Advanced modding: the damage sets and triangle.
This all started because a guildmate asked in chat whether Ewok Scout should use a crit dmg or a crit chance triangle. I figured that crit chance should be best. However, I wasn't sure. So that set off a morning's expedition into computing the various effects mods have on your damage output.
As a start, I am assuming that a 1% boost in offense translates into 1% boost in (base) damage. If this is not the case, then the calculations are off by however much that varies.
So, what is the aim? The aim is to know when it is better to use crit dmg, 2x crit chance or offense sets, as well as whether a crit chance or dmg triangle is better. Using math rather than guesswork. For this, we focus on average sustained damage, and ignore mechanics (meaning, we don't bother about Biggs' guaranteed crits, Nihilus lead making crits impossible, Barriss healing on crits, etc). Sustained damage means we are modding for the average case, not trying to get the highest burst damage to OHKO someone with a perfect setup. If that is your aim (and it often is), then you will have to mod differently. However, the average damage is great for the average joe who has to chip through the thousands of protection on GK/Baze/AAT with a bunch of toons, and wants to do that as fast as possible.
TLDR conclusions: on most toons, use a crit dmg triangle and offense set. If crit chance is really high (>50%), use a crit dmg set. Never use a crit chance triangle unless you have other considerations (see the later calculations for Ewok scout). Using a crit dmg set (the best case scenario for crit chance triangle), the breakeven point is 27% crit (without the triangle, obviously), but with such low crit chance, offense sets are far better (and then the breakeven point between triangles is 7.5%, so just don't do it: use an offense set with a crit dmg triangle).
Now on to the math. How do you calculate what is better? Well, the only thing that can really affect which set will be better is crit chance: crit dmg is pretty much fixed between toons (ignoring a Boba Fett lead, and similar), and we take base dmg as the starting point and only bother about modifiers. So, given a crit chance p, the base formula for average damage modifier is 1.5* crit chance + 1* chance of not critting, which is: d(p) = 1.5p + (1 - p)1 = 1 + 0.5p. Pretty simple, right?
So what are the modifiers? Lets start with crit dmg, which is the easiest:
d(p) = 1 + (0.5 + cdm)p, where cdm is 0.3 for the set bonus, 0.36 for the triangle, and 0.66 for both.
Now offense:
d(p) = (1 + o)(1 + (0.5 + cdm)p, where o is 0.1 for the set bonus. See how offense is a straight up boost to all damage: crit damage is simply a multiplier over your base damage, which is affected by offense, so crits also benefit from offense boosts.
And finally crit chance modifiers:
d(p) = (1 + o)((1 - ccm) + (1.5 + cdm)ccm + (0.5 + cdm)p), where ccm is 0.1 for 2 crit chance sets (4 mods), 0.12 for the crit chance triangle, and 0.22 for both.
Now we can plug in the values, and compare! For instance, a crit damage set with a crit chance triangle gives: o = 0, cdm = 0.3 and ccm = 0.12, resulting in d(p) = 0.88 + 1.8 * 0.12 * 0.8p = 1.096 + 0.8p, and similarly an offense set with a crit dmg triangle gives: o = 0.1, cdm = 0.36 and ccm = 0, and thus d'(p) = 1.1 + 0.946p.
Plugging in the various combinations, we get the following graphs:
https://i.imgur.com/8OkPjmP.png
From which we can see quite clearly, regardless of the triangle: crit chance sets are strictly dominated by the offense set. Basically, don't ever use crit chance sets if you can farm offense sets. The difference between crit dmg and offense is a bit harder. If you use a crit chance triangle (don't do that, but more on that later), you should always use a crit dmg set, and not offense: the breakeven point is below 20%, which is trivial to get on any damage dealing toon. If you use a crit dmg triangle, both offense and crit dmg sets get a boost, the breakeven point moves up to 48%, which is not always easy to get. So if you're using a toon with an innately high crit chance, or a crit chance boosting lead (e.g. Leia), you can easily use a crit damage set. Otherwise you'll need to do quite a bit of work with crit chance secondaries to get your 48% to make it worth it.
Now, onto the second part of the analysis: what is better? Crit chance or crit dmg triangle?
https://i.imgur.com/HIGhwWN.png
As you can see, crit damage triangle overtakes crit chance triangle at fairly low crit rates, regardless of the set bonus. If you use a crit damage set, then the crossover happens the "latest", at 28% crit chance, the crit damage triangle overtakes crit chance. However, combining that with the above information about sets, you should be using an offense set at these "low" crit chances. For an offense set, the crossover is at 7.5%, so basically: always use a crit damage triangle.
Finally, for those like me who haven't bothered with FO toons and thus cannot farm offense sets, what should we do? Well, math tells us, that if you cannot get an offense set, then for very low crit chances (up to 11%, so basically: never), you should ideally run a crit chance triangle with 2 crit chance sets. Between 11% and 28% you should run either 2x crit chance sets with a crit damage triangle, or a crit damage set with a crit chance triangle. And above 28% (most dps toons) full crit damage.
So that concludes the easy part. Now we can get to addressing my guildmate's question: but what if, like Ewok Scout, my toon gains TM on a crit? We have to look at what happens when you gain TM. If you gain, as Ewok Scout does, 30% TM, then you are only dependent on speed for 70% of the bar. In other words, your next turn comes 1/0.7 = 1.43 times faster. In your next turn you will do average damage as calculated above. So what we see is that this will simply speed up how many turns you will get in which to do damage. So we have a second formula, which also depends on the crit probability p, for the multiplier of number of turns: t(p) = 0.43p + 1. And this doesn't vary with offense or with critical damage modifies, but it does change with critical chance modifiers, so the final formula is:
t(p) = 0.43p + 0.43ccm + 1.
To get how these now interact, we simply need to multiply them. So es(p) = t(p)*d(p). This is a quadratic formula, but we can still simply compare them and figure out what works best. And that is: if your crit chance is under 20%, use a crit chance triangle with 2 crit chance sets (notice how the extra turns give a significant boost to the usefulness of crit chance at low crit rates). At higher crit chances, offense and crit damage start taking over, and between 20-50% any of the following combos will give roughly the same return: crit dmg set and crit chance triangle, offense set and crit dmg triangle, or crit chance sets and crit dmg triangle. Above 50% crit chance, full crit damage wins. This is specifically for Ewok Scout. Off the top of my head I cannot think of another toon with TM gain on a crit, but I haven't spent a lot of time looking either. If there is one and you want to redo the math for that toon you'll have to replace the 1.43 by whatever value you get for that toon. For instance, if you only gain 20% TM, that would be: 1.25.
So there you have it. My guildy, with 48% crit chance on his Ewok Scout could use any of the combinations: crit dmg set and crit chance triangle, offense set and crit dmg triangle, crit chance sets and crit dmg triangle, or all crit damage, with roughly the same results. And I hope that, in addition to helping my guildy, this helps people trying ot figure out how to mod their damage dealers.
An important caveat that another of my guildmates mentioned is that you only deal damage if you're alive. So if you have a particularly squishy damage dealer, you may need to sacrifice some damage for survivability by putting either a protection triangle or a health set on that toon. However, the best way of ensuring your DPS survives is, imho, not with mods, but by using a composition that protects your damage dealers: a pre-taunting tank, GK, Zarriss and R2 are all great tools to ensure your damage dealers survive to do as much damage as they can.
E: I didn't do offense triangle, because all my offense triangles are always atrocious (speed is still king, even with all this damage math). If I have time again sometime, I'll try to factor in offense triangles as well at a future time.
As a start, I am assuming that a 1% boost in offense translates into 1% boost in (base) damage. If this is not the case, then the calculations are off by however much that varies.
So, what is the aim? The aim is to know when it is better to use crit dmg, 2x crit chance or offense sets, as well as whether a crit chance or dmg triangle is better. Using math rather than guesswork. For this, we focus on average sustained damage, and ignore mechanics (meaning, we don't bother about Biggs' guaranteed crits, Nihilus lead making crits impossible, Barriss healing on crits, etc). Sustained damage means we are modding for the average case, not trying to get the highest burst damage to OHKO someone with a perfect setup. If that is your aim (and it often is), then you will have to mod differently. However, the average damage is great for the average joe who has to chip through the thousands of protection on GK/Baze/AAT with a bunch of toons, and wants to do that as fast as possible.
TLDR conclusions: on most toons, use a crit dmg triangle and offense set. If crit chance is really high (>50%), use a crit dmg set. Never use a crit chance triangle unless you have other considerations (see the later calculations for Ewok scout). Using a crit dmg set (the best case scenario for crit chance triangle), the breakeven point is 27% crit (without the triangle, obviously), but with such low crit chance, offense sets are far better (and then the breakeven point between triangles is 7.5%, so just don't do it: use an offense set with a crit dmg triangle).
Now on to the math. How do you calculate what is better? Well, the only thing that can really affect which set will be better is crit chance: crit dmg is pretty much fixed between toons (ignoring a Boba Fett lead, and similar), and we take base dmg as the starting point and only bother about modifiers. So, given a crit chance p, the base formula for average damage modifier is 1.5* crit chance + 1* chance of not critting, which is: d(p) = 1.5p + (1 - p)1 = 1 + 0.5p. Pretty simple, right?
So what are the modifiers? Lets start with crit dmg, which is the easiest:
d(p) = 1 + (0.5 + cdm)p, where cdm is 0.3 for the set bonus, 0.36 for the triangle, and 0.66 for both.
Now offense:
d(p) = (1 + o)(1 + (0.5 + cdm)p, where o is 0.1 for the set bonus. See how offense is a straight up boost to all damage: crit damage is simply a multiplier over your base damage, which is affected by offense, so crits also benefit from offense boosts.
And finally crit chance modifiers:
d(p) = (1 + o)((1 - ccm) + (1.5 + cdm)ccm + (0.5 + cdm)p), where ccm is 0.1 for 2 crit chance sets (4 mods), 0.12 for the crit chance triangle, and 0.22 for both.
Now we can plug in the values, and compare! For instance, a crit damage set with a crit chance triangle gives: o = 0, cdm = 0.3 and ccm = 0.12, resulting in d(p) = 0.88 + 1.8 * 0.12 * 0.8p = 1.096 + 0.8p, and similarly an offense set with a crit dmg triangle gives: o = 0.1, cdm = 0.36 and ccm = 0, and thus d'(p) = 1.1 + 0.946p.
Plugging in the various combinations, we get the following graphs:
https://i.imgur.com/8OkPjmP.png
From which we can see quite clearly, regardless of the triangle: crit chance sets are strictly dominated by the offense set. Basically, don't ever use crit chance sets if you can farm offense sets. The difference between crit dmg and offense is a bit harder. If you use a crit chance triangle (don't do that, but more on that later), you should always use a crit dmg set, and not offense: the breakeven point is below 20%, which is trivial to get on any damage dealing toon. If you use a crit dmg triangle, both offense and crit dmg sets get a boost, the breakeven point moves up to 48%, which is not always easy to get. So if you're using a toon with an innately high crit chance, or a crit chance boosting lead (e.g. Leia), you can easily use a crit damage set. Otherwise you'll need to do quite a bit of work with crit chance secondaries to get your 48% to make it worth it.
Now, onto the second part of the analysis: what is better? Crit chance or crit dmg triangle?
https://i.imgur.com/HIGhwWN.png
As you can see, crit damage triangle overtakes crit chance triangle at fairly low crit rates, regardless of the set bonus. If you use a crit damage set, then the crossover happens the "latest", at 28% crit chance, the crit damage triangle overtakes crit chance. However, combining that with the above information about sets, you should be using an offense set at these "low" crit chances. For an offense set, the crossover is at 7.5%, so basically: always use a crit damage triangle.
Finally, for those like me who haven't bothered with FO toons and thus cannot farm offense sets, what should we do? Well, math tells us, that if you cannot get an offense set, then for very low crit chances (up to 11%, so basically: never), you should ideally run a crit chance triangle with 2 crit chance sets. Between 11% and 28% you should run either 2x crit chance sets with a crit damage triangle, or a crit damage set with a crit chance triangle. And above 28% (most dps toons) full crit damage.
So that concludes the easy part. Now we can get to addressing my guildmate's question: but what if, like Ewok Scout, my toon gains TM on a crit? We have to look at what happens when you gain TM. If you gain, as Ewok Scout does, 30% TM, then you are only dependent on speed for 70% of the bar. In other words, your next turn comes 1/0.7 = 1.43 times faster. In your next turn you will do average damage as calculated above. So what we see is that this will simply speed up how many turns you will get in which to do damage. So we have a second formula, which also depends on the crit probability p, for the multiplier of number of turns: t(p) = 0.43p + 1. And this doesn't vary with offense or with critical damage modifies, but it does change with critical chance modifiers, so the final formula is:
t(p) = 0.43p + 0.43ccm + 1.
To get how these now interact, we simply need to multiply them. So es(p) = t(p)*d(p). This is a quadratic formula, but we can still simply compare them and figure out what works best. And that is: if your crit chance is under 20%, use a crit chance triangle with 2 crit chance sets (notice how the extra turns give a significant boost to the usefulness of crit chance at low crit rates). At higher crit chances, offense and crit damage start taking over, and between 20-50% any of the following combos will give roughly the same return: crit dmg set and crit chance triangle, offense set and crit dmg triangle, or crit chance sets and crit dmg triangle. Above 50% crit chance, full crit damage wins. This is specifically for Ewok Scout. Off the top of my head I cannot think of another toon with TM gain on a crit, but I haven't spent a lot of time looking either. If there is one and you want to redo the math for that toon you'll have to replace the 1.43 by whatever value you get for that toon. For instance, if you only gain 20% TM, that would be: 1.25.
So there you have it. My guildy, with 48% crit chance on his Ewok Scout could use any of the combinations: crit dmg set and crit chance triangle, offense set and crit dmg triangle, crit chance sets and crit dmg triangle, or all crit damage, with roughly the same results. And I hope that, in addition to helping my guildy, this helps people trying ot figure out how to mod their damage dealers.
An important caveat that another of my guildmates mentioned is that you only deal damage if you're alive. So if you have a particularly squishy damage dealer, you may need to sacrifice some damage for survivability by putting either a protection triangle or a health set on that toon. However, the best way of ensuring your DPS survives is, imho, not with mods, but by using a composition that protects your damage dealers: a pre-taunting tank, GK, Zarriss and R2 are all great tools to ensure your damage dealers survive to do as much damage as they can.
E: I didn't do offense triangle, because all my offense triangles are always atrocious (speed is still king, even with all this damage math). If I have time again sometime, I'll try to factor in offense triangles as well at a future time.
