Calculating damage soak values

[Lord_Leperman]

Source: Symphony of Destruction's pinned thread in Raven's Haven <a href='http://www.armoredcore.org/forums/index.php?showtopic=2954' target='_blank'>http://www.armoredcore.org/forums/index.php?showtopic=2954</a>

Copy paste for convinience:

Figured I'd post up a condensed version and sticky it since the game's coming out in a few days. Once again, thanks to Aileron of GameFAQs, and our own havok and Ky Kiske for the raw numbers.

The basic point of this is three-fold: defense is linear, and not tiered - a difference from SL, wherein defense increased only in 50 point steps, and increased exponentially the higher it went. But the real point was to figure out at what values Shell Defense and Energy Defense were equal so balanced defense would be possible.

To figure this out, various AC frames were tested using two weapons, one Shell, one Energy, of equivilent damage, and the numbers were recorded. Initially I thought it was one equation, but it turns out there were several, hence the "Predicted Dmg." figures. The acquired data is as follows:

SD______AP Lost*_____Predicted Dmg. Red.__Real Dmg. Red.____Variance
1100____582__________58.57% (410/7)_______58.43% (409/7)____0.14% (1/7)
1200____556__________60.43% (423/7)_______60.29% (422/7)____0.14% (1/7)
1300____529__________62.29% (436/7)_______62.21% (871/14)___0.08% (1/14)
1400____502__________64.14% (449/7)_______64.14% (449/7)____0.00%
1500____476__________66.00% (462/7)_______66.00% (462/7)____0.00%
1600____450__________67.86% (475/7)_______67.68% (475/7)____0.00%
1700____424__________69.71% (488/7)_______69.71% (488/7)____0.00%
1800____398__________71.57% (501/7)_______71.57% (501/7)____0.00%
1900____372__________73.43% (514/7)_______73.43% (514/7)____0.00%
2000____345__________75.29% (527/7)_______75.36% (1055/14)__0.07% (1/14)
2100____319__________77.14% (540/7)_______77.21% (1081/14)__0.07% (1/14)
2200____293__________79.00% (553/7)_______79.07% (1107/14)__0.07% (1/14)
2300____267__________80.86% (566/7)_______80.93% (1133/14)__0.07% (1/14)
2400____240__________82.71% (579/7)_______82.86% (580/7)____0.15% (1/7)

ED______AP Lost**____Predicted Dmg. Red.__Real Dmg. Red.____Variance
1000____591__________57.86% (405/7)_______57.78% (809/14)___0.08% (1/14)
1100____565__________59.71% (418/7)_______59.64% (835/14)___0.07% (1/14)
1200____539__________61.57% (431/7)_______61.50% (861/14)___0.07% (1/14)
1300____512__________63.43% (444/7)_______63.43% (444/7)____0.00%
1400____486__________65.29% (457/7)_______65.29% (457/7)____0.00%
1500____460__________67.14% (470/7)_______67.14% (470/7)____0.00%
1600____434__________69.00% (483/7)_______69.00% (483/7)____0.00%
1700____408__________70.86% (496/7)_______70.86% (496/7)____0.00%
1800____382__________72.71% (509/7)_______72.71% (509/7)____0.00%
1900____355__________74.57% (522/7)_______74.64% (1045/14)__0.07% (1/14)
2000____329__________76.43% (535/7)_______76.50% (1071/14)__0.07% (1/14)
2100____303__________78.29% (548/7)_______78.36% (1097/14)__0.07% (1/14)
2200____277__________80.14% (561/7)_______80.21% (1123/14)__0.07% (1/14)
2300____250__________82.00% (574/7)_______82.14% (575/7)____0.14% (1/7)
2400____224__________83.85% (587/7)_______84.00% (588/7)____0.15% (1/7)

* = 1x CR-WR76B hit (1400 Shell Damage)
** = 1x WH04HL-KRSW hit (1400 Energy Damage)

A few notes:
- The 1000 SD point is apparently unable to attain, and was not included.
- Blue signifies increase from the "mainline" equation, Red signifies decrease from the "mainline" equation.
- All AP Lost numbers were the highest recorded.
- Decimals rounded to the hundredths, all fractions accurate.

From this data, five large-scale equations can be extrapolated:

Shell Defense:
1) Y=(13/700)X+(266/7)
2) Y=(13/700)X+(533/14)
3) Y=(13/700)X+(267/7)
4) Y=(13/700)X+(535/14)
5) Y=(13/700)X+(268/7)

Energy Defense:
1) Y=(13/700)X+(274/7)
2) Y=(13/700)X+(549/14)
3) Y=(13/700)X+(275/7)
4) Y=(13/700)X+(551/14)
5) Y=(13/700)X+(276/7)

It should be noted that these are not the only equations; on a much smaller scale (for example, every 10 defense points, or perhaps even every defense point) several more become apparent. Were you to graph defense, rather than a straight line, it would be several hundred, broken lines, vertically staggered some. However, the differences between most of these lines are minute enough to constitute maybe an AP or two in actual practical applications, and they can therefore safely be ignored.

These equations can, in turn, be plotted, and by using a vertical line, x=n where n is the desired damage reduction percent, the difference between them can be found. That difference is 61.5385. That can, for the purposes of this discussion, be rounded to 62. This results in a good rule of thumb:

If Shell Defense is exactly 62 points higher than Energy Defense, both will yield the same damage reduction; they will be equal.

It should be noted that in practical application this is relatively hard to achieve, and thusfar seems most easily done by humanoid midweights - lights have an Energy Defense skew and heavies have a Shell Defense skew. Other legs present their own challenges. Regardless, it should be of benefit to anyone who might prefer balance when possible.

Addendum: HOW TO COMPUTE YOUR DESIGN'S DAMAGE SOAK

This was requested awhile ago so I figured I'd add it as a somewhat more practical application. Doing this is a pretty simple process:

1) Take your SD / ED values, and using the charts above, identify where they fall (-1/7, -1/14, 0, 1/14, 1/7). This isn't absolutely critical but will make the results more accurate.
2) Go to the SD / ED equations. The one you want corresponds to which "bracket" (the fractions) you fall into. So, if for example, your SD fell into "0", you would pick SD Equation 3, if your ED fell into "1/7" you would pick ED Equation 5, etc.
3) Substitute your SD / ED value for X in the equation and compute it. The value you get will be your Percent Damage Reduction. This is the percent that gets sliced off every hit you take.
4) Subtract your Percent Damage Reduction from 100. This will be your Percent Damage Infliction. This is how much you actually take from each blow.
5) Divide your AP by Percent Damage Infliction.
6) Multiply the resulting number by 100 and round up to the nearest whole number. This is your Shell / Energy Soak Value.

Here's an example:

1) My SD is 1665. This falls within the third bracket ("0") on the chart.
2) This means I use SD Equation 3, or Y=(13/700)X+(267/7)
3) Computing Y=(13/700)1655+(267/7) results in Y=69.064..., or 69.064...% Damage Reduction.
4) 100-69.064...=30.935...% Damage Infliction.
5) My AP is 8540. 8540/30.936...=276.056...
6) 276.056...x100=27605.633..., meaning I have 27,606 SD Soak. Try not to round until this final step.

As a proof to confirm this system is accurate, lets make a check. We can take the PIXIE3, which has 105 Damage, and multiply its damage by the Percent Damage Infliction (30.935...%), and we get 32.4825. Dividing 8540 by 32.4825, we get 263 PIXIE3 bullets to kill.

If we take PIXIE3's Damage Capacity of 84000 (105x800), and divide it by the earlier value of 27606, we get a figure of 32.864...% of PIXIE3's total magazine required for death. (32.864...%)x800=263 PIXIE3 bullets to kill.

This confirms the above six-step system as accurate.

In addition to just figuring out how much Soak you have, this could also be used to weigh the benefits of defense tuning, or frame changes that result in fluctuations of AP and SD / ED.

I hope this is somewhat more useful for mainstream applications.

I've tested the system itself and it is acurate. The stats still hold true for LR as well. Hope it helps anyone's designs.

[Grim]

Very useful.

Pinned.

[Serene]

It's true that it could be applied directly to midweights...
It always happens that an AC's defense stats are extremely balanced whenever the design is a midweight...
If the designer will actually balance it out...

[azuma-blade]

ang daming fomula's

[Goat]

Yeah, ang haba. Well at least magagamit din natin yung mga natututunan natin sa algebra lol XD

[Solitaire]

Waw, hebigats tol... nahilo aq s math!

[darkdragon_ycart22]

This is quite in-depth, really. But as long as you have def increments of 50 or 25, you can notice damage reductions, by one or more points from rifles. Haha.

Btw, if an EN user is equipped with GOLGI [which increases dmg by 7%], the EN values here are still accurate. Just calculate the normal dmg of the EN weapon, then add 7% to the AP loss.

[Lord_Leperman]

So I made this damage soak calculator for LR in MS Excel:

http://www.mediafire.com/?k0iq2hz4eb1tqd5

Just input the AP, Shell, and EN defense values to find out how much damage your AC can soak up before it dies.

It's not 100% accurate, as I haven't plugged in the defense bonuses after a certain amount of defense points, but those are very minor. The difference is around 100-300 points of damage but it can reach to around 1000-1500 when the defense numbers go high. The results of this one are pretty accurate, I've tried them out with the same method as described by SOD in the first post.

[Serene]

Nice one Leperman.

[atdsutm]

it doesnt work for me (i have to convert it)

[Lord_Leperman]

I used Excel 2007, you can get a converter program somewhere on the net that installs directly into Excel 2003 so you won't have any compatibility issues.

[NiX]

Or open with google docs. Or open office.

[TMRaven]

The basic point of this is three-fold: defense is linear, and not tiered - a difference from SL, wherein defense increased only in 50 point steps, and increased exponentially the higher it went.

That couldn't be further from the truth. Defense in Last Raven is still tiered, and still plays basic to a 50 point system, but instead it has tiers of defense alternating between every 23 and 27 points. SL was not exponential, it was parabolic. Defense tiers in Last Rave are more linear, yes (which is a big reason why defense in Last Raven isn't as grand) but it has some points where gains from a tier are considerably higher than the rest. You could think of it as linear with infrequent steps.

[McCale]

thank you for these formulas- Leperman.