I feel that the way bonus calculation is presented on the wiki (http://wiki.starsonata.com/index.php/Formulae) is somewhat arbitrary, leaving many players stuck somewhere in the arithmetic. It's actually a pretty intuitive process, which I'm going to try to demonstrate below. If folks like it, we can modify the wiki entry. Of course, feel free to point out errors.

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Roughly speaking, the way to calculate the effect of multiple augmenter bonuses is to add them together. When all the bonuses are positive, this is exactly what happens. When dealing with negative bonuses, however, the process is slightly more complicated in order to reflect a basic arithmetic fact: 80% of 125% is 1. That is, the combined effect of -20% and +25% should be +0%. For any negative bonus n (e.g. n = -20% = -0.2), there's an easy formula to find the positive bonus that would exactly cancel it out. That formula is -n / (1 + n) (e.g. 0.2 / (1 - 0.2) = 0.25). For this reason, the negative bonus n is converted to n / (1 + n) before adding it with the positive bonus.

So if you have multiple negative bonuses n_1, n_2 and multiple positive bonuses p_1, p_2, convert each of the negative bonuses as shown above, and then add everything together, like so:

n_1 / (1 + n_1) + n_2 / (1 + n_2) + p_1 + p_2

It is now time to apply augmenter tweaking. Let T = 1 + 0.04 x AT + 0.02 x IT + 0.005 x EC, where AT, IT, and EC are the current level in Augmenter Tweaking, Imperial Tweak, and Engineer Class, respectively. Simply multiply the above sum by T, and denote this number by B for bonus.

If B is positive, you're done. If B is negative, it is still in the converted form discussed above, so this must be reversed. To do so, simply compute B / (1 - B).

Examples:
1. p_1 = +25%, p_2 = +20%, T = 2
B = T x (p_1 + p_2) = 2 x (0.25 + 0.2) = 0.9 = +90%
A collection of positive bonus multiplies directly with T.

2. n_1 = -20%, T = 1
B = T x n_1 / (1 + n_1) = 1 x -0.2 / (1 - 0.2) = -0.25
B / (1 - B) = -0.2 = -20%
A single negative bonus with T = 1 goes unchanged.

3. n_1 = -20%, T = 1.5
B = T x n_1 / (1 + n_1) = 1.5 x -0.2 / (1 - 0.2) = -0.375
B / (1 - B) = -0.357 / (1 + 0.375) = -0.27 = -27%
A single negative bonus with T > 1 does not multiply directly with T

4. n_1 = -20%, n_2 = -20%, T = 1
B = T x ( n_1 / (1 + n_1) + n_2 / (1 + n_2) ) = 1 x (-0.25 + -0.25) = -0.5
B / (1 - B) = -0.5 / (1 + 0.5) = -0.33 = -33%
Multiple negative bonuses are not directly added together.

5. p_1 = +25%, n_1 = -25%, T = 1
B = T x (p_1 + n_1 / (1 + n_1) = 1 x (0.25 - 0.25 / (1 - 0.25) ) = 0.25 - 0.33 = -0.08
B / (1 - B) = -0.08 / (1 + 0.08) = -0.07 = -7%
When combining positive and negative bonuses of equal magnitude, the result is negative.

6. p_1 = +20%, n_1 = -25%, T = 2
B = T x (p_1 + n_1 / (1 + n_1) = 2 x (0.2 - 0.25 / (1 - 0.25) ) = 0.4 - 0.67 = -0.27
B / (1 - B) = -0.27 / (1 + 0.27) = -0.21 = -21%

Overloaders and inbuilt bonuses:
Convert any negative bonuses the same way as for augmenters, and then add all overloader and inbuilt bonuses to B. Effectively, overloaders and inbuilt bonuses act as augmenters without augmenter tweaking. Don't forget to still compute B / (1 - B) if B is negative.

Resistance:
Compute B as above. Add in any overloader and inbuilt bonuses appropriately. Do not add your ship's inherent resistance to B. Calculate the percent of damage D you would receive with no resistance augmenters, and divide this by 1 + B. As usual, compute B / (1 - B) if B is negative.

Examples:
1. p_1 = +25%, T = 1, D = 0.4 (60% resistance)
B = +25%
D / (1 + B) = 0.4 / (1 + 0.25) = 0.32 (68% resistance)
The effect of +25% resistance is not as strong as reducing damage taken by 25%.

2. p_1 = +25%, p_2 = +25%, T = 1, D = 0.4 (60% resistance)
B = +50%
D / (1 + B) = 0.4 / (1 + 0.5) = 0.27 (73% resistance)
Multiple resistance bonuses are less and less effective.

AH MATHS!

If +25% and -25% shields cancelled then -25% shields would not correspond to removing a quarter of your shields, but rather removing only 20%. That's no more complicated than the fact that 75% of 125% is not 1.

Please explain. This knowledge interests me.

I suppose no one else just enjoys throwing augs on ships and hoping it works?
I've made some fucking kickass setups doing this

That is the only real way to do it, however I simply am interested in the math behind it all. Knowledge is power!

0.75 x 1.25 = 0.9375

0.8 x 1.25 = 1

Basically, you've got to take your pick. Either the percent bonus is the true effect (-25% <=> 0.75) and you can't just add them all together, or you can add all the bonuses directly but the negative ones won't reflect the actual percent (-25% <=> 0.8).

[x] Disable smilies

haha thanks.

do an example with a positive aug, a negative aug, and T=2

Done. I didn't include this originally because I didn't think it elucidated anything that the other examples did not.

yeh i just wanted to check. In my formula AT is applied before you convert to the system centered around 0, whereas you apply it after the summation. Apparently it doesnt matter. I didn't feel like smooshing stuff around to check lol.

Yes, that's one of the reasons I wanted to write this up, since I didn't like how you insisted on applying AT first.

Hrmm, so just for an example, the calculations of a 6 Hephaestus (50% capacity) Auged Thatch & AT 25 & Support Focus 20 (180% capacity) would be:

1) 55,000 * (1 + (0.5 + 0.5 + 0.5 + 0.5 + 0.5 + 0.5) * 2) * 2.8 = 1,078,000

or

2) 55,000 * (1 + (0.5 + 0.5 + 0.5 + 0.5 + 0.5 + 0.5)* 2 + 1.80) = 484,000

and I'm guessing definitely not:

3) 55,000 * (0.5 * 2 + 1)^6 * 2.8 = 9,856,000

i.e. does the class bonuses get simply multiplied on top? and what about aura/overloaders/item bonus'/tertiary skills/bar skills and such? are they simply an added bonus? or a separate multiplier?

Just asking since I was gonna make some storage thatches