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Message: <blockquote data-quote="Asisreo" data-source="post: 8222506" data-attributes="member: 7019027">Alright, here we go. The Math of Extra Attack.So speaking of averages, standard deviations, and probabilities; I feel we should discuss the distinction between Extra Attack and High Damage single-attacks. First, Let's take a look at a Fighter with a duel-wielding shortsword versus a Fighter with a two-handed greatsword. Assuming the same to-hit and no fighting style, they should be equal to each other, right? Again, yes but only in terms of average damage. Let's say you're fighting a monster with 15 AC and you have a +5 to-hit with a +3 damage modifier. The monster has 28 HP. Which one is better? Remember my example about consistent damage versus swingier damage? Well, the Greatsword not only has a higher variance, but the chances to hit with the greatsword is much lower. Greatsword has a 45% chance of completely missing while TWF has a 20.25% chance of missing. You're more than doubling your chances to-hit. A more guaranteed damage reduction (when a monster isn't at kill range or your character isn't close to dying) is more valuable than swingier high damage because you reduce the chances of unnecessary additional rounds from the enemy while also more predictably reducing them into the kill range for follow-up attacks. Two-weapon fighting obviously has the cost of a bonus action to use, but if your character has no need for their Bonus Action, its a nice boost in damage. Remember that characters like Barbarians can dual-wield whenever they'd like. Of course, there's also turns where even if you do have a bonus action use, its not as good as just getting extra damage. Like a rogue that ran 30ft to do a dagger attack might as well use their BA to attack with their other hand since they can't make use of disengage or hide. But also, I want to discuss how attacking twice for (1d6+3)+1d6 is NOT the same as 2d6+3 because of how accuracy works. Why? When you sum two independent random variable's probability distributions, you take their convolutions.  In simpler, but somewhat inaccurate terms: its the process that turns 1d6 to 4d6 into a bell curve rather than a larger rectangle. Now, the reason why this changes the probability curves isn't because of the damage dice, its the accuracy and the Order of Operations. For the case of extra attack, you first take the probability distribution adjusted by the accuracy, then you convolute. In the case of the greatsword, you first convolute the probability distribution not adjusted by the accuracy, then you account for accuracy. The result is that both have the same averages (over a large number of trials, the averages converge), but the Greatsword has a much higher variance and therefore more suited to killing enemies during last-ditch efforts and dual-wielding is more suited for consistently damaging enemies in an attrition.</blockquote>

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