Graphing shields over time in battle with the new shield recharge mechanic (theoretical).

[Nebulon-B_Frigate_FTW]

Shields recharging more when nearly down means that we can't just rely on shields just dropping linearly, so I set out to solve for s(t), the shield strength at time t of a ship under fire from a continous damage source having damage per second D.

Something I missed initially was that the recharge wasn't 0-25% of the whole capacity, S. Using the formulas shown in the official shield discussion, we get R, the base recharge (not under fire) of a given S being 50*?(5*?(S^3/350^3)/3.5).

I started with the change in shields. Note the second quantity is from that shield recharge percent goes linearly from 0 at s(t) = S (full shields) to 25 at s(t) = 0. The R/100 then converts this into an actual recharge from the percent. The D of course is then the damage.

ds/dt = (R/100)*(-25*s(t)/S + 25) - D

After a bit of DiffEq solving, I got:

s(t) = 4*S*D*e^(-R*t/(4*S))/R - 4*S*D/R + S

This is clearly an exponential of the form f(t) = fss + (f0 - fss)*e^(-t/?), which is of course a general solution for moving from an initial to a final value where the rate of change depends linearly on the current value. For this case, sss = -4*S*D/R + S and s0 = S.

To find minimum damage to take down shields, we can simply solve for D via s(t)= 0 as t goes to infinity. 0 = 4*S*D*0/R - 4*S*D/R + S. S = 4*S*D/R. D = R/4. This should be fairly obvious as the recharge at 0 shields is one quarter of R, but the fact that these concur is useful as it indicates the equation is likely correct.

Now on to the part you've all probably been waiting for: pretty graphs. This first set compares 10K shield capacity with different DPS values. Remember that in-game damage is not continuous and therefore the graphs would appear serrated (having small sharp drops followed by slopes upwards repeated instead of one smooth line) and shields would do slightly better being given time to recharge in-between bursts.

Here you can see that only 100 DPS (1% of target's shield capacity) will not cut it.

Here is the minimum DPS (184.63,

 

[Legolas170]

BLOWN

 

[Trollerbobman]

^ ^

What she said :P

 

[FlyingDebris]

.

 

[Defentrix]

That sir is an incredible fnding you have there.

 

[MichaelSeph]

This was a nice try, but there\'s one BIG mistake which nulifies all of the points behind it. The graph numbers still work the same way, of course, but on wrong values and apparently I notice visual errors in how the graphs go, but this is secondary.

Shield \"capacity per second\" aka shield regen is NOT the Shields capacity stat, it is the shield regen stat marked as ( xx s/sec) in game. The new buff at shield regeneration is 0 to 25% OF the s/sec regeneration stat (the number that dictates how much shield points can go up / second), NOT of the full capacity of the ship\'s shields.


This first set compares 10K shield capacity with different DPS values.



Here is the minimum DPS (184.63,

 

[Trafalgar]

R, the base recharge (not under fire) of a given S being 50*?(5*?(S^3/350^3)/3.5).


The actual equations are

S = ((U*3.5)^0.66666)*350
R = ((U*5)^0.5)*50

Where U is shield units, S is shield capacity, and R is base recharge rate.



sqrt(stuff^3) is just slightly different enough from stuff^(1/0.66666) that you\'ve introduced a slight error into your recharge rate, but considering that it\'s only off by 26 or so s/sec with 8 million shield units (which have over 32 million capacity and over 316 thousand recharge) that I doubt it could affect your conclusions at all.

 

[MichaelSeph]

Yeah, that explains why the graph also looked a bit off/wrong.

But that issue is just secondary to the main issue that the full idea behind those graphs is incorrect. It reversed the balance issues completely.



So in the end, all stats, ideas and graphs are wrong in the first post.

 

[Nebulon-B_Frigate_FTW]

When I say capacity per second, I mean capacity per second. I.e. if you have 10K shield capacity and the enemy does 10K damage per second, they do 100% of your capacity per second. The R in the equations is the recharge you see in game, and is not what I mean when I say capacity per second. The reason I use the phrase capacity per second is that people are used to the old linear system and at higher DPS, the graphs approach linear anyways, because recharge is rather small comparatively. Talking about recharge per second for DPS is not as useful.

I did accidentally start off thinking it was 25% of the full capacity per second a while ago, and that lead to dramatically different graphs.



As for AMC balance, 10K DPS is fine for going up against someone with 100K shield capacity. The issue is what you do about 10 million shield capacity (1.3133 million s/sec recharge). We used to have the hailstorm to easily shred it, but now anything approaching that scale seems to not work. Seeing as AMCs do appear to still scale pretty well in the lower scales, we may end up seeing enormous shield-preference ships that are essentially unkillable while common ships consist largely of AMCs still.

 

[Trafalgar]

When he wrote \"1000 DPS (10% of target\'s shield capacity)\" referring to a 10K capacity shield, he meant 1000 DPS is 10% of 10K, and that has nothing to do with regeneration at all.

(Side note, the last one is wrong. He has 5% when it should be 0.5%.)

You can ignore the derivatives and graphs entirely, anyhow, since you can basically just use the 25% maximum regeneration rate under fire to figure out the boundary between \'My shield is impenetrable\' and \'Shields failed! Hull breaches on decks 3, 6, and 7!\'.

Either take your regen rate and divide by 4, or calculate baseRegen = ((shieldBlocks*5)^0.5)*12.5 for the number of shield blocks you want to use. This is the regen when it is almost empty and under fire, and anything (much?) above that DPS should break them if you are sitting still and letting yourself be shot at constantly, and anything below that should not be able to break them.

In testing with a single AMC, I noticed that it was unable to penetrate a 14-block shield (or that it slowed down so much that it was impossible to tell if it was still working even after firing for an additional minute), despite that 25% of the shield regen for 14 blocks was 104.5, and the AMC\'s DPS was 107.10. This might indicate that even DPSes slightly above the cutoff may be effectively useless.