UPDATE
As of 12 December 2013, the Archery Capstone feat has been changed. The following math no longer applies to the reworked feat, as the new feat has a 20 second cooldown and only applies to encounters. Standby for an update to determine the optimal crit %.
Hello, peoples. I made a post about this earlier on the Preview thread, so I will re-post it here.
I am a lover of math, and I decided to take upon myself to discover what the optimum crit percentage would be to maximize the benefit from the capstone feat from the Archery tree for the Hunter Ranger. This feat states that a critical hit will guarantee that the next hit is a critical hit. The way this works (as far as I know) is that critting will grant you a buff icon that is consumed on your next attack. This buff is the autocrit, so the feat does not stack on itself, as that would be ridiculously overpowered.
So, what percentage of crit would gain the most benefit from this feat? Having too little crit will not proc the feat enough, and too much crit will be redundant and render the feat less effective. So, after much mathematical fun with my brother, a formula was derived to solve this conundrum.
This.
It is beautiful. Solving for p gives us the percentage:
41%.
With the feat, your effective crit chance becomes 58.2%. So, if you really, truly want to maximize the capstone feat of the Archery tree, try to aim for a crit chance around 41%. Of course, this is not going to be too easy to do, so it's not like it's a must have to make the feat viable. However, this does not take into account the feat that increases crit chance for every non-crit (thanks
obsidiancran3 for pointing that out), so in effect, the best crit % will be about 38%.
Any thoughts?
Link to original thread:
Here.
P.S. I am not taking requests to do these kinds of equations . They take a lot of time and effort, and I cannot do it without my brother, who is often busy with more important things.
Comments
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Yes i was just saying though to get grand warden gear along with the best slavemaster rings and CN bow set both Boons that give a total of 375 crit and you can hit 3k crit with out ever having to socket it in a offensive slot.
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I guess its vague but its seemed simple enough for every none crit you get 5% more crit chance means archers dount realy have to stack epic amounts of crit after all. LoL That makes the CN Bow Set the best T2 BOW set we get 442 not bad Imma go ahead and add this Information To My guide OK if you dont minde
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Just in case you weren't aware, the feat "Correcting Aim", doesn't just apply a flat 5% crit bonus when you non-crit, but also stacks for each non-crit you do. For example, hitting two non-crits would give you a 10% bonus, three non-crits would give you a 15% bonus, and so on.
Essentially it will eventually guarantee a crit for you. Knowing this, would this change your optimum crit % of 38% to shoot for?
Correct The buff stack until you crit then it goes away and start re stacking again for every none crit tbh you never have to stack crit as a archer you can just get it from gear and by 60 with at least 1k and high Wisdom you should be at 30% ore more. Mean you can stack more armor pen power or recovery it up to you.
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I did not know that. I only leveled my ranger on the preview to level 17 because I didn't want to become attached to a character on the preview. I never actually got to spec into the paragon feats because of this, so most of what I know about the ranger is theoretical and not based on experience. That said, this makes Correcting Aim better than I previously thought. Since it stacks like that (wow, that's pretty strong) then I would lower the necessary crit % again. I could actually modify the equation to include Correcting Aim, so I'll do that later. It'll take a little time to do that, so in the meantime, I'll just give another estimate: 34%. So, like voltomey said, there really isn't a need to actually purposefully stack crit to get to the optimal percentage. Your gear should easily reach the necessary levels.
Now, if for whatever reason, a person does not take Correcting Aim (why would they not, lol), the optimal crit% would be 41%.
Edit: I have spoken with my brother. According to his supreme wisdom, it would be practically impossible to make an equation when taking Correcting Aim into account. The reason for this is because crit was once isolated, where you would need at least 1% crit chance to activate the capstone. This made it possible to do a calculation based on crit% alone. Now, 0% chance is a viable possibility, so we would have to consider all of the benefits of other stats (arpen, recovery, power, etc) to determine if it is worth having crit at all in light of the benefits received in other stats. Now that he has me considering this, for all I know, the optimal crit% could be as low as 20%.
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Every toon has 5% critical chance even with 0 stats and no ability score bonuses. It is the base crit chance.
So having 0% crit is not a possibility.