Advanced modding: the damage sets and triangle.

Acrofales
1363 posts Member
edited July 2017
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:
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?
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.

Replies

  • Manowar
    288 posts Member
    edited August 2017
    Is this post accurate? It seems to dissent from the majority opinion, which tends toward crit damage sets on most attackers.

    Great article, though I can't pretend to verify the math portion of it.
  • I'm glad you liked it :)

    I am quite confident the math is right. It's not really that hard. However there are some very clear reasons why people recommend crit damage mods:

    The main one, I believe, is obtainability. Jawa are a fairly easy farm: all the Jawas are in stores, except Jawa, who is in a cheap cantina node. Meanwhile, first order has 2! hard node only farms (FOST and FOTP), as well as Kylo on a medium cantina node. That means farming FO is a significantly bigger investment than farming Jawas, and many people have not even unlocked offense mods yet. It also means that most of those who have 3*d the offense challenges, probably 3*d the CD challenges far earlier, and simply have had more time to farm better CD mods. Meaning that a large portion of the players use CD because their best damage mods are CD mods.

    Second one, is that many offensive toons actually have the CC to take advantage of CD mods. Toons like JKA, Rey, Wiggs (not to mention Biggs' special guaranteeing crits), Lando, Leia, the IG droids, etc. have a high crit chance, and it only takes a single set bonus and some mediocre secondary CC to take them over that 48% where crit damage wins out (not to mention Han Solo who doesn't even need mods to take him there). And even if you don't quite manage 48%, anywhere between about 40% and 55% crit chance, the damage difference between offense and CD is not very large. Moreover, some teams benefit from "guaranteed crits". For instance, Biggs' special (pretty much) guarantees a crit, Leia and Han Solo give crit chance up to her whole team, Resistance (under Finn), Sith (under Maul) and FO (under Phasma) have Advantage more often than not, and droids get +30% crit chance under an HK lead. This means these teams can count on critting far more often than the toons' native crit chance indicates, easily pushing them over that 48% threshold in actual battle situations.

    Finally, people like big numbers. Even if on average, a toon doing 20k basic hits and 36k crits (at 50% crit chance) will do more damage than a toon doing 15k basic hits and 40k crits, people will often think the reverse. There is also an in-game reason for wanting this: there are far more toons that heal (or have life steal) than that rez. And thus the ability to OHKO on a crit (even if it happens rarely) *might* be more useful than sustained damage. This depends heavily on your arena team and playstyle. For instance, the old Wiggs teams banked heavily on being able to one-shot one of the opponent's toons before he could move. The Chaze/Nihilus meta was far more about chipping away slowly and steadily (and taking out key toons with annihilate). The CLS meta seems to be a bit of a mix, but is definitely bringing OHKOs back into the game (especially with AA lead offensive teams). And for OHKOs you want big crits. It doesn't matter whether you leave your target at 50% health or at 2% health: leaving him at any health means your OHKO team failed, so big crits are the name of the game in these teams.
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