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*Dungeons & Dragons
The mathematics of D&D–Damage and HP
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<blockquote data-quote="Snarf Zagyg" data-source="post: 8219926" data-attributes="member: 7023840"><p>IME, basic math can be a useful tool when it comes to someone looking to compare things in isolation (aka, optimization or efficiency). </p><p></p><p>To use an easy example, if everything else is equal, what does more damage- 2d6 or 1d12? Easy, right? So if you're presented with an option for damage, with everything else being equal, you would choose the 2d6 option. </p><p></p><p>It's the same in many fields; we've seen increased reliance on these metrics in sports. The value of a three point shot will be higher than a two point shot (of course), and then you can look at the expected field goal percentage (the chance of "hitting" to use a D&D term) to see the expected "damage" from each shot (the expected points). Which is why, in basketball, a lot of teams now play for either the three-point shot or the dunk/close two, and eschew the long-range two point shot.*</p><p></p><p>Which gets to two separate issues:</p><p></p><p>1. What does white room theory have to say about any individual combat? Or, as you put it, how does it account for the "swinginess" of dice? And the answer is- it doesn't. Not at all. The process matters more than the results. Think of it like this by analogy; if someone shoots 40 from the three point line, and 50 percent from within the arc (two points), then they should take the three point shot (1.2 expected from 3, 1 from 2). Even if they happen to miss their three pointer because of swinginess, it was still the correct decision- the theory was correct. </p><p></p><p>2. On the other hand, as many people point out, white room theory in D&D is often flawed. There is a lot of bad math. There is a failure to account for tradeoffs (AC, health, other effects) in combat. And it does not even try to math out "out of combat" effect in D&D. In short, from what I have seen, it tends to be very limited outside of comparing like things, such as DPR, without full context. No one to my knowledge has done a good, holistic, comprehensive statistic like "WAR" (from baseball) for D&D.</p><p> </p><p></p><p></p><p></p><p></p><p>*Of course, as defenses shift, there is now a new efficiency in long twos, but that's a different issue.</p></blockquote><p></p>
[QUOTE="Snarf Zagyg, post: 8219926, member: 7023840"] IME, basic math can be a useful tool when it comes to someone looking to compare things in isolation (aka, optimization or efficiency). To use an easy example, if everything else is equal, what does more damage- 2d6 or 1d12? Easy, right? So if you're presented with an option for damage, with everything else being equal, you would choose the 2d6 option. It's the same in many fields; we've seen increased reliance on these metrics in sports. The value of a three point shot will be higher than a two point shot (of course), and then you can look at the expected field goal percentage (the chance of "hitting" to use a D&D term) to see the expected "damage" from each shot (the expected points). Which is why, in basketball, a lot of teams now play for either the three-point shot or the dunk/close two, and eschew the long-range two point shot.* Which gets to two separate issues: 1. What does white room theory have to say about any individual combat? Or, as you put it, how does it account for the "swinginess" of dice? And the answer is- it doesn't. Not at all. The process matters more than the results. Think of it like this by analogy; if someone shoots 40 from the three point line, and 50 percent from within the arc (two points), then they should take the three point shot (1.2 expected from 3, 1 from 2). Even if they happen to miss their three pointer because of swinginess, it was still the correct decision- the theory was correct. 2. On the other hand, as many people point out, white room theory in D&D is often flawed. There is a lot of bad math. There is a failure to account for tradeoffs (AC, health, other effects) in combat. And it does not even try to math out "out of combat" effect in D&D. In short, from what I have seen, it tends to be very limited outside of comparing like things, such as DPR, without full context. No one to my knowledge has done a good, holistic, comprehensive statistic like "WAR" (from baseball) for D&D. *Of course, as defenses shift, there is now a new efficiency in long twos, but that's a different issue. [/QUOTE]
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