How would one determine a CR for a variable difficulty creature?

Question

Creating a home-brew creature for a 5th edition D&D campaign that will continue to be a threat to players throughout the campaign. The basic idea of the creature is that it is a creature of darkness that feeds and grows off life. The creature starts out relatively weak but each of its attacks increase its HP by a portion of the damage done. With no maximum hp. The amount of damage done is also proportional to the creature's current HP. As a result the creature starts out as weak and easily dispatched, but if ignored can become a TPK waiting to happen.

Most of the rules found under the create a monster chapter of the DMG do not account for a creature that becomes more powerful as a fight progresses and as a result using the standard array for determining CR and XP value can be quickly invalidated.

What method could be used to determine an Effective CR and XP value for such a creature?

Answer 1

A CR is a rough prediction of how difficult a creature will be for the players to defeat. It's impossible to define a valid CR for the creature you have in mind, because how difficult it is to defeat is primarily based on the players' choices. You can't predict how your players will make those choices, which means you can't predict how difficult it will be for them to defeat this creature.

Let's assume the creature starts life with stats around CR 1/4 in power. Taking into account a fairly standard party of 4 level 1 characters, let's think about some scenarios.

If your players kill it immediately, they probably won't even notice that it had any special abilities. We'll call this case 1.

On the other hand, let's assume that it was mixed in with a bunch of other weak enemies, and your players happened to leave it till last. And let's be generous and assume that in that time, its damage and HP rose to that of a CR 3. We'll call this case 2.

In case 1, your players lucked out, and as a result, got an easy fight. In case 2, your players were unlucky, and probably got wiped out as a result, but let's be generous and say they scraped a win. One of these fights was basically effortless, and one was extremely difficult.

Now, let's assign the creature a CR of either 1/4 or 3, and examine the results.

\begin{array}{c} \text{Assigned CR} & \text{Case 1} & \text{Case 2} \\ \hline 1/4 & \text{Easy, very little reward} & \text{Incredibly difficult, hardly any reward} \\ 3 & \text{Easy, hugely inflated reward} & \text{Incredibly difficult, well-deserved reward} \\ \end{array}

3 of these scenarios just kinda suck. In Case 1 | CR 1/4, your creature's fancy abilities didn't even matter, and the extra work you did was pointless. In Case 1 | CR 3, that's still true, but now the players get a bunch of XP for no reason. In Case 2 | CR 1/4, at least your creature got to see some play, right? But your players are going to be pretty annoyed when they finish the hardest fight they've ever seen and you say "OK, 50 XP each."

Finally, in Case 2 | CR 3, the players face a crazily tough fight, and eventually triumph. And they get a great XP reward, and everyone's happy. They're happy because they beat a tough fight (very satisfying in itself) and got a bunch of XP (Yay!). You're happy because your fancy creature got properly used.

So, if assigning it a CR of 3 is the only method that leads to a good result, there's the answer, right? No, not really. It's still a matter of luck whether the players get an easy fight or a tough one. Ok, so how about if we make the special guy visually distinct, or call it out when he grows in power? Well, then the players will just attack that guy and get an easy fight. Hmmm...what if we give them a Perception check to notice it? Great, now we're back to luck.

So if you really want to do this, I wouldn't recommend giving it a static CR. Give your players XP based on the fight that actually happens, not the one that could hypothetically have happened if they did/didn't prioritise the special creature over the rest of them.

Now, all of that was just about XP reward. What about balancing encounters? Well, if you were paying attention to everything else I've said, you might have noticed a theme. It's impossible to predict how difficult this creature will be. That means that it's impossible to create a balanced encounter around it.

Of course, the "balanced encounter" is basically a myth to begin with. You can't predict what the dice will do, and you can't predict what the players will do. If you want to throw this creature at them, go for it! Just make sure you're prepared for the possibility that it will be inconsequential, a TPK, or anything in between. And I feel I have to point out, that means making sure your players are also prepared for the possibility of a TPK.

Answer 2

Well, it depends on the settings that you make.

If the creature is damaging the party and the party is not damaging the creature (Sufficiently) then there comes a tipping point where it will become impossible to kill as its hp expand faster than the party can bring them down - an infinite CR monster

However, it's possible to approximate if you start with the CR you want and use them to derive the numbers.

Let's assume that its base hp is X (which is a number) and its initial DPR is Y (which is a random variable, not a number). If its hp increase by AY and its DPR increases by BY (hopefully A & B are numbers, not random variables). It is relatively easy to write equations for its hp and DPR after N rounds: X + AY + ABY + AB^2Y + ... + AB^(N-1)Y = X + AY(1-B^N)/(1-B) and Y(1 + NB). You can solve these for any reasonable value of N (3 to 5 rounds is the typical durations of combat in D&D 5e). Relatively easy is in reference to those who have a basic college level maths education covering difference equations - so, more objectively, this is a bloody hard problem.