Delta uses "Equivalent Hit Dice" (EHD for short) from simulations for OD&D to determine how strong a monster really is. It expresses how many hit die of player characters have an even chance to win in a fight against that monster.
The reason for measuring monster strength in EHD is that HD or other absolute characersistics are not a fair representation of a monsters' combat strength. Firstly, they cannot consider special abilities. Secondly, there has been a lot of inflation of absolute values between OD&D and 5e. A mighty balrog had 35 hits in OD&D, as much as a lowly wererat in 5e. An ogre had 15 hp, just above a quarter of the 59 hp in 5e, because player characters also got much stronger. An ogre will not be four times harder to defeat in 5e than it used to be in OD&D, nor would a wererat in 5e pose as dire a danger as a balrog in OD&D. So direct comparison of values does not work.
Instead, if we could determine EHD also for 5e, we would have a normalized metric to compare monsters in both editions on equal footing. We could rank the monsters in each edition, and compare how relative strength of monsters has changed between them, by directly comparing their EHD.
Of course that is still a simplification -- a fight between two monsters of identical EHD could easily be very lopsided. For example if one has flight and a ranged attack, and the other has neither, the flier will be able to destroy his earthbound foe without risk.
Still, EHD would be useful, so how can we determine them?
By the book approach
The simple method is to assume Challenge Ratings are a truthful representation of monster strength, so we can try to convert the 5e Challenge Ratings to equivalent hit dice.
Unfortunately, the CR represents a "normal" encounter for a group of four characters of like level, that would maybe consume part of their resources, but would not result in a 50:50 win or lose chance. So we cannot just multiple CR by 4 to determine EHD, this would be too many EHD as the party is much stronger than the monster.
There is a table in the DMG that defines what constitutes a "deadly" encounter at each character level, where one or several characters might die, and the group might lose the fight. This sounds similar to an even fight where either side is equally likely to win, the definition used for EHD. If this assumption is correct, all we need to do is to connect the character levels from that table to challenge ratings from the monster manual via xp, and we can estimate how many character levels are equal to each CR.
The scond thing to observe is that the relationship is not linear, it looks similar to an exponential, or a quadratic polynomial as shown here. It is not the same to use 10 level 1 fighters (able to handle 1,000 xp in a deadly encounter), as it is to use 1 level 10 fighter (able to handle 2,800 xp). Kinda surprising, I would have thought that 10 level one fighters would be more dangerous than 1 level 10, due to bounded accuracy and roughly 5 times the number of attacks. Maybe this is because there is an inflation in XP to move from level to level -- you need more and more XP each level up, while the power gains are much more linear. So using XP overvalues higher levels.
The book assumes that your party consists of 3-5 characters. We will use the average of 4 characters, if possible all of the same level, and each of their levels counts as 1 EHD, so a party of level three characters would be worth 12 EHD. That is, we treat EHD as linear, and additive, even thought the XP values are not.
We can compare this against the XP by CR. The fight is against a single monster, no adjustment multipliers for xp.
The CR ladder only has XP for full CRs, but you can come up with a number that falls between two CRs in XP value by interpolating between them, either with a forumla (as shown above, and inexact), or more precisely by piecewise (linear) interpolation between any to points.
The following chart shows how both the EHD (red) and CRs (blue) depend on the xp value:
The average is about 2.6. As a rule of thumb, you could multiply CR with 2.5 to get EHD. As there are really only 27 CRs, we can instead tabulate how much EHD each CR is worth. The right party strength for an even fight would then have that total of levels.
For example, a CR 10 monster, which by definition is a normal difficulty encounter for a group of four level 10 characters (40 total levels), would be an even or "deadly" encounter for 25 total levels, or four level 6 characters. This confirms the rule of thumb that picking a CR that is 4 higher than the party level gets deadly, even for a single monster.
Simulation
How good is this theoretical method? There used to be a site that allows you to simulate 5e combats programmatically, unfortunately it is not designed for ranking a whole catalogue by EHD.
The programmers who wrote this created a fantastic tool, impressive given the complexity of all the spells and abilitities, and I am grateful they provide it. The program even provides magical weapons at higher levels, which is good as it reflects how a real party might be equipped.
It however has a few flaws, for example, the djinni ends up in doing whirlwinds instead of dealing damage until he dies, the chimera does nothing at all. Were-creatures are difficult to gauge, as the program gives low level characters no chance for magic or silver weapons, so they only can be damaged by spells, and due to an implementation glitch, by the rogue's sneak attack damage. I suspect there are other such small issues.
Nevertheless, let us try it against some example monsters. For doing so, I use a classical party of a fighter, rogue, wizard and cleric, all of as similar level as possible, and use the EHD values predicted by the above method. If the method works right, the fight outcomes all should be about 50:50. The simulator runs 25 combats each time, I try two or three runs.
Will-O'-Wisp, CR 2 = 5 EHD, F2 R1 W1 C1. Party wins 100%, 100%, 100%.
Manticore CR 3 = 7 EHD, F2 R2 W1 C2. Party wins 96%, 100%, 100%.
Black Pudding CR 4 = 10 EHD, F2 R2 W3 C3. Party wins 92%, 84%, 92%.
Gorgon, CR 5 =14 EHD, F4 R4 W3 C3. Party wins 76%, 80%.
Wyvern CR 6 =17 EHD, F4 R4 W5 C4. Party wins 100%, 96%, 100%
Stone Giant CR 7 = 18 EHD, F4 R4 W5 C5. Party wins 60%, 76%, 72%
Hydra, CR 8 = 19 EHD, F5 R4 W5 C5. Party wins 100%, 100%, 100%.
Djinni, CR 11 = 29 EHD, F8 R7 W7 C7. Party wins 100%, 100%, 100%
Purple Worm CR 15 = 42 EHD, F10 R10 W11 C11. Party wins 100%, 100%.
Balrog CR 19 = 55 EHD, F14 R14 W13 C14. Party wins 100%, 100%, 100%.
The conclusion from this is that a "deadly" fight is still far from an even outcome fight. It merely is a fight were sometimes, a character or two might die. Over a broad range of challenge ratings, the player characters win in nearly 100% of these fights.
Actual EHD
To get to something closer to real EHD, let us calibrate how many character levels lead to an about equal outcome experimentally.
For this I trial-and-error to adjust party level, until I get about a 50:50 outcome on the fights. For EHD less than four at low challenge ratings, when I cannot further reduce character level, I drop characters: first the rogue, then the cleric, then the wizard until only the fighter is left. For monsters where one fighter is too strong and leads to high win rates, I add additional monsters. If the fight is about even against two monsters I record that as 1/2 EHD, if against n monsters, as 1/n EHD.
Especially at low challenge ratings, it is often not possible to get close to a 50% outcome - adding a single new level 1 character can flip win percentages from very low to very high. In these cases, I take the result that is closer to 50%, however bad it may be.
Here are the results for a range of monsters from different challenge ratings. 5EHD are the equivalent total hit dice of a party of four characters in 5th Edition. The P colum shows average the win %age of the party for three groups of 25 fights: monsters where the characters have low win% for a given EHD are more dangerous. Ratio shows the ratio between CR and EHD.
Assuming the program is not too far off, and EHD fairly represent how dangerous the ceatures are, then we learn several things:
1. CR ratings are quite inaccurate. They often do not reflect the real strength of the creature in combat. Creatures with the same CR can have a wide variety of EHDs, for example the creatures with CR 5 in our sample range from 4 to 17 EHD. Creatures with lower CR can be far more dangerous than others that have a higher CR. As a result, the ratio between CR and EHD varies widely.
The most undervalued creatures (highest ratio) in our sample are the troglodyte, guard, beholder, elementals and dragons. All of them are far more deadly than their CR would indicate.
The most overvalued (lowest ratio) are the dryad, phase spider, girallon, giant centipede, and unicorn. All of them a cheap pushovers for their CR. It may be that poison does not work right in the simulator, as in my experience, a single level one fighter would not survive attacks from 5 giant centipedes without eventually being paralyzed and then killed before killing all of them.
2. The average ratio of 1.4 EHD to CR is only about half the theoretically calculated value by the book. It also does not have a direct relationship with growing CRs, as it did in the calculated method. The chart shows the ratio for each CR on average, with the bubble size indicating the number of monsters in that CR bucket.
Estimating a deadly encounter CR for your party could be done by looking up the monster in the table above, or running it through the simulator for those not covered.
Using the average factor, you instead could take 2/3 of total party levels as the challenge rating. However, because there is so much fluctuation, this is dangerous and easily can be off by a factor of two and kill your party. In normal play, inexact CRs are less of an issue, as there is a wide margin of safety for normal encounter difficulty.
Conclusion: If you wanted to to retain some margin of safety for deadly encounters half the total party levels as CR is a reasonable the rule of thumb (or full total party levels at level 2-3). In practice, avoid fights that hard. You do not want an even chance of a total party kill. Instead, pick the CR matching the average party level (i.e. a quarter of total party levels), and maybe notch it up a couple CRs.
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