What challenge rating should the Ebondeath stat block have been given?

Question

In the adventure Divine Contention, there's a creature called Ebondeath, and the adventure provides a stat block for this creature, available on D&DBeyond.

This is the ghost of a dragon, which you fight in ghost form as the final boss fight.

This creature's stat block appears to be a modified version of the Ghost's stat block. The Ghost is a CR 4 creature. Ebondeath has also been given a CR of 4, but it has:

significantly more hit points (225 compared to a Ghost's 45), AC of 15 as opposed to 11, a way higher save DC of 20 vs. Possession (rather than the Ghost's 13), and Legendary Resistance. Everything else appears to be the same, including the attack modifier and damage of the Withering Touch attack, and the save DC of Horrifying Visage (13 for both stat blocks).

This looks like a mistake to me, and given that some traits have been updated where others have not been, it also looks like a lazy effort without paying much attention to the details.

Ebondeath is clearly stronger than a Ghost, and therefore surely must be of a higher CR that 4. What CR should¹ this stat block have been given? As a bonus question, what else should be updated to make things more consistent with the CR it should have been given (meaning the Withering Touch attack, and should the save DC of Horrifying Visage be 20 as well)?

_{1. Note that by "should", I mean if it were to be derived from its stat block, not just an opinion (the word "should" often has that association, so I just wanted to make that clear).}

Answer 1

Using the DMG: About 7

On page 274 of the DMG is the "Monster Statistics by Challenge Rating" table, which allows you to quickly come up with stats for a monster based on its CR. You can use the same table to reverse-engineer the CR from a stat block by looking at the CRs for Defense and Offense and averaging them:

Defensive CR should be at least 9

In the table, a monster with 225 HP has CR 11 and AC 17. Since the Ebondeath has only AC 15, we can shave off a few points of the defensive CR for that.

Offensive CR is a mess, but let's assume 4

The ghost appears to be close to right to offensive CR 4 according to the above table (the damage is lower, but is necrotic to compensate). How the adjustment of one out of two save DCs affects this I can't say (I don't have the DMG in front of me, just a picture of that table. If anyone knows more, feel free to edit this post), but it should be noted that Save DC 20 is associated with CR 21 in that table.

If we take the majority vote of things affected and unaffected and change the DC for possession back to 13, then we arrive at the average of 7.

Using the Monster Manual on a Business Card: About 10

As it turns out, somebody did statistical analysis on all entries of the Monster Manual and derived some CR-to-stats formulas from that which differ slightly from the values given in the DMG table. We can use the formulas to reverse-engineer the CRs here as well:

AC: 4 (Range 1/8-10), as AC = 13 + 1/2 CR ± 3

HP: 30 (Range 20-60)

While HP = CR * 15 * (1±0.5) in the relevant range, Possession is one of the few monster abilities which has a statistically significant effect on the statistics: Monsters with it have half the HP of monsters of the same CR without it. This means our HP to compare against is 450, resulting in this ridiculous sounding CR estimate

Attack : 2 (Range 1/8-6), as Attack = 4 + 1/2 CR ± 2

Damage : 3 (Range 2-6), as Damage = (5 + CR * 5) * (1±0.5) in the relevant range

DC : 4 (Range 1/2-8) for Visage, 18 (Range 10-22) for Possession, as DC = 11 + 1/2 CR ± 2

If we now try to put all together by similarly averaging the results (with the two DC CRs pre-averaged before thrown into the pot), we arrive at a total of 10 (Range 4.6-19.4).