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Burnthrough Question

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Shikatanai

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Re: Burnthrough Question

PostSat Dec 23, 2017 9:11 am

What speaks for keeping crits in example 1 and 1a is that you still have several dice - why should you be punished for that?
Concerning rolling single dice: Yes it is allowed but still ingame all those shots occur at the same point in time so rolling all those together is actually more accurate.

Anyway this discussion cannot be solved. It is not clearly written and needs correction in the future and up to then rulings by TOs.
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swampsheep

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Re: Burnthrough Question

PostMon Dec 25, 2017 9:14 pm

I encountered this challenge when I made my first detailed math analysis of BTL (first post about this can be seen here: http://linkedbroadsides.com/some-though ... rnthrough/). The Furnace cannon can also run into this problem.

I chose model 1a and all my analysis is based on that. I think model 2 and 3 can be discarded based on the arguments already presented which only leaves the question of how you roll those dice in the final roll in the case where no critical has emerged yet, but it emerges in the final roll.

What I do is; I look at the final roll and try to add it to my probability tree. If I find that my total number of hits and crits combined is above BT limit I remove hits one at a time from my current roll to see if that gets me below the BT limit. If not, I start removing critical hits to get below the limit.
This translates into looking at the final roll and removing the worst dice first, basically.

It is easy for me to change my algorithm. So I have made a worst-case algorithm; Where I reserve this and give preference to hits over crits if there is a surplus of damage so we can compare the difference. Notice, that this approach is even worse than the one suggested where I roll dice one at a time and stop, when I have reached my limit. In this model I roll all the dice and once and only choose any crits in that roll, if I have insufficient normal hits to reach my BT limit.

What I found was that this basically means nothing, statistically speaking. If I consider average damage against armour save 3+ (where this difference is most important) and using 3 decimals, the Viper prefering crits over hits (what I consider the correct approach) has an average of 5,094 damage whereas the one prefering hits over crits (my worst-case experiment) has 5,093 damage. Or an increase in average damage of 0,02 %.

To simply; it is irrelevant what approach you use as the difference is negligible.
http://linkedbroadsides.com - My blog with analysis, tactics and thoughts about dropfleet. Updates weekly, mostly on Mondays.
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Lordprinceps

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Re: Burnthrough Question

PostMon Dec 25, 2017 9:59 pm

Ah, good to hear that what I've found is corroborated.
Interestingly enough, I've found a difference of almost 1% in the mean damage between the varying models for the Viper, which is still ultimately statistically insignificant. This is more about just closing up ambiguous rules at this point, rather than anything that significantly affects balance.
The variance that I'm finding in my numbers may also be because I'm doing simulations rather than analysis, but it's close enough regardless in this context. In any case, I think I've heard enough arguments to convince me that 1a is the proper choice to go with for any issues, even if it really 'Doesn't Matter'.

Also, nice to see that someone else share's my dislike of the Siphon Power rule!
What are your thoughts on the Saint Petersburg firing a combined "Twin Cobra Laser" on weapons free, with combined stats of 3+ lock, 4 attacks, 1 damage, BTL(12), rather than having Siphon Power?
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swampsheep

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Re: Burnthrough Question

PostTue Dec 26, 2017 12:04 am

Lordprinceps wrote:Interestingly enough, I've found a difference of almost 1% in the mean damage between the varying models for the Viper, which is still ultimately statistically insignificant. This is more about just closing up ambiguous rules at this point, rather than anything that significantly affects balance.
The variance that I'm finding in my numbers may also be because I'm doing simulations rather than analysis, but it's close enough regardless in this context. In any case, I think I've heard enough arguments to convince me that 1a is the proper choice to go with for any issues, even if it really 'Doesn't Matter'.


I must admit, that the difference is less than I expected. You made me go back and check my work, but I can't find any error anywhere. When I look into the detailed numbers, some of the explanation of the small difference seems to come from the fact, that it only really changes some very few probabilities - namely those few where there is a large amount of normal hits, few (or no) criticals and BT limit is maxed out. The biggest difference is the probability of 8 hits and no critical that go from 0,16 % to 0,22 % - all other changes are smaller than that. It makes sense, I guess.

And yes, doing analysis on this by simulation will probably not be very accurate since you need a gargantuan amount of analysis to even out these very small probabilities. I do not know what your sample size is but I guess from intuition would be that 10 or 100 million simulations would be needed to achieve accuracy where you will get the same difference as you do by calculation. :-)

Lordprinceps wrote:Also, nice to see that someone else share's my dislike of the Siphon Power rule!
What are your thoughts on the Saint Petersburg firing a combined "Twin Cobra Laser" on weapons free, with combined stats of 3+ lock, 4 attacks, 1 damage, BTL(12), rather than having Siphon Power?


My intuition tells me that it would be way too good. Generally speaking, splitting a BTL weapon in two more than halves its performance (in short - being combined is better, seen from a damage perspective) so from that, combining them must more than double their effect, which I don't think is a good idea. It basically means that firing them individually is only relevant in the rare case where you have two rather soft targets in your narrow front.

It was a bit of a hassle to run it through the algorithm (I had a couple of places where I made something based on the assumption that BT limit of 8 was the maximum), but I got it done and it gave me the following observations:

  • Average damage vs. 3+ armour save: 6,28
  • Average damage of 1 cobra vs. 3+ armour save: 2,72
  • Damage improvement of double cobra compared to two individual cobras: 15 %

So damagewise, double cobra is 15 % better than two individual cobras and it doesn't require weapons free.

  • Chance of major spike for double cobra: 83,1 %
  • Chance of major spike for two cobras: 84,9 %
  • Chance of at least minor spike for double cobra: 96,6 %
  • Chance of at least minor spike for two cobras: 96,6 %

So spike-wise, they are almost identical with a slight advantage to two individual cobras.

But another interesting observation about the double cobra is the likelyhood of causing enough damage to do an outright kill (assuming that any "roll again" roll will result in 0 damage ono the second roll). Against UCM and PHR cruisers this is as follows:

  • Double Cobra chance to outright kill UCM cruiser: 32,9 %
  • Two individual cobra chance to outright kill UCM cruiser: 20,1 %
  • Double Cobra chance to outright kill PHR cruiser: 24,0 %
  • Two individual cobra chance to outright kill PHR cruiser: 12,9 %

So between 63,7 % (UCM) and 86,0 % (PHR) greater chance of outright kill.

Basically, there is almost no reason to fire the two cobras individually except for the rare case where there are two "softer" targets available.

I'm not sure exactly what the siphon power rule should be (I haven't given it much thought) but it should not make the burnthrough better than the Viper, and it should not make it better than firing the two cobras individually, because that comes with the price of weapons free which is rather steep. I think my best suggestion is either to cut price significantly (and drop "siphon power) or just raise the BTL ceiling even further for a siphon power but not giving any more dice to roll (maybe raise it to 12). Maybe even linking them and raising price for the ship somewhat.
http://linkedbroadsides.com - My blog with analysis, tactics and thoughts about dropfleet. Updates weekly, mostly on Mondays.
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Lordprinceps

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Re: Burnthrough Question

PostTue Dec 26, 2017 2:58 am

swampsheep wrote:And yes, doing analysis on this by simulation will probably not be very accurate since you need a gargantuan amount of analysis to even out these very small probabilities. I do not know what your sample size is but I guess from intuition would be that 10 or 100 million simulations would be needed to achieve accuracy where you will get the same difference as you do by calculation. :-)


Yeah, I'm only running around 500,000 to one million simulations; simply for the fact that I'm working with a ~four year old desktop, as well as me not being a programmer who can optimize this kind of stuff. I don't really think it's all that important to analyze average damages or percentages past the hundredths anyways, considering the scale of the values in the game. A good rule of thumb, I find, is that if it would result in a difference of less than one point of damage over the course of an entire game, it's effectively insignificant.

swampsheep wrote:Burnthrough Stuff

Yep, those are the same values I got as well; thanks! One thing I have to mention is that this hypothetical double cobra would only be fired on WF as well; it would only be fired when both cobras could be fired. On standard orders, the Saint Pete would only be able to fire a single, normal cobra.
Basically, it'd be an alt fire weapon to both of the Cobras, with a special note saying that it could only be fired on weapon's free.

Also, I have to say, I never thought about evaluating weapons and ships by their probability to destroy given ships, as well as effective Time-To-Kill if an outright kill isn't possible. Certainly something I'll have to look at more in any future analysis.
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swampsheep

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Re: Burnthrough Question

PostTue Dec 26, 2017 8:25 pm

Lordprinceps wrote:I don't really think it's all that important to analyze average damages or percentages past the hundredths anyways, considering the scale of the values in the game. A good rule of thumb, I find, is that if it would result in a difference of less than one point of damage over the course of an entire game, it's effectively insignificant.


Agree. It is mainly the perfectionist in me who like to get it done like this, but the engineer agrees that it is a waste of effort, really.

Lordprinceps wrote:Yep, those are the same values I got as well; thanks! One thing I have to mention is that this hypothetical double cobra would only be fired on WF as well; it would only be fired when both cobras could be fired. On standard orders, the Saint Pete would only be able to fire a single, normal cobra.
Basically, it'd be an alt fire weapon to both of the Cobras, with a special note saying that it could only be fired on weapon's free.


Ah, okay. I don't think it will solve the basic problem of the st. Petersburg namely that most enemies will make quite an effort to deny it WF because it is so horribly deadly. That is what is really interesting to me.

Lordprinceps wrote:Also, I have to say, I never thought about evaluating weapons and ships by their probability to destroy given ships, as well as effective Time-To-Kill if an outright kill isn't possible. Certainly something I'll have to look at more in any future analysis.


Most of my analysis is actually "chance of accomplishing X" because average damage is quite misleading (I make a somewhat longer argument for that in this post: http://linkedbroadsides.com/the-difference-between-oculus-beams-and-uf-6400-mass-drivers/). I usually look at the chance of killing a frigate or cause a crippling roll or - if I want it more detailed - the chance of doing 0, 1, 2, etc. damage in a specific case.
http://linkedbroadsides.com - My blog with analysis, tactics and thoughts about dropfleet. Updates weekly, mostly on Mondays.
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