Damage per round per Character level in D&D 5e

For monsters, we have the guidance of how much damage they deal on average in a round based on their CR from the DMG on page 274. In contrast, there is no such explicit guidance for expected PC damage output per round and level.

You can differentiate between average damage (without taking into account the probablity to hit, just the damage die on a hit, including chances to roll a critical, which is the damage number given for the monsters), and expected damage that factors in the probablilty to hit against a typical opponent AC. Both scale together, as the average probablity to hit remains about 65% across all levels without magic weapons. In the end is the expected damage that matters, so  this is what we look at here. 

Expected Damage based on DMG combat guidance  

One idea is to base this on the expected combat duration. The rules give monster hit points for a monster of a given challenge rating and XP value (page 274, DMG).  Encounters for any given level have XP guidance, which we can use to pick an appropriate single monster -- typically one of a CR matching the average character level for medium encounters, or of a CR one or two higher for hard ones.² As we know how many hit points such a monster has, we can deduce how much damage each character must deal per round to kill it in a given number of rounds.

Expected Damage based on actual builds

The other idea is to do this empirically: build various characters, and see how much damage they consistently can put out each round. 

A simple approximation for damage per hit with this approach would be to assume  that characters start start with +3 primary ability bonus and max that with ability score increases every four levels, and that they wield a weapon that deals 1d10 damage (either two handed verstatile weapons, or the average of higher damage d12 or 2d6 and lower damage d8 weapons typically used; few characters need to stoop to using d6 weapons).This results in average damage of 10 points per attack across the first ten levels, slightly lower (9 damage) during the first three levels of the range, and slightly higer (11 damage) during the last three, due to the increasing combat ability bonus. This translates into about 6-7 expected points of damage per attack, and once characters get multiple attacks, a multiple of that. 

However, actual damage output output can vary wildly, both by character build, and by class -- some like wizard, rogue or paladin excel at nova-damage, pouring limited resources into big effects, others like fighter or barbarian are strong on sustained damage over time. 

A more realisistic approximation therefore takes into accounts race and class abilities. The following chart summarizes the findings:

Medium and Hard refer to a Medium or Hard encounter four a group of 4 PCs. The Medium encounter asssumes a monster of the same CR as the average character level, the Hard encounter assumes a monster of one CR higher than the average character level.

The number 3 and number 4 refer to three or four rounds of combat per encounter. Three rounds is assumed to be standard, because the DMG in the monster building rules (page 278) tells us:

If a monster's damage output varies from round to round, calculate its damage output each round for the first three rounds of combat, and take the average

Four rounds is based on empirical data at one specific table.

The Bottom 25%, Mid 50% and Top 75% in contrast to this are the quartile averages from the Optimists' Guide to D&D 5E Damage by Class. This is averaging damage per level for 360 different builds in 13 classes and 48 subclasses. While it has to make some assumptions about hit rates and monster AC per level, those are well established. This approach is orthogonal the first in that the calculations in Optimist do not depend on rounds per encounter, so it provides a great reality check. For the Mid 50% (average PCs) and Top 25% (high damage PCs), the graphic also provides a trend line with associated formula to estimate the approximate damage per level x.

Lastly, the 7 builds line is from seven damage-focused builds without Great Weapon Master or Sharpshooter (Champion and Battlemaster Fighter, Assassin Rogue, two different Hunter Rangers, Vengeance Paladin, Berserker Barbarian), made to compare to Optimist Guide as a check. 

This assumes the same stat progression as in the simple approximation above, four combat rounds and five encounters per day to factor in damage from limited resources like spell slots, and short rest between fights. The battlemaster uses superiority dice for improved damage contribution from to hit, a rogue is assumed to be able to sneak attack, a ranger casts hunters mark the first round, and a paladin is using spell slots to smite each fight if possible. Other than Optimist, we excluded the Great Weapon Master and Sharpshooter feats. They are complicated as they influence also the to-hit probablility and can optionally be employed depending on the opponents AC.³

It is unsurprising that it is a bit higher than the average of 90 above-average builds in Optimist, also because those do not as thoroughly include damage from limited use abilities, as far as I can tell. 

Conclusions

• The average fight would take about 3 rounds. Both against Hard and against Medium encounters, the XP based damage from assuming 3 rounds closely matches the average damage output from Optimist.

• If I had to simplify damage per level to a simple rule of thumb, it would be level plus 7 damage for a typical character (add another half level, rounded up, for high damage characters, or subtract it for low damage ones).

• Damage per PC varies significantly, depending on build. You can have nearly a factor of 2 difference between a high damage PC and a low damage one across the entire spectrum of levels.

• Five rounds as an assumption for an average fight would be high. Fights would require damage outputs even below the low end of the Optimist build spectrum to take that long, which seems improbable unless you have a dedicated pacificst party.

• Builds optimized for damage could do a fair bit more than the 3-round combat encounter implies and may be able to end combat faster. The shorter the combat, the less damage the monsters can deal in return. Such groups might be better challenged with Deadly encounters.

Always keep in mind these are merely averages. In any individual fight, the duration can vary greatly from the expected average: it can be over in the first round, or it can drag out for many, many rounds with sides taking cover, jockeying for position, reinforcements coming in and so on; and likewise the damage output per character can vary wildy with the wizard casting fireball one turn, fire bolt the other, the paladin critting one turn with maxium divine smite damage, and missing altoghether the other, an so forth.

Average Number of Encounters Per Level in D&D 5e

Many class features have a limited number of uses per day, such as the barbarian's Rage, the cleric's Channel Divinity, or the paladin's spell slots for Divine Smite.

How much damage such a feature can be expected to contribute to combat depends heavily on how many encounters you'll have in a day, because once you run out of uses, it won't contribute any more damage. When planning your character and estimating average expected damage, you therefore often have to make an assumption about the number of encounters per day that will use up some of those limited resources. So, what is a good estimate for the average number of encounters per day? The short answer is, theoretically 5 per day, in practical play 3 per day. There are multiple was to derive this estimate for the number of encounters per day.

Calculated from the DMG: 5 per day

The DMG says most parties can handle about six to eight medium or hard encounters per day (p. 84). 

The DMG provides tables of expected experience per character and adventuring day on page 84, and of expected XP per Easy, Moderate, Hard or Deadly encounter on page 82. From this one can calculate the expected number of encounters of each type in a typical adventuring day, if one had only that difficulty of encounter. The numbers vary slightly from level to level, but on average over 20 levels of play they come to

Difficulty	Easy	Moderate	Hard	Deadly
Encounters	13	7	4	3

If all encounter difficulties were equally likely, that would mean on average 7 encounters per day, falling right onto the 6-8 per day of the text. .

The statement on page 84 DMG is "Assuming typical adventuring conditions and average luck, most adventuring parties can handle about six to eight medium or hard encounters in a day". This is slightly higher than these numbers, maybe because encounters are not supposed to go all the way to the point where the party cannot handle them any more.

Easy encounters are described as follows:

Easy. An easy encounter doesn't tax the characters' resources or put them in serious peril. They might lose a few hit points.

So, for the purposes of consuming limited use of daily abilities, we can ignore Easy encounters, as they are supposed to not tax the characters' resources, other then losing a few hits. This also matches my experience: for example, characters rarely waste their limited features on fights they know they can handle with cantrips and routine attacks. We will just average Medium, Hard and Deadly ones, assuming all types of encounter are equally likely.

With this, the average, "theoretical" number of resource-consuming encounters per day based on DMG guidance is 4.6. Rounding it to a full number, it's five encounters per day.

However, from my own experience, these numbers tend to not reflect the actual number of encounters in a normal day, unless you have a fight-heavy dungeon crawl with lots of minor encounters. 

Calculated from Mines of Phandelver and actual play: 3 per day

Now, one counterpoint is that all encounter difficulties may not be equally likely in an actual game or campaign. And we cannot know how the distribution looks like for every game. However, we at least can know it for some of the published campaigns.

Technoskald took the effort to list every encounter in Mines of Phandelver with its difficulty ranking based on the characters' level at the time of the encounter. Over the course of that adventure this is the distribution of encounters:

Difficulty	Easy	Moderate	Hard	Deadly
Encounters	8	9	8	16

That is 41 encounters total, and 33 of Moderate to Deadly difficulty.

Ignoring the Easy encounters again, due to the higher share of deadly encounters in the mix, the average from this published sample is slightly lower, and if you round it comes to four encounters per adventuring day.

However, this assumes that each day is fully filled with encounters, until the characters have exhausted all their resources. In my experience, in the absence of clear time pressure, players often opt to rest and recover before all of their resources are used up. You never know what's coming for you in the night. So, as long as the players have some ability to influence the number of encounters, you can expect it to be lower in the wild than what the XP guidance suggests.

This is borne out by practical experiment. We played LMoP, and even though our DM egged us on through NPCs to press forward whenever he could, we took in total 32 days of in-game time to get through it. There are many days of traveling around the countryside. At 33 resource-taxing encounters, that would just be one such encounter per day. However I think a better way to look at this is by looking at the days were we actually did have encounters.

If we remove all the "empty" days without combat encounters were we were just traveling or shopping or doing research, we had 11 days with encounters, or three encounters per day. Some of these were a single encounter when being ambushed traveling at night, others were dense with high numbers when fighting through one of the major adventure sites.

Player Surveys: 3 per day

ENWorld ran a survey asking players of 5e, "On average, how many combat encounters do you experience per day in a 5e game?". There were 82 answers:

Number	Votes
Less than 1	9
1	9
2	18
3	20
4	7
5	10
6	6
7 or more	3

From this it is clear that nobody seems to be experiencing days with 13 Easy encounters, and two or three encounters per day are the most common. If we count "less than 1" as 1 and "7 or more" as 7, the average here is 3 encounters per day.

This matches our own game experience of three encounters per day. In my experience, in campaigns with no urgent clock, the players often end up fighting fewer fights per day, and the DM responds with making them harder, so the real number might be even lower. Explanations for the difference to the theoretical four or five are therefore:

• very Easy encounters do not register as a challenge and cost no resources
• DMs try to present exciting and dangerous fights, which means Deadly encounters that you can only do three or so of per day
• unless pressed for time, players will try to rest before being pushed to the limit, further undercutting the theoretical encounter numbers

Summary

For building a character for a real campaign, three resource consuming encounters per day seems to be the most useful assumption.

On the rate of Leveling

There are two rates of leveling: first, how long do you have to play, to gain a level. Second, how long does it take in-game for your character to gain a level. 

In-game

How fast you gain experience in-game obviously depends on how your character spends his time. If he is engaged in uneventful overland trecks, weeks of downtime to craft items, or takes a break just relaxing and waiting, little experience will be gained, and it can take months or years. So the real question there becomes, how fast in-game can the character gain levels when engaged in the most strenuous activity, making most of every available resource or minute in an effort to gain exprience. 

"Experience" is licensed under CC-BY 4.0. 

In 5e it takes a little more than a month of in-game time to go from level one to level twenty. You'll spend approximately two days of in-game time on each character level, before moving on to the next one. Of course, with travel, downtime and so on, it may take longer, maybe two or three months of game time. But still, no years of heroics to become a world-dominating legend. 

In D&D 5e the standard experience rules that assign experience primarily for killing monsters, that means dangerous adventures with as many combat encounters as you can stomach, if you follow the DMG guidance on encounters per day and the XP per encounter, you get this table. 

Table 1: Experience and level achieved after number of days adventuring

Day    XP    Level

1 300         2
2 900         3
3 2,100 3
4 3,300 4
5 5,000 4
6 6,700 5
7 10,200 5
8 13,700 5
9 17,200 6
10 21,200 6
11 25,200 7
12 30,200 7
13 35,200 8
14 41,200 8
15 47,200 8
16 53,200 9
17 60,700 9
18 68,200 10
19 77,200 10
20 86,200 11
21 96,700 11
22 107,200 12
23 118,700 12
24 130,200 13
25 143,700 14
26 158,700 14
27 173,700 15
28 191,700 15
29 209,700 16
30 229,700 17
31 254,700 17
32 279,700 18
33 306,700 19
34 336,700 19
35 366,700 20

As a pure spell caster, you gain two new spells every spell level. When you gain a new spells up to character level 5 you get two slots to cast it, after that only one; followed by an extra slot on the next character level, up to character level 10. That means, when spending typically two days on each level,  in the lower levels you have 2, 2, 3, 3 = 10 shots to cast your new spells, before moving to the next spell level. In the mid levels you have 1, 1, 2, 2 = 6 shots. In the higher levels 1, 1, 1, 1 = 4 shots. Starting in the mid-levels, you get to cast each of your new spells maybe 3 times before moving on, in the high levels only twice. And this assumes that you do not find any additional spells adventuring on scrolls or from a captured spell books. If you find just a single new spell per level, then you will barely be able to cast each spell once before moving on mid-levels, and not even that in high levels.

This feels a bit fast for my taste. You do not really get to explore your newfound abilities, already you are on to the next shiny toy. If the progression was slower, maybe even by just a day or two per level, you could explore the spells more, get used to them. Of course, you still can use them later on, when you are on a higher level. But it feels a bit anticlimatic, if you finally get to polymorph someone on level nine. This would speak for slower experience. However, other classes gain less new features per level than spell casters, and for them the current rate may be just fine. 

In real-world time

How long should it take you to gain a level in play time? My answer is between six and eight evening game sessions. 

I think this is more important than how long it takes in-game, if you assume the main goal is to play a full campaign. The three important ingredients are and what level you need to reach, how long a campaign can run if you intend to finish it, and how often and long you get to play. 

In Gygax' original campaign old veterans had PCs with levels in the teens after about 10 years of play. [#8360]. 

That seems rough. With moving around for education and jobs, getting kids, changing life priorities and interests, any single game that requires you to contiuously commit yourself over 10 years is likely to be abandoned. Two years for a campaign looks doable. Keeping it up for four years is already much harder. 

A normal person for whom RPG is a pastime among others and not the center of their life will not play 7 days a week, as Gary did. We are playing about once per week for three to four hours of real time, and that is the same rate I have experienced in other groups, too. One evening a week is as good a rate as you can expect for a hobby, maybe dropping a few weeks each year to vacations. With busy jobs and kids and family, once a fortnight may be more realistic. 

So you are looking at a bit under 50 sessions a year, and you should be able to finish a campaign within two years or so to achieve closure. Campaigns do not have to go to level 20, in fact very few do or did, level 12-13 is entirely fine and may be preferrable. Even in Gary's campaign, nearly all players retired their characters around there. For this, you would need to gain about six levels a year, one level every two months or seven to eight sessions. 

Gary Gygax said I think that 52 sessions to reach 10th level is about right if the time per session is about four hours. [#5188], which is in the same ballpark.  This would come to about six sessions per level, that being action-packed sessions with theatre of the mind. With weekly play, it would take a year. He has other estimates that made it two years. 

We took nearly two years to get to level 10, but we only played biweekly in the first year, and we often play only three hours effectively, after kids are in bed starting around 9 pm, and ending around midnight with work the next day.  Our DM also is slow in adjucating, taking long time to look up adventure text, not feeling at ease with inventing on the spot to keep things moving, taking a lot of time to count squares in battle sitations. We have too many lengthy rules discussions, and virtual tabletop technical issues tend to slow things down further. So this seems to match the above rate given the extra impediments.

I expect it will take another two years to get to level twenty, if we can stick with it -- there is a bit of fatigue showing. [Addendum: We are now 3 years after I wrote this, and are still on character level 16. Play has further slowed down with the DM having not enough time to prepare and master. Effectively, we only progress on weekend retreats.]

Level 20

We never made it all the way to level twenty, and it would be a cool item for the bucket list to have played one character or campaign all the way through. All earlier campaigns and groups faltered after about 10 or so levels, the longest one went to level 14. 

Getting to level 20 is hard in older editions of D&D, because it took forever to get to the higher levels XP wise, but in all editions, because there are not a lot of good adventures for high level play, campaing arcs tend to end at level twelve or so, and the game also is not designed for high level play and less fun there.

Leveling In OD&D

In Gary's campaign, where the same character was played weekly, sometimes more often than that.

Good players could manage to gain low levels for their PC in a half-dozen or so adventures. Poor ones, those just goofing around couldn't manage that in a dozen adventures. [35] 

By the time AD&D was being played, all that had been ironed out, and the good players were still gaining a level for their PCs every couple of months until mid-level, say around 8th. [35]

The number of XPs given to rise a level was initially intuitive, later on based on the play of my campaign group. I think that 52 sessions to reach 10th level is about right if the time per session is about four hours. Longer sessions would reduce the number accordingly. #5188

A group playing once a week for three to four hours, playing well as a team, should see a 1st level PC that make about one level every three or four months on average. So that should get the typical party member to 9th level at the end of two or three years as you suggest. [35]

Its ambiguous what adventures relates to in the first sentence - game sessions? There were no adventure modules per se in the early days, only forays into the dungeon. This interpretation would mean six to twelve sessions per level, six with competent play. The third statements indicates gaining a level on average every six sessions (nine levels over 52 sessions), eight or more i.e. "a couple of months" towards the end, so maybe around four in the beginning. The fourth statement assumes much slower progression, one level per twelve or more slightly shorter sessions. 

The old veterans had PCs with levels in the teens after about 10 years of play.  [#8360]

A 15th level PC in AD&D requires years of gaming, and when arriving at thay level the character is generally retired. In new D&D arriving at that level takes a mere few months, and that PC is nothing compared to the half-dragon/half-vampire multi-prestige class one that the kid next door stomps around the campaign world with #3850

After name levels, this slowed down significantly, taking about two more years per level if you reached 15th after 10 years. This slowdown mirrors my own experience from second edition, and may also reflect that the high level PCs were played much less regularly. 

In-game time to level in OD&D

If play was intensive dungeon crawling, the 52 play sessions might take up only a few weeks of game time, with several adventure sessions being the continuation of a single day of delving. Also, when magically sent to another location time was generally different, and one reappeared in the original place with only a fraction of subjective time while away having passed in the home universe.  #5189

At  low levels if you gain ten levels in the span of a year of real-time sessions equaling "a few weeks" of dungeoneering game time, then your character would gain a level every two to three days of game time, same as in fifth edition. If it takes you two years and twice as many sessions to get to level 9, these 52 sessions and "few weeks" would only get you to leve five, and it would take you four or five days in game to level, half as fast as in fifth edition. 

Outdoor adventures might consume months of game time, of course. The latter posed a problem for players used to adventuring as a group when they were not with the others on an outdoor foray, so the regulars would often seek their fellows on such jouneys. To answer in general, the time span for 52 adventure sessions was generally anywhere from as many weeks to two years or longer. #5189

Also note that in OD&D, XP and leveling was defined much more by the treasure found, than by the monsters defeated. So if you made the mistake to hand out a huge treasure that was inapropriate, this could wreck havoc with accelerated progression. 

I am not particularly find of playing one game session and going up a level. That hardly qualifies as "eaned," to my way of thinking. However, if the campaign is set up for very high level play, such increase might be warranted. I did play in and enjoyed that sort of gaming with my French fellows, Francois Froideval being the DM. (My 12th level fighter was a mere peon, akin to a low-level PC, in that campaign.) [35]

I don't think you should ever allow a PC to gain more than one level from an adventure success. #1683

Mechanics: Equivalent Hit Dice for 5e

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 first thing to observe is that there is no straightforward mathematical formula to map between xp and character level. That is because 5e fudges power at certain levels, like on level 5 characters make a jump in power when they get access to fireball and second attacks. 

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:

It is obvious that at at low levels the EHD are a lower multiple of the CR than at high levels. Here are the factors, using piecewise linear interpolation for EHD for each CR point.

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.

CR	EHD	CR	EHD	CR	EHD
1/8	1/4	7	18	16	45
1/4	1/2	8	19	17	48
1/2	1	9	22	18	51
1	2	10	25	19	55
2	5	11	29	20	59
3	7	12	32	21	67
4	10	13	37	22	74
5	14	14	40	23	80
6	17	15	42	24	85

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. 

Name	CR	5EHD	P	Ratio
Giant Centipede	1/4	1/5	45	0.8
Stirge	1/8	1/3	56	2.6
Giant Weasel	1/8	1/3	49	2.6
Giant Rat	1/8	1/3	45	2.6
Kobold	1/8	1/3	44	2.6
Bandit	1/8	1/3	38	2.6
Giant Crab	1/8	1/3	37	2.6
Cockatrice	1/2	1/2	73	1.0
Goblin	1/4	1/2	60	2.0
Guard	1/8	1/2	57	4.0
Skeleton	1/4	1/2	56	2.0
Giant Poisonous Snake	1/4	1/2	48	2.0
Zombie	1/4	1/2	45	2.0
Wolf	1/4	1/2	43	2.0
Dryad	1	1/2	36	0.5
Gnoll	1/2	1/2	29	1.0
Hobgoblin	1/2	1	89	2.0
Ghoul	1	1	77	1.0
Troglodyte	1/4	1	76	4.0
Orc	1	1	63	2.0
Giant Wasp	1	1	48	2.0
Harpy	1	1	48	1.0
Lizardfolk	1	1	44	2.0
Shadow	1	1	40	2.0
Giant Spider	1	1	32	1.0
Giant Toad	1	2	73	2.0
Specter	1	2	72	2.0
Dire Wolf	1	2	72	2.0
Bugbear	1	2	67	2.0
Giant Octopus	1	2	63	2.0
Will-O'-Wisp	2	2	57	1.0
Phase Spider	3	2	53	0.7
Brown Bear	1	2	52	2.0
Giant Boar	2	2	49	1.0
Bandit Captain	2	2	39	1.0
Carrion Crawler	2	2	35	1.0
Berserker	2	2	33	1.0
Doppelganger	3	3	65	1.0
Ogre	2	3	63	1.5
Basilisk	3	3	59	1.0
Wight	3	3	59	1.0
Giant Scorpion	3	3	56	1.0
Gargoyle	2	3	48	1.5
Manticore	3	3	45	1.0
Griffon	2	3	45	1.5
Awakened Tree	2	3	44	1.5
Girallon	4	3	41	0.8
Gelatinous Cube	2	4	71	2.0
Black Pudding	4	4	64	1.0
Wererat	2	4	61	2.0
Knight	3	4	51	1.3
Minotaur	3	4	44	1.3
Veteran	3	4	40	1.3
Unicorn	5	4	36	0.8
Werewolf	3	4	36	1.3
Owlbear	3	5	68	1.7
Ettin	4	6	41	1.5
Displacer Beast	3	6	37	2.0
Wraith	5	7	44	1.4
Giant Crocodile	5	9	40	1.8
Wereboar	4	10	56	2.5
Invisible Stalker	6	11	44	1.8
Fire Elemental	5	12	64	2.4
Mind Flayer	7	12	52	1.7
Roper	5	12	47	2.4
Gorgon	5	12	45	2.4
Medusa	6	12	43	2.0
Wyvern	6	13	56	2.2
Giant Shark	5	13	53	2.6
Air Elemental	5	13	52	2.6
Umber Hulk	5	14	51	2.8
Mammoth	6	15	53	2.5
Golem, Flesh	5	15	41	3.0
Hydra	8	17	56	2.1
Giant, Stone	7	17	53	2.4
Earth Elemental	5	17	50	3.4
Water Elemental	5	17	49	3.4
Treant	9	18	60	2.0
Giant, Frost	8	18	52	2.3
Tyrannosaurus Rex	8	18	47	2.3
Oni	7	20	71	2.9
Efreeti	11	20	48	1.8
Giant, Cloud	9	21	57	2.3
Giant, Fire	9	22	47	2.4
Golem, Stone	10	22	44	2.2
Vampire	13	23	60	1.8
Roc	11	24	61	2.2
Purple Worm	15	27	51	1.8
Golem, Iron	16	28	61	1.8
Giant, Storm	13	32	56	2.5
Empyrean	23	38	47	1.7
Green Dragon, Adult	15	43	49	2.9
White Dragon, Adult	13	43	45	3.3
Black Dragon, Adult	14	43	45	3.1
Blue Dragon, Adult	16	44	53	2.8
Balor	19	45	53	2.4
Dragon Turtle	17	46	59	2.7
Lich	21	46	48	2.2
Beholder	13	48	47	3.7
Red Dragon, Adult	17	50	48	2.9
Kraken	23	50	45	2.2
Gold Dragon, Adult	17	51	47	3.0

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.