The Bowazon

Food
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I didn't do any hard math because I'm lazy, but I dabbled in those sort of things and I think Barack Obama here is right.
suchbalance wrote:Both events can occur and they are mutually independent, so P(L10 U L1) = 0.25 + 0.1 - 0.25*0.1 = 32.5%. This is the probability that on every strike you get a lvl1 arrow or a lvl 10 arrow or two arrows.

This is correct

suchbalance wrote:Now if instead the bow also had a lvl1 arrow proc the probability of getting a projectile would be 35%.

This is also correct.

What is wrong is the assumption that probability of events = number of projectiles. The first event is less likely, but sometimes two projectiles are spawned. The second event is more likely, but it can at most spawn one projectile.

Exactly what Obama said here
Barack Obama wrote:However that is not equal to the (average) number of arrow procs in 100 strikes, because the intersection of events (that is, both procs go off of one strike) should count double.


So, long story short, the events have different probabilities but the average number of projectiles spawned is the same, so it's better to equip the maximum possibile CtC rather than trying to match the type and level of projectiles.

Edit: Oh and by the way, your guides are incredibly good in every possible way.
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suchbalance
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You both have a point - the average number of arrows is the same in both cases. However there is a subjective reason on why I prefer the 35% over 25% & 10%. I didn't want to include the argumentation of it in there because it's a bit too much (even for an appendix), but I can understand why there can be disagreements. Essentially on this character you hit very hard, due to the enormous amounts of flat damage, and monsters die in a few hits.


Now, to model the problem you need the following setup:

In the "only arrow 1" case the number of procs is a Binomial Random Variable (let's call it 1) such that 1 ~ B(n, 0.35). So you end up with E[1] = 0.35n; V[1] = 0.2275n

Now in the other case (let's call it 2) you have two independent Binomial RVs s.t. A ~ B(n, 0.25) & B ~ B(n, 0.1).

The sum of those two is a new random variable X (not binomial of course) with E[X] = 0.35n and V[X] = 0.2775n.


OK now that we have the setup out of the way the reason I prefer the first case boils down to the smaller variance.

1) Because we hit so hard, it does not take many hits to kill something i.e. n is small. Thus variance is a lot more important to the outcome in these cases, than in cases where you have 100 trials.

2) The positive standard deviation matters less than the negative one (this is where the subjectivity comes in). What I mean here is that if you hit a monster and your hit procs at least one arrow which also hits the monster it should already be dead. I.e. the double hit is most likely overkill. Basically I prioritise having a better chance of getting at least one arrow over the very small chance of getting double arrows, because against non-boss mobs the double damage will most likely be overkill.
Food
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I didn't think about that. I see what you mean and I agree, but doesn't it only matter if the double proc is guaranteed to target the same monster? Let me put up a scenario to see if I completely understand what you mean.

Let's call 1 the configuration in which you have 35% CtC, and 2 the one in which you have 25% + 10% CtC.

Let's say we are facing a monster (call it A). The assumption is that A will never survive a direct hit + an arrow proc, so it's better to maximize the chance that at least an arrow will proc (configuration 1), because in the event of a double proc (configuration 2) A will be hit directly, then hit by an arrow proc and then he'll be dead, effectively making the second arrow proc useless.

I agree, but let's now suppose there are two monsters, A and B. Now, in the event of a double proc your second point stands only if both the spawned arrows will target the same enemy, but if A and B have an equal chance to be targeted by every proc then it shouldn't make a difference because it's true that at least an arrow will proc less often in configuration 2, but when a double proc is triggered the arrows will target A or B independently.

Which means that it could happen that both the arrows of the double proc will target the same monster (the more monsters on the screen, the less likely to happen), but it could also happen that you get a double kill when the arrows target different monsters (the more monsters on the screen, the more likely to happen). Of course, the fact that you could double kill will balance itself with the fact that we proc less often, because as you stated configuration 1 procs 35% of the time while configuration 2 procs 32.5% of the time.

So, at the end of the day I disagree with your explanation, but I still think you're right, because configuration 2 is exactly as good as configuration 1 in the best scenario (infinitely many monsters on screen) but worse in the worst scenario (only one monster on screen).

Of course, if the two arrows of the double proc always target the same monster, then configuration 1 is always better than configuration 2, but I don't think the engine works like this. Or at least it shouldn't.

I hope my examples were clear, I often suck at explaining things :\
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suchbalance
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Food wrote:So, at the end of the day I disagree with your explanation, but I still think you're right, because configuration 2 is exactly as good as configuration 1 in the best scenario (infinitely many monsters on screen) but worse in the worst scenario (only one monster on screen).


No your explanation was fine and I do think this is the gist of our theoretical "simulation". And I believe you are right - multiple procs can target different monsters, although I am unsure if target selection is random in the 15yrd arrow target range or if preference is given to closer monsters.

Truth be told I hadn't thought about it in such depth, until our current discussion, or evaluated every possible angle when I wrote this. All that I concluded at the time was that it seemed that no matter how many more variables you take into account, it appears that "case 1" is always at least equal to or better than "case 2".

For example some monsters might survive more than 2 hits from Barrage due to low RNG rolls on Dragonlore (which has values 0-3.5k if i remember correctly on my endgame geared zon), in which case the 2 arrows would not be wasted. On the other hand even if said monsters survives 2 hits, it still may fall in some sort of life "breakpoint" where the second hit of a double proc goes to waste.

In addition we have to consider the movement aspect, say a single monster is stationary for 1 second and then moves 5 yards to the left. In this case a double proc is very desirable if it hits the monster before it moves, but at the same time you risk losing more than a single arrow if the projectiles are flying in right as it starts to shift.

Anyway this is all kind of a moot point, since in practice the best in slot gear forces you to have miss-matched projectile procs and one could argue you destroy non-boss mobs so quickly that it doesn't matter at all, but the discussion is interesting nonetheless.
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suchbalance wrote:it appears that "case 1" is always at least equal to or better than "case 2".

Yeah, I think this hits the nail squarely in the head.

suchbalance wrote:Anyway this is all kind of a moot point, since in practice the best in slot gear forces you to have miss-matched projectile procs and one could argue you destroy non-boss mobs so quickly that it doesn't matter at all, but the discussion is interesting nonetheless.

Exactly, and I like having these kind of discussions because I invariably learn something new, so that's good :D

Dankeschön, I'm trying the guide and It's smooth sailing right now (very early on), but I have doubts on my ability to play squishy builds so the 0 defence worries me, but I take it as a good opportunity to learn something new :D
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Barack Obama
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Good points. However, it could be argued that case 2 is better still. Because normal monsters die quick enough in both cases, but against bosses, or some mob getting onto your face, then having option 2 and being lucky might actually save you.
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Well, it's mostly a matter of preference I guess.
Over the course of all the incounters the character has during its lifetime the two cases will tend to average out.

The difference lies primarily in the fact that case 1 is more reliable (procs more often and when it does you know exactly what'll happen), while case 2 is more chaotic (procs less often, but when it does it coud either be worse, as good or better than when case 1 procs).

Obviously the difference is very tiny, but I feel case 1 suits this build slightly better, because having 0 defence means you'll have to be more methodical in your approach (scouting, kiting etc) so I feel reliability fits it better.

But as I said the difference it's very tiny and obviously if you prefer the second approach then by all means do use it :D
blytsz
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This is a great guide! Thank-you for all the effort!

I hate to ask you to do anymore, but, one quick thing, do you have any merc you recommend? Any gear tips?

Thank-you again and all the best!
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hellgrind
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For bowzon a2 examplar or a5 barb merc. For gear you should get high armor,res, on melee/on attack/on striking proc (for a5 merc get for him -100enemy fire res). Basically all items with survi options.
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Made some layout changes to the gear sections. Hopefully they are easier to read, especially now that there are no more "dual huge spoilers of doom" in the midgame section.