AC and HP balancing calculator

[Decorayah]

Hey there guys. Let's say a creature has 18 AC and 250 hp. Another creature has 20 AC and 200 hp. How do you calculate which of the two is tougher statistically? I am after a rough calculation of course. For an example the Tarrasque has 25 AC and 676 hp. If I want to make a creature of similar endurance but with 1200 HP what AC would be adequate? Maybe 16? What do you think?

Also this is a scenario where I have 5 players levels 17-19.

(Yes I know there are a lot more factors like resistances, immunities, legendary resistance etc. In this scenario everything but the AC and hp is the same).

[Unoriginal]

Hey there guys. Let's say a creature has 18 AC and 250 hp. Another creature has 20 AC and 200 hp. How do you calculate which of the two is tougher statistically? I am after a rough calculation of course. For an example the Tarrasque has 25 AC and 676 hp. If I want to make a creature of similar endurance but with 1200 HP what AC would be adequate? Maybe 16? What do you think?

Also this is a scenario where I have 5 players levels 17-19.

(Yes I know there are a lot more factors like resistances, immunities, legendary resistance etc. In this scenario everything but the AC and hp is the same).

Have you read the DMG rules about CR calculations? Because they include this.

[Sjappo]

Let's see if I can make any sense.

A 17th level PC has, roughly, a +10 to +15 hit bonus. The Tarrasque has an AC of 25

At +10 the PC hits on a 15 or higher, or 30% of the time. If I double the HP and want the PC to kill it in the same amount of time I need to double the hit-chance to 60%. The PC needs to be able to hit on a 10 or higher. I need to lower the AC to 20.

At +15 the PC hits on a 10 or higher, or 55% of the time. If I double the HP and want the PC to kill it in the same amount of time I need to double the hit-chance to 110%. The math breaks down around here.

You cannot indiscriminately exchange AC for HP for high AC creatures.

Your other example:
Using average damage and disregarding critical hit or other damage enhancers:
The AC 20 creatures is a bigger threat from +1 to +6 hit bonus .
They are equal from +7 to +10 hit bonus
The AC 18 creature is the bigger threat at hit bonuses from +11 up.

So it all depends on PC level, hit bonus optimisation, availability of magical weapons ...


Right. At 10 damage average per hit the next table gives the average number of hits needed to kill a monster. By no means perfect, but hey.

AC 18 20
HP 250 200
Hit
bonus
1 42 100
2 31 50
3 25 33
4 21 25
5 18 20
6 16 17
7 14 14
8 13 13
9 11 11
10 10 10
11 10 9
12 9 8
13 8 8
14 8 7

[Decorayah]

Let's see if I can make any sense.

A 17th level PC has, roughly, a +10 to +15 hit bonus. The Tarrasque has an AC of 25

At +10 the PC hits on a 15 or higher, or 30% of the time. If I double the HP and want the PC to kill it in the same amount of time I need to double the hit-chance to 60%. The PC needs to be able to hit on a 10 or higher. I need to lower the AC to 20.

At +15 the PC hits on a 10 or higher, or 55% of the time. If I double the HP and want the PC to kill it in the same amount of time I need to double the hit-chance to 110%. The math breaks down around here.

You cannot indiscriminately exchange AC for HP for high AC creatures.

Your other example:
Using average damage and disregarding critical hit or other damage enhancers:
The AC 20 creatures is a bigger threat from +1 to +6 hit bonus .
They are equal from +7 to +10 hit bonus
The AC 18 creature is the bigger threat at hit bonuses from +11 up.

So it all depends on PC level, hit bonus optimisation, availability of magical weapons ...


Right. At 10 damage average per hit the next table gives the average number of hits needed to kill a monster. By no means perfect, but hey.
AC 18 20
HP 250 200
Hit bonus
1 42 100
2 31 50
3 25 33
4 21 25
5 18 20
6 16 17
7 14 14
8 13 13
9 11 11
10 10 10
11 10 9
12 9 8
13 8 8
14 8 7


Thanks for the response. Was very helpful :)

[PhantomSoul]

At +15 the PC hits on a 10 or higher, or 55% of the time. If I double the HP and want the PC to kill it in the same amount of time I need to double the hit-chance to 110%. The math breaks down around here.


As a minor note, thinking of it here as "halving the miss rate" (45% --> 20% or 25%) fixes the problem of math apparently breaking down. (Of course, it doesn't account for rolling a 20 -- a guaranteed hit -- to have greater power, but that's a separate issue that tends to get overlooked!)


EDIT: For some reason I was thinking a 60% hit rate was the starting value, but that was the doubled value for example 1. Numbers fixed!

[Unoriginal]

Thanks for the response. Was very helpful :)

Seriously, Decorayah, just look at the CR calculation rules in the DMG. It shows the relationship between HPs and AC.

[Decorayah]

Seriously, Decorayah, just look at the CR calculation rules in the DMG. It shows the relationship between HPs and AC.

Yeah I'm aware that quite a lot of these kinds of questions are answered in the DMG. Problem is that it's a 300+ page book and at least in my experience it doesn't always do the best job explaining things. Asking the way I did makes it possible for people that have probably struggled with the same problem to share their knowledge. You can make the argument that I should just read and not ask unless positive it is not explained in the DMG but that would end up taking a lot longer and is plain unnecessary. The idea of forums is for people to exchange knowledge and ideas. I am doing exactly that and would have no problem being on the other side of the exchange (answering someone else's question even if it is explained somewhere in the DMG).

[Unoriginal]

I'm not telling you to read 300+ pages, though. I'm pointing you to a specific section that literally has a "how to calculate defensive CR" paragraph and a table to help do that, which is exactly what you're asking for.

[Sjappo]

As a minor note, thinking of it here as "halving the miss rate" (45% --> 20% or 25%) fixes the problem of math apparently breaking down. (Of course, it doesn't account for rolling a 20 -- a guaranteed hit -- to have greater power, but that's a separate issue that tends to get overlooked!)


EDIT: For some reason I was thinking a 60% hit rate was the starting value, but that was the doubled value for example 1. Numbers fixed!
My calculations are a rough estimate. Criticals are a thing and guaranty that every monster is killable because any idiot with a stick can damage it once every 20 hits, on average. But:

Double the hit rate =/= half the miss rate.

Example: hit rate 50%, miss rate 50%.
Double the hit rate: hit rate 100%, miss rate 0%
Halve the miss rate: hit rate 75%, miss rate 25%
See what happens.

If I need to double the damage output I need to hit twice as often, hence double the hit rate. Halving the miss rate doesn't double the damage.

[Sjappo]

Seriously, Decorayah, just look at the CR calculation rules in the DMG. It shows the relationship between HPs and AC.
This is true, those calculations are very useful. They take in account things like PC's getting more HP, higher AC, healing options, higher damage, more powerful spells etc. But it's not an exact science and some logic is not backed by math.

The table referred to says that the defensive CR is raised by 1 is you raise AC by 2 points. this works out as +0.5 CR for +2 AC. Or +4 AC raises the CR by 1. +4 AC can be huge.
If you start with the suggested AC for the CR it's not a big deal. The table expects a base hit chance of about 70%. +4 AC changes this to 50%. Note that the base AC for a CR 30 monster is only 19.
If you start with a high AC monster like a dragon or the Tarresque things go sideways quite fast. Like I tried to explain with my rough calculations.

[Contrast]

I'm not telling you to read 300+ pages, though. I'm pointing you to a specific section that literally has a "how to calculate defensive CR" paragraph and a table to help do that, which is exactly what you're asking for.

Specifically P273 onwards.

[PhantomSoul]

My calculations are a rough estimate. Criticals are a thing and guaranty that every monster is killable because any idiot with a stick can damage it once every 20 hits, on average. But:

Double the hit rate =/= half the miss rate.

Example: hit rate 50%, miss rate 50%.
Double the hit rate: hit rate 100%, miss rate 0%
Halve the miss rate: hit rate 75%, miss rate 25%
See what happens.

If I need to double the damage output I need to hit twice as often, hence double the hit rate. Halving the miss rate doesn't double the damage.

Entirely agreed, and it definitely affects the math, but I'm finding that it "feels" similar to the players -- they remember crits (constant) and misses more than explicit hits... and the CR system is so... uh... approximate... that this seems to give the right feel anyway as a cheat. (I also don't expect anyone bothers adjusting for crits, barring MAYBE expanded crit ranges and/or extra crit damage. But if you do that in much detail, you're probably not using CR too directly anyway, most likely!)

Also to expose an issue with the cheat: If you flip it around, the apparent fix breaks in the same way as the thing it's "fixing"; if the miss rate is 60%, you can't double it to 120% (instead you would want to halve the hit rate... and potentially take pity on your players!). Flipping between the two systems in practice "feels" better from what I've seen because the perception of accuracy (like the perception of most things) is on a curve, not on a line. (Note this is impressionistic, not absolute universal fact for game feel!) But really, converting everything to a logit curve is DEFINITELY overthinking it... (But I've got lots of work to do, so maybe it would be fun! :P )

EDIT: The math is in principle for the actual hit rates and not for perception of accuracy, but the players will probably not perceive the math directly, so to speak! (In other words, avoid pushing towards the more extreme values/deviations, which is where the difference between the math and the feel will tend to be biggest.)

[Eric Diaz]

So, we are not considering things such as fireball, etc?