Most boosts stack - damage out, damage resistance, sci skills, extra power for subsystem, crit hit and crit severity, shield cap, shield heal etc. How the effect of each stack is calculated varies, some simply add and apply in a simply way like crit H, where three 1.6% boosts give a 4.8% boost that can be read from ship stats when in orbit; some add then go through cryptic math to generate an effect like boost damage resistance or boost sci skill whatever, for example damage rsistance adds then goes through a formula such that each extra point of resistance adds a smaller percentage point of resistance.
The original question is too general to give a decent answer, if you have a particular console in mind try searching the references for it in the search box or ask specifically.
There are different kinds of stacking. Suffice to say, this game uses one in particular.
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Additive stacking: STO generally adds the percentages together and applies the calculation after that. If you have four tactical consoles, each giving you 20%, then their additive stacking is 80%. For example, if you have 100 base damage then your four consoles will boost that damage to a final and total damage of 180.
Multiplicative stacking: this type of stacking involves multiple calculations. It means that the 20% for each console is applied one after the other on each subsequent result. The first console would apply its 20% on 100 damage. The second console would apply its 20% on the result from the first calculation. The third console would then do the same but to the second result and the fourth console would apply its calculation from the 3rd result. This type of stacking generally yields higher results if many different % values are multiplied in a long chain of subsequent calculations.
It is also important to note that STO also applies that % parameter to different values. For example, the tactical consoles apply their % bonuses directly to base damage, resulting in low yields. The Pedal to the Metal starship trait, however, applies its bonus directly at the end of all previous subsequent calculations, resulting in a significant yield. Here is an example of how it may be done with several different kinds of stacking.
First calculation: 100 base damage * 100% (5 consoles at 20%) = 200 damage
Second calculation involving the skill tree and weapon power: 600 damage end result. Note that tactical consoles do not apply their % bonus to this value, which is mistaken by many players.
Third calculation involving Pedal to the Metal starship trait (20% bonus) at the end of the chain of subsequent calculations: 600 damage * 20% = 720 damage.
Then you also have your % damage buffs from Attack Pattern Alpha and so forth.
First calculation: 100 base damage * 100% (5 consoles at 20%) = 200 damage
Second calculation involving the skill tree and weapon power: 600 damage end result. Note that tactical consoles do not apply their % bonus to this value, which is mistaken by many players.
Third calculation involving Pedal to the Metal starship trait (20% bonus) at the end of the chain of subsequent calculations: 600 damage * 20% = 720 damage.
Then you also have your % damage buffs from Attack Pattern Alpha and so forth.
So to obtain the highest yields with tactical consoles, which are the things you come in first and direct contact with and more often adjust, you need to increase that base damage. This done with the help of Mark (MK) upgrades and rarity upgrades. For example, the epic (gold) rarity gives you the [DMG] mod. These modifiers may seem insignificant at first but ever since they changed how the [DMG] modifier works, I would say it can boost your continuous damage pretty significantly once you start applying all the variety of damage % boosts.
So let's say you focus primarily and entirely on the tactical skill tree and then also on the weapon power related skills in the engineering skill tree. Also let's say you have epic Antiproton CritDx4, DMG (who knows what DMGx5 would do to this formula).
1) 503 base damage (cursor over equipment) or 1257 damage (skill tree, 125 weapon power)
Above * 4 tactical consoles at 37.5% = 670 weapon damage, or 1675 with skill tree and 125 weapon power included.
Above * Pedal to the Medal starship trait (20%) = 797 weapon damage or 1994 damage with skill tree and 125 weapon power included.
Above * Potentiality starship trait at 30% (10 stacks) or Super Charged Weapons (30% at 3 stacks) = 1038 weapon damage, or 2596 with skill tree and 125 weapon power included.
So as you can see you can get tremendous damage output in the end. However, it is important to bear in mind that weapon power heavily affects damage, causing it to fluctuate a lot. But with that in mind you want to increase the range at which this fluctuation happens in terms of lowest peak and highest peak.
You also have the [AMP] warp core mod which can apply a 3.3% damage boost for each power system above at or above 75. If you are lucky you can bring 3 of these to 75, giving you another 10% damage boost. However, the [AMP] mod is applied directly to the base damage and can basically be counted as an extra console that provides 10% boost. Nonetheless, when all calculations are done I would say you may see an increase of 100~150 damage with the [AMP] mod. So 2596 damage would maybe have been 2700 damage with the [AMP] modifier.
If you have a very high critical chance and also critical severity you have a very potential build, I would say.
For the resist consoles another way to look at it is "Reductive stacking". IE each stack reduces by a certain percent. 100-20%=80 80-20%=64 But, although it's the same premise, it's not as easy to calculate as that would suggest.
For the resist consoles another way to look at it is "Reductive stacking". IE each stack reduces by a certain percent. 100-20%=80 80-20%=64 But, although it's the same premise, it's not as easy to calculate as that would suggest.
Global response:
If you are a programmer (or coder) these mathematical formulas are generally constructed in a way how a computer would think/interpret rather than how a human would think. For that reason some of these formulas can be very difficult to understand because a computer needs parameters and operators to perform a calculation. So do we humans, but where we may only do mind-math with 2 values a computer may have an abundance of formulas to reach the same conclusion. So all of these debuffs, buffs and cooldowns can be a mystery sometimes. Now for example, reductive stacking as MarkHawkman mentioned can actually be multiplicative stacking with negative returns, and I will explain why.
Multiplicative stacking can be used to increase a number but also to reduce number. For example it can be used to reduce enemy damage resistance and damage resistance rating which are two very closely connected parameters. Let's say you have two debuffs that reduce resistance rating by 20% and they are applied subsequently and multiplicative. What you would experience is that the first calculation would have higher yields than the second calculation. If the target initially has 100 resistance rating (40% damage resistance etc.), the first calculation would bring that rating down to 80 (-20 return) but the second one would only yield a -16 return resulting in a final rating of 64.
This is also where diminishing returns come into play. Diminishing returns usually involves two or several values where the first ones in order are used to calculate the final result. Rating is one such value where it is used to calculate the % resistance. Diminishing returns also involves a threshold which determines the final result or yield. Here is an example:
This is also where armor penetration comes into play. In this game we have two types of armor penetration. One that is % based (trait) and one that is rating based (weapon modifier). The % based armor penetration will reduce resistance by a flat %. It means it ignores rating completely and will debuff the target's % resistance by the % penetration which could be let's say 20%. The other armor penetration found on weapons [PEN] will ignore 10 rating. This means that the [PEN] weapon modifier is excellent early on but pretty insignificant the steep curve of diminishing returns begin. For example, reducing 800 rating down to 790 is gonna yield perhaps -0.01% resistance, but reducing 20 rating down to 10 yields -10% resistance.
Simple answer for basic tac consoles @20%, two of them would give +40% of base damage where your base damage is what the weapon tooltip reads before everything else applies including weapon power - what it would read on the ground if looking at your space gear.
Thing is people run high weapon power, which boosts damage, then add tac consoles and see only a proportionally small additional gain as the tac consoles are boosting the base damage.
Comments
The original question is too general to give a decent answer, if you have a particular console in mind try searching the references for it in the search box or ask specifically.
¨
It is also important to note that STO also applies that % parameter to different values. For example, the tactical consoles apply their % bonuses directly to base damage, resulting in low yields. The Pedal to the Metal starship trait, however, applies its bonus directly at the end of all previous subsequent calculations, resulting in a significant yield. Here is an example of how it may be done with several different kinds of stacking.
So to obtain the highest yields with tactical consoles, which are the things you come in first and direct contact with and more often adjust, you need to increase that base damage. This done with the help of Mark (MK) upgrades and rarity upgrades. For example, the epic (gold) rarity gives you the [DMG] mod. These modifiers may seem insignificant at first but ever since they changed how the [DMG] modifier works, I would say it can boost your continuous damage pretty significantly once you start applying all the variety of damage % boosts.
So let's say you focus primarily and entirely on the tactical skill tree and then also on the weapon power related skills in the engineering skill tree. Also let's say you have epic Antiproton CritDx4, DMG (who knows what DMGx5 would do to this formula).
So as you can see you can get tremendous damage output in the end. However, it is important to bear in mind that weapon power heavily affects damage, causing it to fluctuate a lot. But with that in mind you want to increase the range at which this fluctuation happens in terms of lowest peak and highest peak.
You also have the [AMP] warp core mod which can apply a 3.3% damage boost for each power system above at or above 75. If you are lucky you can bring 3 of these to 75, giving you another 10% damage boost. However, the [AMP] mod is applied directly to the base damage and can basically be counted as an extra console that provides 10% boost. Nonetheless, when all calculations are done I would say you may see an increase of 100~150 damage with the [AMP] mod. So 2596 damage would maybe have been 2700 damage with the [AMP] modifier.
If you have a very high critical chance and also critical severity you have a very potential build, I would say.
My character Tsin'xing
If you are a programmer (or coder) these mathematical formulas are generally constructed in a way how a computer would think/interpret rather than how a human would think. For that reason some of these formulas can be very difficult to understand because a computer needs parameters and operators to perform a calculation. So do we humans, but where we may only do mind-math with 2 values a computer may have an abundance of formulas to reach the same conclusion. So all of these debuffs, buffs and cooldowns can be a mystery sometimes. Now for example, reductive stacking as MarkHawkman mentioned can actually be multiplicative stacking with negative returns, and I will explain why.
Multiplicative stacking can be used to increase a number but also to reduce number. For example it can be used to reduce enemy damage resistance and damage resistance rating which are two very closely connected parameters. Let's say you have two debuffs that reduce resistance rating by 20% and they are applied subsequently and multiplicative. What you would experience is that the first calculation would have higher yields than the second calculation. If the target initially has 100 resistance rating (40% damage resistance etc.), the first calculation would bring that rating down to 80 (-20 return) but the second one would only yield a -16 return resulting in a final rating of 64.
This is also where diminishing returns come into play. Diminishing returns usually involves two or several values where the first ones in order are used to calculate the final result. Rating is one such value where it is used to calculate the % resistance. Diminishing returns also involves a threshold which determines the final result or yield. Here is an example:
10 rating = 10% resistance
20 rating = 20% resistance
30 rating = 30% resistance
40 rating = 40% resistance
50 rating = 50% resistance
100 rating = 60% resistance <-- diminishing returns starts here and increases exponentially hereafter
200 rating = 70% resistance
400 rating = 80% resistance
800 rating = 90% resistance
1600 rating = 100% resistance
This is also where armor penetration comes into play. In this game we have two types of armor penetration. One that is % based (trait) and one that is rating based (weapon modifier). The % based armor penetration will reduce resistance by a flat %. It means it ignores rating completely and will debuff the target's % resistance by the % penetration which could be let's say 20%. The other armor penetration found on weapons [PEN] will ignore 10 rating. This means that the [PEN] weapon modifier is excellent early on but pretty insignificant the steep curve of diminishing returns begin. For example, reducing 800 rating down to 790 is gonna yield perhaps -0.01% resistance, but reducing 20 rating down to 10 yields -10% resistance.
Thing is people run high weapon power, which boosts damage, then add tac consoles and see only a proportionally small additional gain as the tac consoles are boosting the base damage.
The wiki has a good piece about subsystem power.
http://sto.gamepedia.com/Starship_(Power_and_Subsystems)