Crystal plating and armour in the asimov beta

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misterderp

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In the asimov beta patch the Crystal-Forged Plating has it’s hp boost reduced by 25%. From 100 to 75 for the small component.. Whereas the armour values are still the same.

This alters the balance of when the crystal plating is better than armour. In the how armour works thread I have shown simulations of when armour would be better than crystal plating under the old patch. Considering how useful such information is I decided to create a new thread using the new numbers! I will only use highest tier armour and highest tier crystal plating, and only for the battleships. (base HP 2400, base armour 24).

I will compare for 30 small components equivalents their added value for ship survivability. Small components equivalents are chosen since medium has 2x the benefit of small components and large 4x the benefit of small components. This linearity makes using only the equivalent of small components easy on the simulations!. Given the utility slots of the battleship cores a total 40 small components equivalents are available, some arbitrary guestimation states about 10 of those will go to powering the weapons. NO shields are done in this simulation their power requirement in addition to the the presence of the shield components that are required makes for a bit more complicated simulations (I might do those later).

As a final note before we get into the specifics of my method, no combinations of different components are done only pure all armour and only pure all crystal plating. It is quite likely that the most optimal of optima is hidden somewhere in a x amount of extra armour and x amount of extra hp. Doing such simulation is however not in the scope of this thread.

For every small component added either 5 armour or 75 hp will be added to the ship. For the smoothness of the graph 1 dps is chosen. Increasing the DPS will only decrease the ship survivability while still respecting the overall trend.

As to the specific formulas used. For armour damage reduction. Reduction = armour/(60+armour). The Standard equation that can also be found in the defines.lua file. For damage done calculation: damage done = dps*(1-armour_ignore_fraction)*(1-reduction) + dps * armour_ignore_fraction. This means that the percentage of the damage that can ignore armour ignores it and the fraction that does not does not do this. HP of the ship is the result of current_hp-damage done.

So forward to the interesting stuff!

If the enemy has no armour ignoring weapons on his ships slapping on more armour will be better than adding crystal plating. As shown in the graph below.
no armour ignoring.png


It is however not very likely the enemy would be as sporting as not having such ghastly weapons, that ignore your glorious and noble armour, the xenos they are. With 50% armour piercing damage the crystal plating will always be more useful then slapping on more armour, as shown in the graph below.

50% armour ignoring.png


At 30% of damage output armour ignoring things become interesting! Here up until and including the eighth components adding more armour adds more survivability then crystal plating does! However, from the eighth component onwards crystal plating is more favourable! (a close up is available for closer inspection)
30% armour ignore.png



close up 30%.png


With 35% armour ignoring damage output up to 3 small armour components are better then up to 3 small crystals, but only slightly.
35% armour ingnoring.png


Further reducing the percentage of armour ignoring damage output will only further increase the amount of components at which armour is better then crystal plating. To the point at which adding armour is always better then adding more plating.

I hope you find this information useful! If you have any questions please feel free to ask them!

edit: I forgot to add the (1-reduction) in my formula in this post (not in the inital simulations)! Thank you Artannon for pointing this out.
 
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Artannon

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Hm. Can you share your actual numbers? Based on the previous thread, the armor graph shouldn't curve, just change in slope for different % armor piercing.

Additionally, you list this formula: dps*(1-armour_ignore_fraction)*reduction + dps * armour_ignore_fraction

As I read it, that is incorrect. Reduction would be the amount reduced ( so 28.5% for a battleship's 24 armor) so the formula should actually be dps*(1-armour_ignore_fraction)*(1-reduction) + dps * armour_ignore_fraction.

Alternatively, switch the formula to 60 / (60 + armor) and you'll get "%Damage Taken", and then you can just slot that into reduction without inverting the percentage.

Don't know if that accounts for the slope of the graphs or not.
 
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misterderp

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Hm. Can you share your actual numbers? Based on the previous thread, the armor graph shouldn't curve, just change in slope for different % armor piercing.

Additionally, you list this formula: dps*(1-armour_ignore_fraction)*reduction + dps * armour_ignore_fraction

As I read it, that is incorrect. Reduction would be the amount reduced ( so 28.5% for a battleship's 24 armor) so the formula should actually be dps*(1-armour_ignore_fraction)*(1-reduction) + dps * armour_ignore_fraction.

Alternatively, switch the formula to 60 / (60 + armor) and you'll get "%Damage Taken", and then you can just slot that into reduction without inverting the percentage.

Don't know if that accounts for the slope of the graphs or not.

Even in the old thread if armour piercing weapons were introduced there was a curve ( This curve was less obvious due to the fact a higher dps was chosen). Only if no armour piercing damage was simulated did it result in a straight line (if we ignore the instances of overkill).

oeps I made a typo in my inital post I should have copy pasted my code. Thank you for pointing this out! dps*(1-armour_ignore_fraction)*(1-reduction) + dps * armour_ignore_fraction Is indeed what I used for my calculations! I will adres my error in the OP, good to know people read this closely enough so errors in my post get pointed out!



If you were to make best fitting line for the armour in this graph it would be a curve!
$R7W3LKP.png


this calculation was done without armour ignoring damage output and then the number of shots taken increases linearly indeed ;).
$RQAU2FZ.png
.
 

Derp

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I'd be curious to see how different ratios of armor/plating compare for a given number of slots
 

misterderp

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I'd be curious to see how different ratios of armor/plating compare for a given number of slots

Hello fellow derp! How do you mean? as in 5 slots of armour and 5 slots of plating on the same ship? I am working on it but have some difficulties getting it to work in a short time frame so if this is wat you want, stay tuned, if I can get it to work properly I will post it!.
 

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Hello fellow derp! How do you mean? as in 5 slots of armour and 5 slots of plating on the same ship? I am working on it but have some difficulties getting it to work in a short time frame so if this is wat you want, stay tuned, if I can get it to work properly I will post it!.
Yep, that's what I mean. I suspect that some mix would give a higher total EHP (since the increased DR would play off the increase base HP) but I'm not sure.
 

Pode

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Armor is linear EHP for a given amount of HP, but crystal adds HP, so you reach a point where you should alternate adding CFP and armor.

Misterderp, I gave up trying to find a closed form equation solution for these sorts of things and just built a spreadsheet that calculates the EHP differential for adding one more small slot component of each type based on the EHP from the components already present. So I add 1 component of the highest payoff type at a time until I run out of slots and see where I end up, instead of trying to predict the result in advance. You may find a similar approach pays off for you. Or you may be smarter than me and able to find the closed form solution.
 

misterderp

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@Derp I have completed the analysis.

The same formulas as before were used! in the spoilers a text variant of the different simulations are presented. Please take the shots taken with a grain of salt as dps increases the shots taken should decrease, however the relationsships between the different conditions should remain the same. In short it is an arbitrary measure of toughness, higher is better.

conditions 30 small component equivalent of armour and 0 of crystal plating to 1 of armour and 29 of crystal plating. either 0%,30% or 50% armour piercing enemy total damage output.

giving the following results: for 0 armour piercing enemy damage output 19 small armour equivalents and 11 small crystal plating equivalents give the highest survivability.

How to read the x axis in these graphs is 30-x = armour components x= crystal components. (text in the spoilers contains more detailed descriptions).
component analysis.png


With 50% armour ignoring enemy damage output the optimum is at 3 small armour equivalents and 27 small crystal plating equivalents with 6351 shots taken.

component analysis 50.png


For 30% enemy armour ignoring damage output the optimum is 8 small armour equivalents and 22 small crystal plating equivalents with shots taken 7203.
component analysis 30.png


Personally I think that the 30% optimal value might be the best value to incorporate in your ships on avarege! I think it is quite unlikely the enemy will have very high percentages of armour piercing weapons,(Baring perhaps the fallen empires, and the unbidden). However it is clear form these simulations that if the percentage of armour piercing damage increases the is a shift in how much better more plating will be. However even at 50% of total damage output being armour ignoring slapping on some armour is still better then not having any armour at all. So if you choose to ignore adding even some armour to your ships you are effectively making them weaker.


no armour ignoring dps
for 30 armour and 0 crystal plating shots taken is 9361
for 29 armour and 1 crystal plating shots taken is 9542
for 28 armour and 2 crystal plating shots taken is 9707
for 27 armour and 3 crystal plating shots taken is 9855
for 26 armour and 4 crystal plating shots taken is 9987
for 25 armour and 5 crystal plating shots taken is 10102
for 24 armour and 6 crystal plating shots taken is 10200
for 23 armour and 7 crystal plating shots taken is 10282
for 22 armour and 8 crystal plating shots taken is 10347
for 21 armour and 9 crystal plating shots taken is 10396
for 20 armour and 10 crystal plating shots taken is 10427
for 19 armour and 11 crystal plating shots taken is 10442
for 18 armour and 12 crystal plating shots taken is 10440
for 17 armour and 13 crystal plating shots taken is 10422
for 16 armour and 14 crystal plating shots taken is 10387
for 15 armour and 15 crystal plating shots taken is 10335
for 14 armour and 16 crystal plating shots taken is 10267
for 13 armour and 17 crystal plating shots taken is 10182
for 12 armour and 18 crystal plating shots taken is 10081
for 11 armour and 19 crystal plating shots taken is 9962
for 10 armour and 20 crystal plating shots taken is 9827
for 9 armour and 21 crystal plating shots taken is 9676
for 8 armour and 22 crystal plating shots taken is 9507
for 7 armour and 23 crystal plating shots taken is 9322
for 6 armour and 24 crystal plating shots taken is 9121
for 5 armour and 25 crystal plating shots taken is 8902
for 4 armour and 26 crystal plating shots taken is 8667
for 3 armour and 27 crystal plating shots taken is 8415
for 2 armour and 28 crystal plating shots taken is 8147
for 1 armour and 29 crystal plating shots taken is 7862

50% armour ignore dps
for 30 armour and 0 crystal plating shots taken is 3821
for 29 armour and 1 crystal plating shots taken is 3962
for 28 armour and 2 crystal plating shots taken is 4102
for 27 armour and 3 crystal plating shots taken is 4239
for 26 armour and 4 crystal plating shots taken is 4374
for 25 armour and 5 crystal plating shots taken is 4507
for 24 armour and 6 crystal plating shots taken is 4637
for 23 armour and 7 crystal plating shots taken is 4764
for 22 armour and 8 crystal plating shots taken is 4889
for 21 armour and 9 crystal plating shots taken is 5010
for 20 armour and 10 crystal plating shots taken is 5128
for 19 armour and 11 crystal plating shots taken is 5243
for 18 armour and 12 crystal plating shots taken is 5354
for 17 armour and 13 crystal plating shots taken is 5462
for 16 armour and 14 crystal plating shots taken is 5565
for 15 armour and 15 crystal plating shots taken is 5664
for 14 armour and 16 crystal plating shots taken is 5758
for 13 armour and 17 crystal plating shots taken is 5846
for 12 armour and 18 crystal plating shots taken is 5930
for 11 armour and 19 crystal plating shots taken is 6008
for 10 armour and 20 crystal plating shots taken is 6079
for 9 armour and 21 crystal plating shots taken is 6143
for 8 armour and 22 crystal plating shots taken is 6201
for 7 armour and 23 crystal plating shots taken is 6250
for 6 armour and 24 crystal plating shots taken is 6290
for 5 armour and 25 crystal plating shots taken is 6321
for 4 armour and 26 crystal plating shots taken is 6342
for 3 armour and 27 crystal plating shots taken is 6351
for 2 armour and 28 crystal plating shots taken is 6349
for 1 armour and 29 crystal plating shots taken is 6332


30% armour ignore dps
for 30 armour and 0 crystal plating shots taken is 5006
for 29 armour and 1 crystal plating shots taken is 5172
for 28 armour and 2 crystal plating shots taken is 5334
for 27 armour and 3 crystal plating shots taken is 5491
for 26 armour and 4 crystal plating shots taken is 5643
for 25 armour and 5 crystal plating shots taken is 5789
for 24 armour and 6 crystal plating shots taken is 5931
for 23 armour and 7 crystal plating shots taken is 6066
for 22 armour and 8 crystal plating shots taken is 6196
for 21 armour and 9 crystal plating shots taken is 6320
for 20 armour and 10 crystal plating shots taken is 6437
for 19 armour and 11 crystal plating shots taken is 6547
for 18 armour and 12 crystal plating shots taken is 6650
for 17 armour and 13 crystal plating shots taken is 6746
for 16 armour and 14 crystal plating shots taken is 6834
for 15 armour and 15 crystal plating shots taken is 6914
for 14 armour and 16 crystal plating shots taken is 6985
for 13 armour and 17 crystal plating shots taken is 7047
for 12 armour and 18 crystal plating shots taken is 7099
for 11 armour and 19 crystal plating shots taken is 7141
for 10 armour and 20 crystal plating shots taken is 7173
for 9 armour and 21 crystal plating shots taken is 7194
for 8 armour and 22 crystal plating shots taken is 7203
for 7 armour and 23 crystal plating shots taken is 7199
for 6 armour and 24 crystal plating shots taken is 7182
for 5 armour and 25 crystal plating shots taken is 7150
for 4 armour and 26 crystal plating shots taken is 7104
for 3 armour and 27 crystal plating shots taken is 7042
for 2 armour and 28 crystal plating shots taken is 6963
for 1 armour and 29 crystal plating shots taken is 6867
 
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Derp

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Very interesting, thank you
 

f98alda

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I think your formula for damage done is off, unless I'm missing something. Most of the weapons don't have "ignore x armour", they have "x armour penetration", meaning the formula would be: dps*(1-armour_reduction*(1-armour_penetration)).

Please correct me if I'm missing something in how damage calculation is done.
 

misterderp

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I think your formula for damage done is off, unless I'm missing something. Most of the weapons don't have "ignore x armour", they have "x armour penetration", meaning the formula would be: dps*(1-armour_reduction*(1-armour_penetration)).

Please correct me if I'm missing something in how damage calculation is done.

If you have 50% armour penetration that means 50% of you damage does not get the armour damage reduction but is applied directly to HP of the ship. Whereas the other 50% does, at least to my understanding of how the damage works.
Could you please tell me if you read this or found this formula somewhere in the game files, I would be very interested in looking some deeper into this.
 

f98alda

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If you have 50% armour penetration that means 50% of you damage does not get the armour damage reduction but is applied directly to HP of the ship. Whereas the other 50% does, at least to my understanding of how the damage works.
Could you please tell me if you read this or found this formula somewhere in the game files, I would be very interested in looking some deeper into this.
According to the wiki (which may very well be wrong, admittedly):

Armor a in the presence of armor penetration p reduces hull damage by a percentage
(a/(a+60)) * (100%-p%)

I.E. 60 armor will reduce hull damage by 50% against 0% armor penetration, or 25% against 50% armor penetration.

I haven't looked enough in the game files to check if this is actually true, but it's the best information I have...
 
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