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Message: <blockquote data-quote="Mike Sullivan" data-source="post: 962475" data-attributes="member: 9824">Re: Small sidetrackHeya, Dreeble.Actually, I generally just use this as a shortcut for determining critical damage (I'll explain why afterwards):If crit range/multiplier is:20/x2 then multiply damage by 1.0520/x3 or 19-20/x2 then multiply damage by 1.1020/x4 or 18-20/x2 then multiply damage by 1.1519-20/x3 or 17-20/x2 then multiply damage by 1.2018-20/x3, 19-20/x4, or 15-20/x2 then multiply damage by 1.3018-20/x4 or 12-20/x2 then multiply damage by 1.45(Basically, a martial weapon like a longsword or battle axe gets a 10% bonus for criticals, "special" weapons like a pick or rapier get a 15% bonus, "bad" weapons like monk weapons or most simple weapons get a 5% bonus.  Double or triple the bonus for Keen and improved critical as necessary.)Okay, so how does that work?A critical hit is determined by two D20 rolls -- one of them is within your critical threshold, and the other is within your to-hit threshhold.The chance of rolling into your critical threshhold is set -- if your threshold is 20, then it's 5%, if it's 19-20, it's 10%, etc.As you probably know, the odds of succeeding in two unrelated things (like two die rolls) are the odds of each event multiplied by each other.Obviously, your chance of rolling high enough to hit is the same as your chance to hit.  And the chance to roll your threshold is noted above.  So, for example, if you have a 19-20 threshhold, obviously your chance of succesfully critting is 10% of your chance to hit.So, taking that case above, 90% of the time, you do a normal hit, and 10% of the time, you do a critical hit.  Let's assume that your critical multiplier is x2.  That means, if d is your damage, that your total expected damage can be written as:.9d + .1*2dRight?  (90% of the time, you do normal damage, 10% of the time, you do twice normal damage).Expanding that out, we see that it goes like this:.9 + .2d1.1dSo multiply normal damage by 1.1, and you'll get your damage taking into account critical hits.Similarly, what if you have a 20/x3 crit?.95d + .05 * 3d.95d + .15d1.1dEtc.So that's how I derived all of the above numbers.  The only thing you have to watch out for is this:  If your to-hit roll is bad enough that you don't hit on some part of your critical threshold (for example, you have a 12-20/x2 thresh, and you hit on a 14+), then your threshold effectively "shrinks" (to 14-20/x2, in our example).  Then, you can't just use the normal figures above, you have to recalculate.  In this case, it'd be:.65d + .35 * 2d.65d + .7d1.35dIs that relatively clear?</blockquote>

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