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Message: <blockquote data-quote="Sword of Spirit" data-source="post: 9761910" data-attributes="member: 6677017">[USER=7040979]@tomedunn[/USER] , I could use some help with some of your calculations.After further analysis, I believe your method of calculating a monster's XP and then assigning it a CR based on that XP is what WotC actually uses. I think you've almost certainly basically cracked the code. On my list of simplest test monsters (where the only factors that should influence CR are hit points, DPR, attack bonus, and AC), the best version of your calculations (the exponential version, and I used 14/13ths rather than 1.077) have extremely high accuracy.For these 45 basic monsters, the DMG rules give the correct MM CR on only 27, my system works for 30, but your XP-based system works on 41 out of the 45 monsters. It incorrectly listed camels, mules, and merfolk as CR 0 rather than CR 1/8, and places the cyclops at CR 7 instead of CR 6.That is so much closer, that I find it extremely unlikely your highly analyzed mathematical framework just happened to produce numbers that lined up. Sure, it's theoretically possible that it's a coincidence, but I seriously doubt it. However, there are still those 4 really basic monsters that doesn't calculate correctly. I tried adjusting some things (changing the -15 to another value, tweaking the XP bands, in case the XP value they give us isn't exactly what they used, even totally messing with the equation to try to correct for it possibly having problems with high attack bonus and low AC) and none of them worked.It is entirely possible that they set the actual cut-off value for something to be treated as CR 1/8 rather than 0 at 5 xp rather than the 10 xp we are directed to award for them, which would make 3 of the monsters work. But that still leaves the cyclops. My alteration to account for low ACs and high attack bonuses got the same results as your unaltered system, with the exception that instead of being wrong on cyclops, it had stegosaurus incorrectly at CR 3 instead of CR 4.Here is where I need your help. I suspect that the only reason your calculations aren't holding up perfectly (and discovering WotC's actual math is the most foundational part of what I have to do) is because of the approximation introduced at (22) on this page: <a href="https://tomedunn.github.io/the-finished-book/theory/effective-hp-and-damage/" target="_blank">Effective HP and Damage</a> . What would the formula be if we avoided all approximations? Since I'm using a spreadsheet, length doesn't matter, as long as it can take AB, AC, HP, and DPR as inputs and spit out the XP result.I would have figured this out myself, but my math skills are not up to par. (I don't even know how to use the sigma function.)</blockquote>

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