makes sense":

  • Atlanta, Bayard, Bogatyr, Budyonny, Buffalo, Chapayev, Colbert, Dallas, Danae, De Grasse, Des Moines,  Dresden, Duca Degli Abruzzi, Duguay-Trouin, Emden, Flint, Hindenburg, Irian, Kolberg, Königsberg, Kuma, La Galissonnière, Lazo, Marblehead, Marakov, Mikhail Kutuzov, Murmansk, Novik,  Nürnberg, Omaha, Perth, Salem, Seattle, Shchors, Smolensk, Worcester

Looking forward to analysis, comments, and questions. Thanks!

Here's my formula … 

Firestarter DD/Cruiser + DE = Gud :)

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1 hour ago, LaurenBacall said:

All ships can benefit from DE, but some more than others. My assumption of what is "good enough" is at least a 2% increased probability of setting a fire every second (which is, obviously, theoretical, since ship reload times are longer than that.)  That makes it a better investment of 3 commander skill points on those cruisers listed above in my initial post.

(P.S. So far, none of the BBs I've analyzed "qualify" for DE. I'm sure most DDs will.)

I can’t imagine any bb would. RN already have high fire rates. Maybe the JB or Republic but AP is a bbs real strength. 
 

DDs typically have a better use of 3 points outside of Russians and the French. Plus the right rate of fire increase the fire chance. 
 

IJN cruisers I guess Vigilance could be useful but DE seems like the right choice.  

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On 2/17/2020 at 5:32 PM, LaurenBacall said:

Is the formula and method above accurate? (Check my work!) 

Obvious mistake: when adding DE, the base becomes (1 - (H + 0.02)) = (1 - H - 0.02)

More subtle problem that hints at bigger theoretical problems:
Exponents must be dimensionless.  The exponent should be G / R * t.  I think you've implicitly set t = 1s. 
The difference can be calculated for any time, which I've plotted for the Atlanta, along with the ratio, just to look at the shape of the curves. Figure_1.png.3d4806d651b731aa413eea07069e537f.png

It looks like the timescale matters, but I'm not sure what timescale would be the most meaningful to use.

The bigger question is is this the right metric to judge the effectiveness of the skill?

LWM uses expected fires per minute to measure fire starting ability in her reviews, which assumes all shells hit a ship section not already on fire.
Your approach is the opposite extreme, considering only the probability of having started at least one fire on a single section.
Neither is a perfect measure.

The choice of whether to take the skill also depends on what other skills are competing for the points.

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13 minutes ago, Pseudovector said:

Figure_1.png.3d4806d651b731aa413eea07069e537f.png

It looks like the timescale matters, but I'm not sure what timescale would be the most meaningful to use.

That's why I was suggesting 'time to 75% chance of setting a fire'. The timescale is mattering there because if you set it really high, obviously an Atlanta that shoots the same ship for two minutes straight is going to set a fire at some point whether or not it has DE. I don't see an obvious time to use.

Another option would be to ignore the rate of fire and just take the chance of one or more fire per salvo.

 

I think the OP's approach is more useful than fires per minute. Fires per minute has the problem that if you shoot one ship (unless it's a CV with damage control on cooldown) you can't really set more than three or four fires in a minute anyway.

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1 hour ago, WernerHerzdog said:

That's why I was suggesting 'time to 75% chance of setting a fire'. The timescale is mattering there because if you set it really high, obviously an Atlanta that shoots the same ship for two minutes straight is going to set a fire at some point whether or not it has DE. I don't see an obvious time to use.

Another option would be to ignore the rate of fire and just take the chance of one or more fire per salvo.

Yeah, this looks like a better approach.

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Once I saw your algebra I stopped attempting to understand it. Remember at tier ten all ships have a 50% fire reduction chance built in. Before the flags and captains skills and modules are calculated. If you have a tier ten with 20% fire chance shells at tier ten using DE +2%/50% it is really 11%.

That scale slowly slides downward per tier which increases fire per ship.

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14 hours ago, Pseudovector said:

Obvious mistake: when adding DE, the base becomes (1 - (H + 0.02)) = (1 - H - 0.02)

Not a "mistake", just a difference in terms used in the formula. As you illustrate, they mean the same thing.

14 hours ago, Pseudovector said:

Exponents must be dimensionless.  The exponent should be G / R * t.  I think you've implicitly set t = 1s.

Good point - thank you. Here's are streamlined formulas:

X1 = 1 - (1 - H) ^ ((G * 60 sec / R sec) / 6)

X2 = 1 - (1 - H - 0.02) ^ ((G * 60 sec / R sec) / 6)

13 hours ago, WernerHerzdog said:

I think the OP's approach is more useful than fires per minute. Fires per minute has the problem that if you shoot one ship (unless it's a CV with damage control on cooldown) you can't really set more than three or four fires in a minute anyway.

I think you're both right and this is a critical observation, since the duration considered has a large effect on the probability gap between non-DE and DE. I agree that measuring the probability gaps at 1 second and 1 minute are both too extreme. How about a more "reasonable" 10 seconds? At 10 seconds (the '6' in the above, amended formulas), a 5% probability increase to set a single fire seems more measurable - I want to get new fires set in a reasonable amount of time. Therefore:

If (X2 - X1) >= 5% then taking DE is "good enough", assuming all other factors are equal.

The list of top-hull, HE-firing cruisers that meet this criteria is now a lot different from my OP:

  • Admiral Hipper, Albany, Atlanta, Aurora, Belfast, Boise, Bogatyr, Buffalo, Charleston, Chester, Chikuma, Dallas, De Grasse. Diana, Dimitri Donskoi, Dresden, Duca d'Aosta, Duca Degli Abruzzi, Duguy-Trouin, Emden, Émile Bertin, Flint, Friant, Helena, Huanghe, Indianapolis, Jurien, Karlsruhe, Katori, Kirov, Kolberg, Königsberg, Krazny Krym, Kuma, La Galissonnière, London, Marblehead, Marakov, Mogami (155mm), Molotov, Murmansk, New Orleans, Novik, , Nueve de Julio, Nürnberg (B) and (C), Oleg, Omaha, Pensacola, Perth, Phoenix, Prinz Eugen, Roon, Shchors, St. Louis, Svietlana, Tenryū, Varyag, Yahagi, Yorck, Yūbari

That a lot of cruisers! (but not all of them) - if you "lower your standards" then you could argue that DE has a measurable impact on every HE-firing cruiser in the game...but is it still worth the 3 commander skill points? Personal preference. I'd rather use those points elsewhere.

Again, thank you all!

 

 

Edited by LaurenBacall

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5 hours ago, LaurenBacall said:

Not a "mistake", just a difference in terms used in the formula. As you illustrate, they mean the same thing.

Your OP had "(1 - H + 0.02)", which is not the same.

10s seems just as arbitrary a choice as 1 or 60.  Same with the threshold.

I'd find this work much more useful if you showed the numbers for each ship, showing how much better DE is for these ships than the ones for which you claim it's not worth it.

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