I'm fond of numbers, and decided to explore a few values and ratios that can be derived from the monster creation rules/guidelines. I thought some others might find them interesting, so I'm sharing what I found :).
I did this in Excel, I'll give steps to follow along if anyone wants to play with the formulas themselves.
Setup:
Copy the table into Excel from A1, it should reach down to K33. Then if your Excel's like mine, paste A4 into A3 and then change A3 to 0.5, since Excel decides 1/2 must mean a date.
The table includes hit points as well as "high" and "low" damage for each CR. The first can be divided by one of the second for a (very simplified) idea of the relative damage 2 monsters of equal CR would do to each other in a single round.
Formula + Results:
In Cell M3: =B3/F3
In Cell N3: =B3/G3
Select and drag down to duplicate across rows 3 to 33.
After some early inflation, the values stabilise in a fairly consistent place, which I found interesting and wondered about being intentional.
Of course, even setting aside the massive list of excluded conditional factors (damage types/resistances, healing, non-HP damage etc.), this is missing a basic step. Under the table, Average Damage is defined as "This is the average amount of damage dealt by a creature of this CR if all of its attacks are successful. To determine a creature's average damage, add the average value for all of the damage dice rolled (as determined by Table: Average Die Results) to the damage modifier for each attack". So one, this is only if all attacks hit, and two, it does not take critical hits into account.
I can't properly fix the latter (if anyone can I'd be interested), but for the former, the table provides both AC values and high attack/low attack bonuses. The principle's similar even if the formula is trickier.
Formula + Results:
In Cell O3: =((D3+21)-C3)/20
In Cell P3: =((E3+21)-C3)/20
Select and drag down to duplicate across rows 3 to 33.
While the length of combat for "low" monsters generally lengthens as CR increases (probably cus they put more and more into fighting with other non-HP means), the "high" monsters that primarily fight through HP stay within a 1-round range. If you average this (formula "=AVERAGE(Q3:Q33)" for those playing along), you get a result of 4.088195707, or about 4.1.
In summary, monsters who fight mainly through AC and HP would take 4ish rounds to beat (or be beaten by) an equal foe at any CR. The table also includes saves and DCs, but since failed saves can mean anything from a fighting handicap to instantly dead, I couldn't think of much to derive.
Thoughts, criticisms etc. welcome, including telling me I have way too much spare time :).
You linked to the same thing he did in the first post. All of his statistics are derived from that vey thing.
Consider this a "dot" - I'm unlikely to weigh in on the conversation much (okay, well, at present, at least not likely to engage with the main topic), but I find the analysis very interesting. I'd tend to guess that the stability of both consistent high end damage rounds and increase of low end damage rounds is intentional, as is shows the monster growing more powerful against expected "normal" assaults (even "normal" assaults based on level) and hypothetically leads to appropriate-feeling encounters.
One of the interesting things about this chart is that it implies (by game effect) a similar PC-oriented chart. I've always wanted to see a chart like that. It would settle so very, very many rules-oriented "intent" arguments (though not always in a way that a given PC or GM would like). I suspect its is supposed to be replaced by the WBL chart, but that doesn't really do the same thing - WBL only really works if you hit expected norms. Of course having such a chart will probably be seen by some as "proof" that Paizo hates variety or something, and many will gladly boast about beating it or some who take it as a "minimum" or even some who overly-adhere to it beyond Paizo's intent as a vague guideline, but whatever: people do that about everything else, anyway. But it sure would be extremely handy.
(To some extent, the Unchained built-in-bonus progression gives more hints at this, but it still doesn't quite clarify as much as I'd like.)
((Paizo, if anyone of you reads this and like the idea, please use it. I need zero credit, compensation, or anything resembling such and nearby waive whatever right I have to such. I'm sure I'm not the first person to have ever thought of this. I shouldn't be the cause of people avoiding it.))
From some other posts I read I'm sure Mark S is well versed in the gears and cogs in the back ground math.
It makes sense for ratios on the base type items to hold true as you go up; and likely for the PCs as well. You need to have some ability to show more power on paper, but still keep combats relatively the same length as a 1st level.
Add in the nice variability of the d20 and things are still some-what predictable.
Where the math probably starts breaking down is area of effect spells; special magic items like Arrows of Slaying; Breath Weapons; etc.
But maybe there is a similar ratio even for these types of game effects so at least it scales on a close matter from level 1 to 20. IE perhaps AoE and BW get something like a damage density per 5' square per level, so a 1st level burning hands vs CR1 monster does proportionally the same damage to anyone in the AoE as a 10d6 Fireball vs a CR10 monster etc.
Of course there are action economy killers like paralysis, hold-person etc that can also break the math, but severity, length of effect, and save DC may also be able to be somewhat ratio'd to provide level proportionality.
At the far end of the spectrum though, magic will always have potential to break the underlying mechanics if you can cast something that doesn't do a scaling amount of damage. IE: There is probably no way to mechanically account for Wish and other spells that don't have a true scaling ratio.
I'm guessing that lack of ability to compare new class abilities and feats to some kind of scale template is what tends to power-creep many game systems.
