Kinematics
Hero
So, the DMG infamously suggests 6 to 8 encounters per day (of the medium-to-hard variety), which most gaming tables find... untenable. However I've discovered data that has led me to a different conclusion.
This is fallout of the work of trying to define prices for magic items. That in turn required an understanding of the rates of treasure generation, which led to the number of expected hoards of loot per leveling tier. The number of hoards needed explaining, and an easy enough assumption is that they come from the hard+ encounters, generally.
That in turn was back-calculated to see whether the assumption fit — and it did. It turns out that if you assume that hard encounters account for 30% of all experience gained (which was derived based on the ratio of the necessary number of such encounters versus the maximum number possible), and that each hard encounter generated a hoard of loot, you end up with exactly the number of expected hoards per tier, distributed evenly for everything except the first four levels, which instead progress with 1, 1, 2, 3 hoards for levels 1, 2, 3, 4.
Of course that leads to the question of, how is the rest of your experience distributed?
Well, an interesting pattern comes up. If you get 2 or 3 hoards per level, corresponding to the hard fights, then you expect that there's easier stuff that led up to it. And if you divide, say, level 6's experience by 3, and then subtract out the amount allocated to the hard fight, the remainder fits pretty nicely into a pattern like 5 easy + 2 medium + 1 hard.
And suddenly you have an encounter arc, of easy stuff leading to harder stuff.
A few easy encounters, that lead to medium encounters, that lead to the final boss. Or perhaps a couple easy that lead to a medium, and then another easy that leads to a different medium, and put the clues together to get to the hard fight. That sort of thing. It provides a structure for how to organize encounters, from the easier beginnings to the harder endings. (At least for campaigns that are more story-focused, rather than dungeon-focused.)
Of further interest, it turns out that you reach the "expected experience per day" using splits like: 3 easy, 2 medium, 2 hard; or 5 easy, 2 medium, 1 deadly; 5 easy, 2 medium, 1 hard, plus 1 more easy; etc. Basically, you don't need a flat 8 medium encounters.
So I put the XP numbers in a spreadsheet to compare, and found something odd. The table for XP per day doesn't add up to 6 to 8 encounters for hard and medium, respectively. For hard encounters, the daily XP gain would need between 4 and 5 encounters per day. For medium encounters, you'd need between 6 and 7 encounters per day to reach the daily total. That's about 1.5 encounters less than the recommendation.
How do you get 6 to 8 encounters? Or, a better question is, what combinations of easy/medium/hard/deadly encounters generates the commonly recommended XP per day? Well, the best pattern I got was 3 easy + 2 medium + 2 hard. That's 7 encounters, and generally keeps you within 5%-10% of the recommended daily XP. It's also a good pyramid setup, where you can progress from easy to medium to hard encounters (possibly twice).
Of course you're also getting 45% to 50% of all your XP from the hard encounters, which means you can't just use the hard encounters for loot. Rather, maybe 2 out of 3 encounters actually rolls on the loot hoard tables, which actually kind of helps out in giving more options for choosing when to give treasure hoards.
So overall, the layout is two small arcs per day: 2 easy, 1 medium, 1 hard, then 1 easy, 1 medium, 1 hard. Though obviously you can mix up the order, or swap an easy+hard for a deadly, etc.
The easy encounters are unlikely to be combat, which means you're probably only dealing with perhaps 4 combats per game day, which is far more reasonable than 6-8, while still allowing for one or two short rests, to balance towards the short rest classes.
If you don't want easy encounters, you can also do 3 hard and 2 medium for 5 total encounters per day, which is again easy to work into a pair of short rests (ie: medium+hard, short rest, medium+hard, short rest, hard), though it's more combat-intensive.
Summary: The 6-8 medium-to-hard encounters per game day is a lie. The XP per day is balanced more towards 4 medium or hard encounters, with a few easy encounters to fill in the gaps (totalling up to about 7). This also fits reasonably well with the treasure hoards gained, which might be provided for 2 out of every 3 hard encounters.
Have I missed anything?
This is fallout of the work of trying to define prices for magic items. That in turn required an understanding of the rates of treasure generation, which led to the number of expected hoards of loot per leveling tier. The number of hoards needed explaining, and an easy enough assumption is that they come from the hard+ encounters, generally.
That in turn was back-calculated to see whether the assumption fit — and it did. It turns out that if you assume that hard encounters account for 30% of all experience gained (which was derived based on the ratio of the necessary number of such encounters versus the maximum number possible), and that each hard encounter generated a hoard of loot, you end up with exactly the number of expected hoards per tier, distributed evenly for everything except the first four levels, which instead progress with 1, 1, 2, 3 hoards for levels 1, 2, 3, 4.
Of course that leads to the question of, how is the rest of your experience distributed?
Well, an interesting pattern comes up. If you get 2 or 3 hoards per level, corresponding to the hard fights, then you expect that there's easier stuff that led up to it. And if you divide, say, level 6's experience by 3, and then subtract out the amount allocated to the hard fight, the remainder fits pretty nicely into a pattern like 5 easy + 2 medium + 1 hard.
And suddenly you have an encounter arc, of easy stuff leading to harder stuff.
A few easy encounters, that lead to medium encounters, that lead to the final boss. Or perhaps a couple easy that lead to a medium, and then another easy that leads to a different medium, and put the clues together to get to the hard fight. That sort of thing. It provides a structure for how to organize encounters, from the easier beginnings to the harder endings. (At least for campaigns that are more story-focused, rather than dungeon-focused.)
Of further interest, it turns out that you reach the "expected experience per day" using splits like: 3 easy, 2 medium, 2 hard; or 5 easy, 2 medium, 1 deadly; 5 easy, 2 medium, 1 hard, plus 1 more easy; etc. Basically, you don't need a flat 8 medium encounters.
So I put the XP numbers in a spreadsheet to compare, and found something odd. The table for XP per day doesn't add up to 6 to 8 encounters for hard and medium, respectively. For hard encounters, the daily XP gain would need between 4 and 5 encounters per day. For medium encounters, you'd need between 6 and 7 encounters per day to reach the daily total. That's about 1.5 encounters less than the recommendation.
How do you get 6 to 8 encounters? Or, a better question is, what combinations of easy/medium/hard/deadly encounters generates the commonly recommended XP per day? Well, the best pattern I got was 3 easy + 2 medium + 2 hard. That's 7 encounters, and generally keeps you within 5%-10% of the recommended daily XP. It's also a good pyramid setup, where you can progress from easy to medium to hard encounters (possibly twice).
Of course you're also getting 45% to 50% of all your XP from the hard encounters, which means you can't just use the hard encounters for loot. Rather, maybe 2 out of 3 encounters actually rolls on the loot hoard tables, which actually kind of helps out in giving more options for choosing when to give treasure hoards.
So overall, the layout is two small arcs per day: 2 easy, 1 medium, 1 hard, then 1 easy, 1 medium, 1 hard. Though obviously you can mix up the order, or swap an easy+hard for a deadly, etc.
The easy encounters are unlikely to be combat, which means you're probably only dealing with perhaps 4 combats per game day, which is far more reasonable than 6-8, while still allowing for one or two short rests, to balance towards the short rest classes.
If you don't want easy encounters, you can also do 3 hard and 2 medium for 5 total encounters per day, which is again easy to work into a pair of short rests (ie: medium+hard, short rest, medium+hard, short rest, hard), though it's more combat-intensive.
Summary: The 6-8 medium-to-hard encounters per game day is a lie. The XP per day is balanced more towards 4 medium or hard encounters, with a few easy encounters to fill in the gaps (totalling up to about 7). This also fits reasonably well with the treasure hoards gained, which might be provided for 2 out of every 3 hard encounters.
Have I missed anything?
