For example take Rogue Tech Collector.

http://galaxylegion.com/wiki/index.php/ ... _Collector

Based on the data people had per rank, I was able to devise a formula. It's most likely the same for all matched things, with different multipliers. Step function and rounding means it may be approximate.

Shields: 60 * Sqrt(Rank)
Hull: 80 * Sqrt(Rank)
Attack: Rank * 6 + 50
Defense: Rank * 9 + 50
Damage Cap: Rank * 2.5
Minimum Shots: (140 * Sqrt(Rank)) / (Rank * 2.5) ; possible: 4 shots @ rank 196 , 3 shots @ 349 , 2 shots @ 784, 1 shot @ 3136.


Dark Runner:

Shields: None
Hull: 75 * Sqrt(Rank)
Attack: Rank * 4.5 + 50
Defense: Rank * 7.5 + 50
Damage Cap: Rank * 2.5
Minimum Shots: (75 * Sqrt(Rank)) / (Rank * 2.5) ; possible: 4 shots @ rank 51, 3 shots @ 100, 2 shots @ 225, 1 shot @ 900.

Thanks for coming up with this data. It seems to further show that matched NPCs become easier at higher levels, as long as you don't let your attack get terribly behind them.

The next step is to analyze att/def relationship to see if you kept matching a similar ratio what happens. For example enemy has 5k def, you 5k att, then later on you both double, ratio is the same but if you also do 2x the damage, then you do more relative to its health which is only raised Sqrt(rank).

The "flamehawk" damage analysis is a standard I use because its stat doesn't change...

Flamehawk : Attack: 2000 / Defense: 2800

Attack: 4750 / Defense: 2881 --> 337 ave. damage/shot / 14.09 att/damage ratio / 1.696 att/enemy def ratio
Attack: 6223 / Defense: 3989 --> 425 ave. damage/shot / 14.64 att/damage ratio / 2.222 att/enemy def ratio
Attack: 7277 / Defense: 7584 --> 484 ave. damage/shot / 15.03 att/damage ratio / 2.599 att/enemy def ratio
Attack: 11693 / Defense: 6481 --> 667 ave. damage/shot / 17.53 att/damage ratio / 4.176 att/enemy def ratio

It is known to be non-linear, for example being drannik and adding weapons when I gained att +60.2%, I gained damage +37.7% only.

Attack: 14982 / Defense: 7232 --> ~756 ave. damage/shot (small sample size) , 19.82 ratio, 5.351 att/def ratio.

If you get a lot higher att than def, you lose efficiency. It's not known how this affects matched enemies, since you normally are trying to keep up with them.

I'm pretty sure if your attack stays proportionate to their defense then your damage will stay proportionate to their damage cap, which means you do more to their relative health (as shown by the decrease in minimum number of shots to kill).

EDIT: Based on my experience and something Dan said, I believe the damage is something like tanh(attack/(x*defense))*damageCap. I think x is 6, but with how fine-grained the equation is, and the randomness, it's hard to say for certain. The important thing though is that your damage is based on the damage cap no matter how much you do, and the attack to defense ratio is the key. I could be wrong, I haven't done extensive tests, but from what I have seen that appears to be the case.

EDIT2: I haven't been able to figure out if the random factor changes your attack or your damage, though I'm leaning towards attack. Furthermore, I think a critical hit doubles your attack and not your damage, which means the higher your attack compared to their defense the less of a bonus you get from critical hits.

"x" is between 4 and 5 based on my results.

I noticed about 90% of shots were between some base value and twice that value(ie, effective attack in the formula is (random(0.5)+0.5) * attack ) , and 5% were higher and 5% were lower and didn't fit the line (ie, "crits"). But this is not clear since it's not clear what a crit does or if it even exists, but it may simply give you 2x attack for that shot or 1/2 attack for that shot. There is the case where if you do more than your opponent in damage you seem to get bonus damage, but that's different. I would have to sample with different scan value and same attack to see, but I don't think the effect is large.

Also, regarding rank difficulty, tanh(5000 / 5000) equals tanh(10000 / 10000) (like my example) , if you keep up with the increase in enemy def, then you do the same % of damage cap, so you would in fact at double rank do double damage, however the enemy health is only sqrt(rank) and so it DOES take less shots to kill. So, the key is prisoner rank points -> attack increase to keep up or exceed the growth rate. In fact we KNOW from the initial post here how much they get per rank for the ones that take more than 2 shots (not worrying about chargers) : 7.5 and 9.0 defense per rank. I get 4.9 attack per rank point in tac officers with drannik bonus + all buff. So, I need 2 rank points / rank into tac officers to maintain a set ratio to max damage cap.

Figured ide show what it is at my rank attack is -100 from the first post formula

Alright, I was thinking it was 5 at first, but with rounding and just looking at average damage it became difficult to tell because I didn't use lower attack/defense ratios, so the difference between 4 and 6 was hardly noticeable.



Yeah, that's exactly what I was thinking.

Note it's almost linear up to attack = 2x defense. Since 87% or so of enemies are common, the highest def you see is typically the tech collector, at def = 9x rank. So, you can have about attack = 20x rank before diminishing returns hits. Also, 20k attack should 7-shot (minimum hits) on a flamehawk on average, while I think 23-25k would consistently do so. I need to sample tech collector damage to see if it holds true.

update: Appears that x = 5 via sampling tech collector hits. Also treating the random number as a variation in attack, I get: damagepershot = tanh((attack * randomPIdiv) / (5*npcdefense))*npcdamageCap

randomPIdiv, basically the attack is multiplied by a random number between 0.64 and 1.57, which I noted since we are using trig here is 2/PI to PI/2 (there is probably some modification of a trig function). The average however is 1.1 . The only function with that shape I can find is arcsin(x) :



The actual data I compiled on tech collectors which has a similar shape:



1188 samples, 817 ave, 482 min, 1317 max, 13926 att vs. 10945 npcdef, 1193 expected max, 759 expected average (838 min/max average), 483 expected min. There appears to be 1.7-2.0% of "crits" or hits that otherwise violate the expected random multiplier range, but it's small (values above the gray line).