Average Rounds of Combat in 5e

The number of combat rounds has a strong influcence on how costly it is to use an action, for example a spell that produces an effect for a minute, enough to last the whole fight: if the fight only takes three rounds, you will only benefit from it for two rounds. If the fight however takes eight rounds, you get seven rounds of benefit. 

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

And on p.281, in the Monster Features section for factoring Regeneration in CR calculations:

Increase the monster's effective hit points by 3 x the number of hit points the monster regenerates each round. 

Both indicate that the game seems to expect combat to take three rounds. 

More importantly, this length is also supported by the amount of damage characters deal against the hit points of a an appropriate monster: a group of four would reduce such a monster to 0 hits in about three rounds.  

A higher end of five rounds is based on empirical data at one specific table.

You often do not attack every round in every fight when you spending time to manoever or take cover, so the fight duration in rounds might increase, but the number of rounds where you fully attack may not. This would make for longer combat, but in a way that is not material for resource use math. 

In my experience, larger and more deadly battles take longer, sometimes much longer, as opponents not only move around and jockey for cover, but as there are many more opponents and hit points to grind down, while small fights or fights against weaker opponents are over even faster. 

In reality you will tend to have fewer, deadlier encounters than the DMG guidance suggests. Instead of 5 or so medium combats, you end up with only three deadly ones per day, sometimes even only a single really huge monster-ball battle. This will lead to longer combat in the wild than what the DMG math implies. 

For these reasons, I think four rounds per combat encounter is a better average than three. 

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.

In-Game Economy

An economy is a complex thing, becuase there are so many interacting agents. There is a reason economists have lots of complicated mathematical models. For a fantasy role playing game, where the goal is to have exciting stories and adventures, all you normally need is some prices for goods characters want to buy or sell, typically adventuring equipment, later on maybe costs for armies, and building keeps.

For selling it is useful to have a discount rate by item type: how much cheaper than what they sell it for would a merchant be willing to buy something for? You need this for the types of things the adventurers win in adventuring. I typically use

• Coins: 95% Obviously they can pay with 100% of the coin value, but if they want to exchange coin types, for example a heavy bag of 1,000 copper pieces for a platinum piece, there will be a money changer's fee of 5%. 
• Jewels: 95% The same applies for exchanging coins into jewels for lighter transport. I allow to pay with jewels at full value, just as with coins, but you could charge a 5% discount even for that.
• Trade goods: 80%It does not make sense to buy goods at the same price you'd sell them, so instead of 100%, I give 80% for goods on the list of trade goods. This allows at least to reasonably have some level of trade, even if the value is still high. Bars of copper, silver or gold would be treated as coins or jewels at 100% to pay with, and 95% to exchange. 
• New weapons, armor and equipment: 50%  you need to find a merchant trading in them, and they will pay half price, if they are interested to buy. If the characters have too many items (say, hundreds of swords) that they will have a hard time selling again near term, they may only buy a limited amount or ask for a lower bulk price. Note that it is very rare to find new items -- maybe sometimes in a storage room or armory. Most items are being used. 
• Used weapons, armor and equipment: 0-25%Especially for monster derived weapons and armor, that would be ugly and not fit in style and balance to human needs, it often will be close to 0%. For equipment, or human weaopns it might be between 25%, most commonly I use 10%. 
• Art and Jewlery: 50% This is a bit tricky, as Jewelry could be broken down into jewels and precious metals, that could be used to pay at 100% or 95%. However, the value of jewelry is often a multiple of that of the pure gem and metal value, due to the art and workmanship that went into them, just as a beatuiful painting is many times the value of the paints and canvas. I simple use the same 50% as for other goods. 

The economy in the game as described does not work, really -- for example trade goods always cost the same to buy and sell. If that were so, there would be no traders or merchants for them, because without a price difference and profit margin, they could not survive. Why would you pay for horses, carts, drivers to transport grain or metal wood somewhere, when you cannot sell it for more than what you bought it for? And why would you maintain a stall or shop doing so?

In a real economy, anything that is produced must be sold more dearly than what the input materials cost, an what the living costs of any labor to produce it cost, or it could not be produced in the long run -- the manufacturer would go bankrupt. 

Setting prices for in-game economy

What should an item cost in the game that is not on the equipment table? 

A naive approach is to see what it costs today and apply a conversion factor from modern time prices to gp. It is a pretty common question how much a gp would be worth in today's money. However industrial manufacturing, technology and automation has changed how much it costs to produce some things like clothing, but has little influenced others, like the cost to raise a living animal, so this approach will not work. 

We'll first consider how much a gold piece might be worth on average to settle that, and then look at how to instead usefully determine the price of items in the game.

How much is a gold piece worth?

Thre are at least two ways to determine a conversion factor for the value of a gp: the value of gold, or the value of a basket of goods you could buy with a piece of gold. 

Value of gold as a commodity

Maybe the least biased comparison for measuring the value based on a single good could be made using the price of gold itself? In the game, gold coins are made of gold, and 50 coins weigh one pound, so one pound of gold is worth 50 gp. The original purpose of minted coins was to guarantee purity and weight of material (although that was subsequently undermined by the nobles that could mint coins, to stretch their finances, as nicely detailed in Wealth of Nations).

The price of gold fluctuates in modern time as the gold standard has been given up. Money is not tied to gold at a fixed ratio any more. How much you pay for gold is entirely dependend on people believing how much it might be worth (or, conversely, how much the money might be worth). Typically the price of gold goes up when people distrust the value of money, and are looking for alternatives to store their wealth.  While I am writing this, the value of one pound of gold is about 30,000 US$, which would mean one gp would be worth about 600 US$. In the year 2000, it was only about 4,800 US$, or about 100 US$/gp. 

Value of a basket of goods

You could caluclate purchasing power parity across a basket of goods. For example, determine the current prices for all the items from the equipment list, and for each figure out how much the price ratio it, then average the resulting ratios. This will give you an average conversion factor for the gp across many goods. Unfortunately, because the factor differs so much depending on the nature of each individual item, using the average conversion leads to prices that would not reflect how much any given item should really cost.

For example,  a spyglass costs 1,000 gp in the game and from about $25 in the modern world -- a ratio of 40 gp per US$. A hand-made riding saddle costs 10 gp in the game and can cost thousands of US$ (prices ranging from about $500 to $4,000), so assuming $2,000, a ratio of 1/200th gp per US$. That means there is a 8,000-fold difference in the conversion factor for these two items. Clearly any average value would be meaningless. If we used $100 per gp, based on the lower range from metal conversion value above, a spyglass should cost only 2.5 sp, clearly too cheap, while a saddle would cost 20 gp.  

Estimating the price based on what it costs to manufacture

Instead, if you want to estimate how expensive something would be, base it on how much the raw materials would cost and how much the labor would cost. So essentially you are looking what it costs to craft the item. You can apply any level of profit margin on top of that, if you like. 

Crafting rules

If you look at the crafting rules, which presupose skilled labor (PHB p. 187), you can craft items at a rate of 5 gp per day, and a material cost of half the total value in materials. Under these rules, crafting a riding saddle would only take 2 days, and cost 5 gp for raw materials like leather.

The labor cost in the crafting rules is 2.5 gp per day, not 2 gp, but the rules are directed at the PCs, who are supposed to be individuals out of the ordinary. Skilled PCs can craft a saddle faster than the average craftsman. To determine prices for goods crafted by ordinary folk, we instead should assume a crafting rate of 2 gp per day, the cost of paying for a day's labor. 

Labor costs

Labor is fundamental for economic value, because if a laborer could not afford the necessities of life, you would not have a sustainable economy, and if they could amass riches and would not need to work any more. The idea that all value can be derived from labor is essentially Adam Smith's Labor Theory of Money (This theory since has been supplanted by the subjective theory, that value is measured by how useful something is to someone; you may see that reflected in what characters are willing to spend on a magic weapon.)

In the game, the cost for an unskilled laborer is 2 sp per day (see Services, p. 159 PHB), but most manufactured items will requrie a skilled artisan. A skilled laborer is paid 2 gp per day in the game. 

Material Costs 

In theory, material costs also come down to labor costs, and maybe rent extracted from access to limited resources like land (for pasture), mines (for ore or metal) and so on. But in practical terms, you can get the material prices for many raw materials from the list of trade goods. 

For those that are not on that list, you could estimate it from exisiting items based on the crafting rules in the PHB (p. 187) that state half of the cost is raw material. For example, leather is not on the list. Leather armor is made of leather, weighs 10 pounds and costs 10 gp, meaning a pound of leather could cost up to half a gp. This is not exact, because in reality, some things require much less material and more labor than others, but it can give you an idea.

If determined in this way, unless an item requires highly unusual components, the material costs will often be much smaller than the labor cost.

The crafting rules instead base the material cost on the cost of labor, which in many cases leads to a higher price than adding raw trade good values to the labor cost. So, instead of adding the material cost explicitly, a simplification of the crafting rule would be to add half the labor cost again, and only add extra cost for unsual or especially costly components on top of that. That will be the final item manufacture cost. 

Market Price

If you want the market price of an item, the cost calculation based on labor and material does not factor in profit margin on top of the labor for the trader (for goods that are imported) and merchant, each of which likely would apply 30% onto the costs if not more. The economy in the game does not really work anyways, with all trade goods costing the same everywhere, so no profit can be made on them, and nobody would trade them. 

If you assume only one trader, or a profit margin of only 30%, you get labor cost x 1,5 (for material) x 1,3 (for margin), ending up with about two times laber cost for the market price of the item that a PC can buy. Some Examples

Riding Saddle. Manufacturing a riding saddle takes about 50 hours of work by a skilled laborer, and that work has not changed much due to modern machinery or automation. At 8 hours and 2 gp per day, we would arrive at a price of 12.5 gp for the labor and a market price of 25 gp for the saddle. So this method would be off by 2.5x vs the saddles list price. If it indeed would only 20 hours to make a saddle, it would end up at exactly the 10 gp from the PHB.

Spyglass. In medieval times lenses were made from gemstones, typically beryllium, which might explain the high material cost. If we did not know the spyglass cost, and would estimate it would take about a month (30 days) to grind and polish the lenses and manufacture the precision housing, we would be at 60 gp labor, or 120 gp total cost. Chrysoberyl according to the DMG p. 134 cost 100 gp per gem. Because they are a special, costly material, we add them on top, which gives us a total of 320 gp. This still would be 3x lower than the PHB, and seems to be a more reasonable in-game price for a spyglass.

Conclusion

There is no generic formula for converting modern day prices of goods into gp costed ones that makes sense for a medieval-magical world. And there is not a lot of support in the rules for it, for good reason. It is a complex subject. 

If you are interested in what the price for an item could or should be, and enjoy research on historical prices, or medieval manufacturing methods, the best way is to do it item by item.

For practical purposes, you probably can spend your prepration time better than doing this, unless you enjoy reading up on how things were done. Either use a price from the internet where sombody has already done the work, or frome a similar game with more comprehensive price lists (Pathfinder comes to mind), or just ballpark the price based on other items on the equipment list.

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.