Now for the hard part. DPR. The numbers come from Teos at Alphastream, calculating DPR for each monster statblock in the new Monster Manual, and determining the average for each CR. They are for "Damage Per Round" against a single target. (Not area effects against multiple targets.) For purposes of calculations the attacks are assumed to always hit, and any saves against them always fail.
There are many ways to deal damage, and monsters can vary significantly by concept. For example, one monster might deal less damage but be more accurate, tough, and relentless. Even so, higher CR monsters tend to deal more damage than lower ones. Overall a pattern emerges, that represents the feel of D&D as a combat game.
The monsters at each CR average an overall amount of damage-dealing. Because the damage averages can diverge considerably from the expectation, there are actually two ways to interpret what the expected progression actually is. One interpretation is, the expected damage is improving linearly and steadily at each higher CR. The other interpretation is, the expected damage is gently accelerating, dealing more and more damage, according to a geometric curve across each higher CR. The acceleration might be taking into account the higher CRs having more attacks to multiply the damage, effects that add ongoing damage, and so on. The curve is probably more accurate to describe the actual numbers in the Monster Manual. But the line is simpler, easier to implement, and might be the intended guideline that the monster designers use as the guideline, for which, a particular monster modifies according to concept. Whether the line or the curve is "better", ultimately depends on which approach seems to make the monsters that are the most fun for the most players.
The simplest formula is linear: DPR = 9CR. At CR 1, the monster is expected to deal somewhere around 9 hit points of damage per round. At CR 10, the monster is expected to deal somewhere around 90 hit points of damage. And so on for any CR. The formula is surprisingly simple for an aspect of the math that is so complex with so many variables.
When comparing the 9CR formula to the averages in the Monster Manual, many CRs deviate significantly from it. Yet the straight line has points of contact with it, at the some of the lowest CRs, higher CRs, and across some of the central CRs. It may well be the intended guideline.
Yet when looking at the actual averages in the Monster Manual, all of the deviations from the line at lower CRs are lower than the linear expectation, while all of the deviations at higher CRs are higher than the linear expectation. The expectation itself may be a curve, that starts low but curves higher and higher at the higher CRs.
As a kluge, I offer a geometric formula that seems to describe the curve well enough. Where the averages deviate from the curve, the formula suggests obvious corrections, such as for when the average of the next higher CR has almost no improvement. This "curve formula" is a convenient description of the averages. It doesnt derive directly from any specific gaming mechanic. Here the exponent, "to the power of" ^1.4, describes a gentle curve upward. The curve tightly follows the averages, so trying to tweak the formula to match more closely the average at one CR tends to skew it away from it at an other CR.
DPR = 10 + 3(CR^1.4)
In comparison, the line formula produces DPR that is deadlier at lower CRs. The curve formula produces DPR that is deadlier at higher CRs. Which is better for the game?
In the DPR table below, the average DPR for each CR in the Monster Manual appears in parentheses in the central column. On the left, is the simple line formula, 9(CR). On the right, is the curve formula, 10 + 3(CR^1.4). A number in red means the formula generates a DPR that is lower than the average in the Monster Manual, being 90% of it or less. A number in blue means the formula generates a DPR that is higher than the average, being 110% or more. Note, for the curve formula at CR 30, the DPR is high, but right on the edge only slightly beyond the 10%, and is a reasonable guideline to produce monsters at this CR.
