Critical % and AoE attacks: they were made for each other!
Jun 23, 2014 7:55:23 GMT -5
ncaoa, John Robinson, and 1 more like this
Post by TeeWee on Jun 23, 2014 7:55:23 GMT -5
I made an observation in my ongoing party report thread (startradersrpg.proboards.com/post/89612/thread) that I think is important enough to warrant its elevation into its own thread.
The observation is that Critical% and AoE attacks are made for each other!
As a somewhat math-y geek this should have been obvious to me from the start, but it only hit me yesterday. The intuition for the non-math-y is that while it's a pretty low chance that a single normal die roll will be a six, but as you roll more dice, it gets likelier and likelier that at least one of them is a six. Anyway, on to the math section for the proof!
Critical hits
The effect of a critical hit is that it multiplies the damage by 150% - 300% (startradersrpg.proboards.com/post/81244/thread). This can be huge: I've seen critical hits of over 200 points of damage. Tamilin often hits for over 100 points of damage. So this is significant damage, often taking over a quarter to a third of an opponents total amount of HP. As such, increasing Critical hits can be huge if you can build on it.
If I understand the combat mechanics correctly, the Critical% means the following:
If an opponent is hit, after rolling damage, you then get that % chance of a critical hit. So a critical hit of 10% means that your hits have a 10% chance of being a critical hit. If you succeed in this roll, your damage multiplies. Stealth crit has the same effect, but increases the chance of a critical if you win the stealth roll.
Criticals and AoE, the math
Now, if you factor in AoE attacks, the fun starts:
Say, you have Ranged Onslaught, which gives Tamilin a potential of 4 targets at its first level. Say, you actually hit 3 targets, which is common enough. Also, say you have a critical% of 15%.
This result of this attack is not a mere 15% of a critical hit though, but a 39% chance of at least 1 critical hit on these three hapless victims! Why this increase? Because your one attack is attacking multiple targets at the same time and with each extra hit, it becomes more unlikely that no critical damage is dealt at all.
The math is as follows:
For every hit, there's a 15% chance that the hit is critical. In other words, there's a 85% chance of it being normal. In a math-friendlier notation, this is written down as a 0.85 probability of it being a normal hit.
This is trivial is there's only 1 hit, but what if there are more hits, for example, 3 hits.
For three hits, the chance of a critical hit (or more critical hits) is inverse probability that all hits are normal hits. So it's:
1 - probability(all hits are normal).
The probablitiy of all hits are normal is easy to calculate. You simply multiply these three events with each other, because they are independent events.
probability(all hits are normal) = 0.85 * 0.85 * 0.85 = 0.61
And this makes the probability of at least 1 critical hit scored: 1 - 0.61 = 0.39, or 39%!
Conclusions
The implications are huge: a good AoE attack results in a significantly higher probability of there being a critical hit than if you're aiming for a single target. With the numbers in my example, it starts to already compete with Silent Stalker regarding crit%!
Are there no downsides then? Of course there are. You are not guaranteed to be able to make a good AoE attack that hits multiple targets. And you cannot control who gets hit critically, unlike a true sniper talent like Silent Stalker.
But if you don't care enough about who gets killed first and wearing down a big clump of enemies is good enough, AoE + Crit is much more effective than at first sight! The obvious beneficiary is Tamilin as she has easy access to both, but more subtly, a crit% specced AoE Vincent or Kjartan can rely much more on critical damage than initially thought given their much more difficult access to crit%. Pinning Shot Selen may even be much more interesting than I was thinking previously.
The observation is that Critical% and AoE attacks are made for each other!
As a somewhat math-y geek this should have been obvious to me from the start, but it only hit me yesterday. The intuition for the non-math-y is that while it's a pretty low chance that a single normal die roll will be a six, but as you roll more dice, it gets likelier and likelier that at least one of them is a six. Anyway, on to the math section for the proof!
Critical hits
The effect of a critical hit is that it multiplies the damage by 150% - 300% (startradersrpg.proboards.com/post/81244/thread). This can be huge: I've seen critical hits of over 200 points of damage. Tamilin often hits for over 100 points of damage. So this is significant damage, often taking over a quarter to a third of an opponents total amount of HP. As such, increasing Critical hits can be huge if you can build on it.
If I understand the combat mechanics correctly, the Critical% means the following:
If an opponent is hit, after rolling damage, you then get that % chance of a critical hit. So a critical hit of 10% means that your hits have a 10% chance of being a critical hit. If you succeed in this roll, your damage multiplies. Stealth crit has the same effect, but increases the chance of a critical if you win the stealth roll.
Criticals and AoE, the math
Now, if you factor in AoE attacks, the fun starts:
Say, you have Ranged Onslaught, which gives Tamilin a potential of 4 targets at its first level. Say, you actually hit 3 targets, which is common enough. Also, say you have a critical% of 15%.
This result of this attack is not a mere 15% of a critical hit though, but a 39% chance of at least 1 critical hit on these three hapless victims! Why this increase? Because your one attack is attacking multiple targets at the same time and with each extra hit, it becomes more unlikely that no critical damage is dealt at all.
The math is as follows:
For every hit, there's a 15% chance that the hit is critical. In other words, there's a 85% chance of it being normal. In a math-friendlier notation, this is written down as a 0.85 probability of it being a normal hit.
This is trivial is there's only 1 hit, but what if there are more hits, for example, 3 hits.
For three hits, the chance of a critical hit (or more critical hits) is inverse probability that all hits are normal hits. So it's:
1 - probability(all hits are normal).
The probablitiy of all hits are normal is easy to calculate. You simply multiply these three events with each other, because they are independent events.
probability(all hits are normal) = 0.85 * 0.85 * 0.85 = 0.61
And this makes the probability of at least 1 critical hit scored: 1 - 0.61 = 0.39, or 39%!
Conclusions
The implications are huge: a good AoE attack results in a significantly higher probability of there being a critical hit than if you're aiming for a single target. With the numbers in my example, it starts to already compete with Silent Stalker regarding crit%!
Are there no downsides then? Of course there are. You are not guaranteed to be able to make a good AoE attack that hits multiple targets. And you cannot control who gets hit critically, unlike a true sniper talent like Silent Stalker.
But if you don't care enough about who gets killed first and wearing down a big clump of enemies is good enough, AoE + Crit is much more effective than at first sight! The obvious beneficiary is Tamilin as she has easy access to both, but more subtly, a crit% specced AoE Vincent or Kjartan can rely much more on critical damage than initially thought given their much more difficult access to crit%. Pinning Shot Selen may even be much more interesting than I was thinking previously.
