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Message: <blockquote data-quote="Johnny Angel" data-source="post: 4189100" data-attributes="member: 13334">Either, really, since I'm assuming that you (Bad Axe) are making explicit what WotC is making obscure.  The model seems roughly likely just on the basis of some trials I've run in Excel generating values for each level's actual Defense and Offense values between 0.5 and 1.5 (just as a rough idea of how the values could vary from the ideal 1).  What I found is that the results conformed closely enough to the y=x^2 curve in random generations that I concluded that reasonable deviations in the values of these hypothetical quantities evened out over time.  I may be making a mistake in assumptions, but I'm getting the notion that deviation from the ideal 1 defense gain and 1 offense gain per CR kind of works itself out through the magic of the process.It also seems to turn out that deviations from the ideal get averaged out as you go up levels, which makes me wonder why the "sweet spot" disappears after about 13th level.  Seems like the averaging effect would make the risk vs. reward calculations less wonky at higher levels.  Somehow, I got diverted from my physics degree into a degree in philosophy, but I am dusting off a lot of mental furniture.The version of the original joke I heard went something like this:A gambler approached a mathematics professor looking for a way to beat the horse races.  The mathematician worked on it for several months, with the gambler constantly calling for updates and preliminary results, but the mathematician wouldn't give any information until his work was done.  Finally, he called the gambler and said, "I have worked out the system you wanted.  The outcomes are predictable in the aggregate, and we will both be rich."  The gambeler said, "Fantastic!  Tell me, how does it work?"The mathematician said, "First of all, assume the horses are spherical..."Later I heard the version that ends with the horses being "identical and spherical" but I'm not sure which I prefer.  But it illustrates in a way that comes across intuitively the problem of mathematical models.  And it also arises in less rigorous models.  In a graduate course in the conflict between science and religion, I found that attempts to reconcile the two tended to assume that everybody's idea of God was, as it were, identical and spherical.Yet, it baffles me that this is from people who, when this was TSR, approved the psionics system that came with the Dark Sun Boxed Set version 2, in which your power points were also your psionic hit points, but attacking damaged you more quickly on average then it did your enemy, and defending did more damaqge to you than not defending.  After that saw print, can it really be that these people understand math better than I do?</blockquote>

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