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Message: <blockquote data-quote="orsal" data-source="post: 2496179" data-attributes="member: 16016">What does that have to with the difference between a uniform distribution and a bell curve? But the outcome of a particular attack is random. Where we disagree is how best to evaluate an option with uncertain outcomes. I go with expected value, which takes into account both the values of the various possible outcomes and their probabilities.Oh, and to go back to the original question... if you're deciding what feat to take, the decision will affect many attack rolls over the course of your adventuring campaign. Not just one. Of course, by my standard (expected value of damage), it doesn't make a difference.I certainly did read it, but it is very difficult to argue with someone who repeats his own assumptions about what his interlocutor has or has not read. If you persist in making such allegations I shall not continue to argue, since I see no point in it; such aspersionsmake it very difficult to have a remotely respectful discussion. I answered the question asked by the OP, which was phrased as an either-or. There are plenty of reasons why you might be concerned to take one or the other -- you might be thinking medium-term (before your next feat-gaining level), or might have other feat choices selected and just trying to fill one more slot. All small percentages. In other words, that extra +2 won't fell them, unless there have been other hits. Therefore, it is the aggregate of many hits rather than a single roll that matters.Oh, and the fighter's hit points aren't relevant; the monster's HP are. And that's more variable. Most adventuring parties will encounter both large groups of low-HP opponents and individual high-HP opponents.  On that we agree.The advantage to probability theory is that it can identify some parameters that capture the key aspects of a distribution. I know enough probability theory to use them.  From the customer's perspective: "My friend the probability geek tells me that insuring my house against natural isn't worth it, because the probability that I'll collect is only 2%, but the policy costs 3% of what it will pay me. In his words, the expected payoff is only half the cost of the policy. Big deal. The cost of the policy doesn't mean a lot to me -- I make enough money that, barring unforeseen catastrophes, the cost of insurance won't substantially affect my standard of living. But that unforeseen catastrophe worries me. IThe affect on my standard of living of the cost of the policy is less than 1% the affect of losing my house to flooding. So if I think in terms of standard of living, rather than money, it is worth it."From the company's perspective: "The expected value is positive for us. Since we will insure many policies with the same terms, our long-term average payoff per policy will be approximately the expected payoff. So we use the expected payoff to decide that this is a good policy to offer."Guess again. Once again, please let your interlocutors decide for themselves what they do and do not want to do.Unless you want to argue that the fighter's situation is analogous to the homeowner's, no, I don't see how it supports your point. I don't see making a single hit with neither a critical nor a damage bonus beyond your strength modifier is equivalent to losing your house to flooding.  Which is why I began *my* calculations with a hit -- since neither feat under consideration affects the probability of getting that hit, we can ignore it. I was merely pointing out that your description of a bonus that affects every attack was inaccurate incontext. Tangential to the point of discussion, so I see no need to repeat it too often, but worth pointing it out once.  Which numbers do you have in mind? When you first mentioned a bell curve, I understood you were talking about attack rolls, and as I noted above, they have a uniform, not bell-shaped, distribution. It is completely unclear from the context which random variable you are referring to here. Please clarify if you wish me to decide whether I agree that the distribution is bell-shaped.</blockquote>

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