This is long and a bit mathy, but figure people might be interested:
5th edition encounter and daily budgets are designed to measure resource expenditure: you have a certain amount of resources available for use every day, and after a full day you’re expected to have mostly depleted them.
For sufficiently simple martial characters, they really only have two expendable resources: hit points and hit dice. Both of them are depleted by damage. Thus, we can basically model the challenge of an encounter by the number of hit points it depletes at a given level, and in fact that’s roughly what 5e seems to do.
Simple math tells us that number of hit points a monster can be expected to inflict on a party is DPR*Survival Time, and for our simple martial characters, that means DPR*HP/Party DPR. Since we don’t adjust xp value based on party level, that probably means xp value scales with DPR*HP. This turns out to be mostly true: looking at published monsters, DPR averages about 5*(CR+1), hp averages about 15*(CR+1), and xp value averages about 50*(CR+1)^2, which is DPR*HP*⅔. The scaling for PCs is similar, the daily xp budget is pretty close to 75*(level+1)^2.
The above assumes one monster. If you have N monsters, their total DPR is multiplied by some number between 1 and N, depending on how efficiently they are able to attack (in a mob, some monsters will be unable to attack because they can’t reach the PCs), and survival time is also multiplied by some number between 1 and N, depending on the mix of attacks being used (1 for area effect attacks hitting the entire group, N for single target attacks), and thus total xp value should be multiplied by some value between 1 and N^2. The actual rules in the dmg are reasonably close to N^1.5, which is not an absurd middle ground (intermediate between Lanchester’s Linear Law and Lanchester’s Square Law).
Now… why is this broken? Two reasons
The formulas basically ignore armor class and attack bonus. There isn’t that much variation in ac and attack bonus between 4xCR ⅛ and 1xCR 1, probably not more than 1-2 points, which is too small to really notice, but between 4xCR7 and 1xCR20 you’re probably looking at around 4 points of AC and 6 points of attack bonus, and that’s not ignorable.
The formulas assume both dpr and available daily resources are roughly proportional to (level+1). This is decently true for martial characters at low levels (once they max their attack stat, they may start putting points in con, which will significantly alter the curve), but available resources for spellcasters scale significantly faster than that.
Thanks for the post, it's interesting maths. Overall I find all the calculations to be wonky.
It's just not possible to do an accurate calculation because a party of 4 x level 5 characters have the same difficulty rating and XP whether it's the only fight in the day, or it's their 8th gruelling fight and they have no resources left. Action economy and party size also really messes with things.
The higher in CR you go, the less these things work, and unfortunately monster design is very flawed this way; most big monsters get a one-shot mega attack that deals 10dX+ damage and half on a save, and then a few basic attacks. But once PCs are higher level, stuff like Evasion, Mass Cure Wounds and so on can easily negate it completely.
I recommend abandoning calculations altogether and just throw what seem like impossible challenges at the party. I've found that past a certain level it's nearly impossible to hurt the characters unless you throw far out CR'd challenges at them over and over again.
I saw someone Tweeting today that "Strahd can really do some damage, especially with mass invisibility - even against a level 11 party." I found it baffling. He barely has any damage output and 11th level characters will cut through him like a hot knife through butter, and on a long rest they'll likely take him out in 1-2 turns at most. My current PCs party is level 10 and the GWM barbarian is hitting for 2d6+20 damage with reckless attacks, the Blood Hunter deals 1d10+d6(rite)+d6(hex)+15(sharpshooter) for the same average.
Don't even get me started on adult dragons with 215 hit points!
My mistake. I got caught up in the math and missed the beginning where you referred to the daily budget. When I commented at first, I thought you were referring to XP awards. The Adventuring Day XP table does indeed refer to adjusted XP as you say. Apologies.
Thanks for the post, it's interesting maths. Overall I find all the calculations to be wonky.
It's just not possible to do an accurate calculation because a party of 4 x level 5 characters have the same difficulty rating and XP whether it's the only fight in the day, or it's their 8th gruelling fight and they have no resources left. Action economy and party size also really messes with things.
The 'expected damage to party' metric does not care about how many fights per day, it cares about the party's damage output (obviously, using up only 1/3 of your resources because there's only one fight in a day isn't terribly challenging, but that doesn't mean it didn't use up that many resources).
People grotesquely overstate the value of action economy. Unless there's action denial abilities being used, it doesn't matter if the 50 dpr comes from one action or ten, what matters is that it's 50 dpr.
Party size both increases party dpr and increases party total hit points, and therefore should adjust the xp thresholds of a party in the same way as number of monsters adjusts xp value (what 5e actually does is clunky and not reliable).
Party size both increases party dpr and increases party total hit points, and therefore should adjust the xp thresholds of a party in the same way as number of monsters adjusts xp value (what 5e actually does is clunky and not reliable).
Indeed. Also, unless you're running straight combat encounters in a PvP arena, there are a number of factors that change the encounter difficulty (e.g. terrain, surprise) without changing the adjusted XP value or the XP reward value.
But then ... I was never really satisfied with the way previous editions handled XP or scaled to high level play either. It always seemed to me that the XP system was about as good at being an abstraction of learning as the GP system was at being an abstraction of an economy. And that the game was better at being about becoming a high level hero than it was at actually being one.
Thanks again for the post and running the calculations. I'm definitely noting some of this down.
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This is long and a bit mathy, but figure people might be interested:
5th edition encounter and daily budgets are designed to measure resource expenditure: you have a certain amount of resources available for use every day, and after a full day you’re expected to have mostly depleted them.
For sufficiently simple martial characters, they really only have two expendable resources: hit points and hit dice. Both of them are depleted by damage. Thus, we can basically model the challenge of an encounter by the number of hit points it depletes at a given level, and in fact that’s roughly what 5e seems to do.
Simple math tells us that number of hit points a monster can be expected to inflict on a party is DPR*Survival Time, and for our simple martial characters, that means DPR*HP/Party DPR. Since we don’t adjust xp value based on party level, that probably means xp value scales with DPR*HP. This turns out to be mostly true: looking at published monsters, DPR averages about 5*(CR+1), hp averages about 15*(CR+1), and xp value averages about 50*(CR+1)^2, which is DPR*HP*⅔. The scaling for PCs is similar, the daily xp budget is pretty close to 75*(level+1)^2.
The above assumes one monster. If you have N monsters, their total DPR is multiplied by some number between 1 and N, depending on how efficiently they are able to attack (in a mob, some monsters will be unable to attack because they can’t reach the PCs), and survival time is also multiplied by some number between 1 and N, depending on the mix of attacks being used (1 for area effect attacks hitting the entire group, N for single target attacks), and thus total xp value should be multiplied by some value between 1 and N^2. The actual rules in the dmg are reasonably close to N^1.5, which is not an absurd middle ground (intermediate between Lanchester’s Linear Law and Lanchester’s Square Law).
Now… why is this broken? Two reasons
I found this breakdown to be interesting. I wonder if you might clarify your thoughts on why you are comparing 4xCR⅛ to 1xCR1 and 4xCR7 to 1xCR20.
4x CR 1/8: adjusted xp 200. 1x CR 1: adjusted xp 200
4xCR 7: adjusted xp 23,200. 1x CR 20: adjusted xp 25,000.
Thanks for the post, it's interesting maths. Overall I find all the calculations to be wonky.
It's just not possible to do an accurate calculation because a party of 4 x level 5 characters have the same difficulty rating and XP whether it's the only fight in the day, or it's their 8th gruelling fight and they have no resources left. Action economy and party size also really messes with things.
The higher in CR you go, the less these things work, and unfortunately monster design is very flawed this way; most big monsters get a one-shot mega attack that deals 10dX+ damage and half on a save, and then a few basic attacks. But once PCs are higher level, stuff like Evasion, Mass Cure Wounds and so on can easily negate it completely.
I recommend abandoning calculations altogether and just throw what seem like impossible challenges at the party. I've found that past a certain level it's nearly impossible to hurt the characters unless you throw far out CR'd challenges at them over and over again.
I saw someone Tweeting today that "Strahd can really do some damage, especially with mass invisibility - even against a level 11 party." I found it baffling. He barely has any damage output and 11th level characters will cut through him like a hot knife through butter, and on a long rest they'll likely take him out in 1-2 turns at most. My current PCs party is level 10 and the GWM barbarian is hitting for 2d6+20 damage with reckless attacks, the Blood Hunter deals 1d10+d6(rite)+d6(hex)+15(sharpshooter) for the same average.
Don't even get me started on adult dragons with 215 hit points!
Yes. I see. Why are you making that adjustment?
My mistake. I got caught up in the math and missed the beginning where you referred to the daily budget. When I commented at first, I thought you were referring to XP awards. The Adventuring Day XP table does indeed refer to adjusted XP as you say. Apologies.
The 'expected damage to party' metric does not care about how many fights per day, it cares about the party's damage output (obviously, using up only 1/3 of your resources because there's only one fight in a day isn't terribly challenging, but that doesn't mean it didn't use up that many resources).
People grotesquely overstate the value of action economy. Unless there's action denial abilities being used, it doesn't matter if the 50 dpr comes from one action or ten, what matters is that it's 50 dpr.
Party size both increases party dpr and increases party total hit points, and therefore should adjust the xp thresholds of a party in the same way as number of monsters adjusts xp value (what 5e actually does is clunky and not reliable).
Because that's what evaluating encounter difficulty tells you to do.
Indeed. Also, unless you're running straight combat encounters in a PvP arena, there are a number of factors that change the encounter difficulty (e.g. terrain, surprise) without changing the adjusted XP value or the XP reward value.
But then ... I was never really satisfied with the way previous editions handled XP or scaled to high level play either. It always seemed to me that the XP system was about as good at being an abstraction of learning as the GP system was at being an abstraction of an economy. And that the game was better at being about becoming a high level hero than it was at actually being one.
Thanks again for the post and running the calculations. I'm definitely noting some of this down.