Today, I’m going to follow on from my previous post on level scaling and take a look at how PCs would fare against enemies of higher and lower tiers. This post may be best viewed on a larger screen, because there are some large tables in it.
Accuracy
As a baseline, let’s take a look at the accuracy of a PC facing an enemy of their tier, and vice versa.
In the previous post, I discussed how PCs will advance if they max out every aspect of their character, which is to say, they’ll gain +4 to attacks and defenses over 20 levels. While in practice this won’t necessarily be a smooth progression of +1 every 5 levels/1 tier, we’ll assume that for purposes of this discussion.
The math for enemy design that I have settled on provides enemies with that same +1 per tier as they advance, but they start with a slight handicap, equivalent to about 5 levels of advancement. This means a PC will hit a level-appropriate enemy on a 9 instead of a 10 (72% of the time), and the enemy will hit the PC on an 11 (55%).
If a PC faces an enemy 1 tier higher, then both they and the enemy will hit on a 10 (64%). So the PC will be 64/72 = 89% as effective offensively as when they faced an enemy at their tier, and the enemy will be 64/55 = 116% as effective. Together, this translates into the PC being 89/116 = 75% as effective when fighting an enemy 1 tier higher, just from accuracy effects.
If they are fighting an enemy 1 tier lower, then the PC is 79/72 = 110% as effective, and the enemy 45/55 = 82% as effective. Overall, the accuracy effects will make the PC 134% as effective from accuracy effects. (Though more of this will come from the enemy being less accurate than the PC being more so.)
If you’re noticing that 134% is roughly the reciprocal of 75%, very good! This is designed into the system, and means that the overall difference in accuracy going one tier down should feel about as big as the difference going one tier up.
Damage
Calculating the difference in difficulty that comes from damage is going to be more complicated than it was for accuracy. This is because with every tier, typical damage increases by 2, armor resistance by 1., and hit points by 4.
Let’s start with one concrete example: a Tier 0 PC vs. a Tier 0 enemy. The PC will deal typical damage of 8.5, and the enemy will typically have 0 AR and 28 HP. So the PC will deal 30% of the enemy’s HP per hit.
The enemy will deal 6.5 typical damage, against 1 AR and 32 HP. This will be 17% of the PC’s HP.
Applying the same math to different tier pairings, we can fill out the following tables for a PC facing an on-tier enemy…
| Tier | PC Damage | Enemy AR | Enemy HP | % Damage | Enemy Damage | PC AR | PC HP | % Damage | % Damage Ratio |
| 0 | 8.5 | 0 | 28 | 30% | 6.5 | 1 | 32 | 17% | 1.77 |
| 1 | 10.5 | 1 | 32 | 30% | 8.5 | 2 | 36 | 18% | 1.64 |
| 2 | 12.5 | 2 | 36 | 29% | 10.5 | 3 | 40 | 19% | 1.56 |
| 3 | 14.5 | 3 | 40 | 29% | 12.5 | 4 | 44 | 19% | 1.49 |
| 4 | 16.5 | 4 | 44 | 28% | 14.5 | 5 | 48 | 20% | 1.44 |
…an enemy one tier higher…
| Tier | PC Damage | Enemy AR | Enemy HP | % Damage | Enemy Damage | PC AR | PC HP | % Damage | % Damage Ratio |
| 0 | 8.5 | 1 | 32 | 23% | 8.5 | 1 | 32 | 23% | 1.00 |
| 1 | 10.5 | 2 | 36 | 24% | 10.5 | 2 | 36 | 24% | 1.00 |
| 2 | 12.5 | 3 | 40 | 24% | 12.5 | 3 | 40 | 24% | 1.00 |
| 3 | 14.5 | 4 | 44 | 24% | 14.5 | 4 | 44 | 24% | 1.00 |
| 4 | 16.5 | 5 | 48 | 24% | 16.5 | 5 | 48 | 24% | 1.00 |
…and an enemy one tier lower:
| Tier | PC Damage | Enemy AR | Enemy HP | % Damage | Enemy Damage | PC AR | PC HP | % Damage | % Damage Ratio |
| 0 | |||||||||
| 1 | 10.5 | 0 | 28 | 38% | 6.5 | 2 | 36 | 13% | 3.00 |
| 2 | 12.5 | 1 | 32 | 36% | 8.5 | 3 | 40 | 14% | 2.61 |
| 3 | 14.5 | 2 | 36 | 35% | 10.5 | 4 | 44 | 15% | 2.35 |
| 4 | 16.5 | 3 | 40 | 34% | 12.5 | 5 | 48 | 16% | 2.16 |
Overall Effectiveness
Coupling these values with accuracy, we can compute A PC’s relative effectiveness against an enemy a tier above or below them. We’ll define this overall effectiveness as the accuracy effectiveness computed above (0.75 vs. a tier above, 1.34 vs. a tier below), times the % Damage Ratio for an enemy a tier above or below, divided by the % Damage Ratio for an on-tier enemy.
| Tier | % Damage Ratio vs. Equal Tier | Accuracy Factor vs. Tier Above | % Damage Ratio vs. +1 Tier | Effectiveness vs. Tier Above | Accuracy Factor vs. Tier Below | % Damage Ratio vs. Tier Below | Effectiveness vs. Tier Below |
| 0 | 1.77 | 0.75 | 1.00 | 0.42 | |||
| 1 | 1.64 | 0.75 | 1.00 | 0.46 | 1.34 | 3.00 | 2.44 |
| 2 | 1.56 | 0.75 | 1.00 | 0.48 | 1.34 | 2.61 | 2.25 |
| 3 | 1.49 | 0.75 | 1.00 | 0.50 | 1.34 | 2.35 | 2.12 |
| 4 | 1.44 | 0.75 | 1.00 | 0.52 | 1.34 | 2.16 | 2.02 |
So what does this tell us? Well, just numerically, a PC will be around half as effective, or a little less at low levels, against enemies a tier higher than they are, and around twice as effective, or a little more at low levels, against enemies a tier lower than they are.
EV Scaling
Now, we want to take this result (that each 1-tier difference makes an enemy about twice as difficult) and translate it into a rating that captures how difficult the enemy is. And you’d think that the way to do that is to have the rating double with each tier added to an enemy. But, there’s a problem with that…
When building an encounter, there are two easy ways to adjust its difficulty: you can adjust the difficulty of the individual enemies, holding their number constant…or you can adjust the number of enemies, holding the difficulty of the enemies constant. The problem is that these two factors work on different scales.
If you take every enemy in an encounter and bump them all up by one tier (adjusting their stats, or replacing them with similar enemies of a higher tier), that doubles the difficulty of the encounter, as we’ve just seen.
But if you instead double the number of enemies in the encounter, this actually quadruples the difficulty of the encounter, because it will take twice as much work (and twice as many rounds) for the PCs to defeat them, and in that time, the enemies will collectively be dealing twice as much damage per round since there are twice as many of them.
What About AoE Damage?
The assumption that twice as many enemies will take twice as long to defeat is based on the PCs using single-target attacks. In practice, many PCs will have access to area attacks or other ways to attack more than one enemy per turn: these tend to do less damage than equivalent single-target attacks, but more damage total if they can catch enough enemies with them.
Having more enemies in an encounter means that they will likely be more densely packed, making area damage more effective. This will slightly reduce how long it takes to defeat a hypothetical twice-as-large encounter.
On the other hand, having twice the damage output means that the PCs will likely need to fight more cautiously, passing up opportunities to deal damage in favor of healing themselves or staying in defensible positions. This will slightly increase how long it takes to defeat a hypothetical twice-as-large encounter.
And, with twice as many enemies, they will find it more easy to flank the PCs. This will slightly increase the damage they deal before being defeated.
In playtesting, these three factors have appeared to roughly cancel each other out.
What About Focus Fire?
In reality, the enemies in an encounter won’t all be defeated at the same time. If the PCs focus their attacks on one enemy at a time, this will reduce the overall damage they take.
Consider an encounter with, let’s say, four goblin warriors that each take the PCs r rounds to defeat, and deal d damage per round until defeated. They collectively deal 4d damage for the first r rounds, 3d damage for the next r rounds, etc., for a total of 10dr damage.
An encounter with eight goblin warriors will instead have them dealing 8d damage for the first r rounds, 7d damage, for the next r rounds, etc., for a total of 36dr damage. That’s almost four times as much.
So the idea that doubling the number of enemies quadruples the difficulty of the encounter holds even with the PCs focusing fire.
The problem here is that doubling the number of enemies in the encounter will only double the total EV of the enemies, while quadrupling the encounter’s difficulty. We want to make it so that raising all of the enemies by two tiers, which will also quadruple the encounter’s difficulty, also doubles the encounter’s total EV. This means we want the EV scale to scale something like this:
| Level / Tier | EV (Option 1) | EV (Option 2) |
|---|---|---|
| 0 / 0 | 100 | 100 |
| 1 | 110 | 108 |
| 2 | 120 | 116 |
| 3 | 130 | 124 |
| 4 | 140 | 132 |
| 5 / 1 | 150 | 140 |
| 6 | 160 | 152 |
| 7 | 170 | 164 |
| 8 | 180 | 176 |
| 9 | 190 | 188 |
| 10 / 2 | 200 | 200 |
| 11 | 220 | 216 |
| 12 | 240 | 232 |
| 13 | 260 | 248 |
| 14 | 280 | 264 |
| 15 / 3 | 300 | 280 |
| 16 | 320 | 304 |
| 17 | 340 | 328 |
| 18 | 360 | 352 |
| 19 | 380 | 376 |
| 20 / 4 | 400 | 400 |
The first option uses rounder numbers and is likely easier for a GM to remember and use for that reason, but the second option will give slightly smoother scaling. The differences are relatively small, and in any case this is largely meant as a rough guide to encounter difficulty, so I’m going to go with the first option.
Fewer Enemies of Higher Tier
In the details about focus fire above, I did some math to show that doubling the number of enemies still roughly quadruples the encounter’s difficulty, even with the PCs using focused fire. Let’s apply the same approach to consider what happens when substituting higher-tier enemies for lower-tier ones does:
Consider an encounter with four goblin knights that are individually twice as difficult as the goblin warriors. For simplicity, assume that “twice as difficult” means that they take 1.4r rounds to defeat and deal 1.4d damage per round, so that the damage an individual goblin knight could deal before being defeated is 1.96dr, or roughly twice as much. This encounter will have the goblins deal 5.6d damage for the first 1.4r rounds, 4.2d damage for the next 1.4r rounds, etc., for a total of 19.6dr damage before the last one is defeated. Which is, yes, about twice as much in total as the four goblin warriors.
But (and this is the complicated bit), two goblin knights, which it’s tempting to assume would be equivalent to the four goblin warriors, would deal only 5.88dr damage before being defeated. This is because halving the number of enemies cuts the encounter difficulty to roughly 1/4, and making the individual enemies twice as difficult only brings it back up to roughly 1/2. You would actually need between two and three of the goblin knights to have an encounter of roughly the same difficulty as the goblin (three would deal 11.76dr damage), and this is what the EV scales above accomplish.
If we say, for the sake of argument, that goblin warriors are Tier 0, then their combined EV is 400; the goblin knights, being twice as difficult, must be Tier 1, and the combined EV of three of them is 450 (or 420, using the more precise scale), which is pretty close to an appropriate EV for an encounter that would deal 11.76dr damage when compared to four goblin warriors dealing 10dr.
In Practice
All of the above is theoretical and purely numeric. I did use this math to help me calibrate PC and enemy level scaling, but it’s not enough to rely on numbers alone: the pure math misses a few factors that are difficult to model simply.
One factor is that at higher levels, both PCs and their enemies will also have a wider selection of actions and special traits. For enemies at least, some of these will be, for lack of a better word, “nastier” than at low levels. Some high-level enemies can do things like teleport out of a battle and bring back reinforcements, which is not a factor at low levels. PCs have their own nasty tricks at higher levels, due to how certain powers and feats can be combined in a way that is greater than the sum of the parts.
So, I’ve run some playtests, pitting groups of PCs against variations of the same encounter that used enemies at their tier, a tier above, and a tier below, with their numbers adjusted accordingly. The consensus? There are definitely differences in how these encounters played out and felt…but they’re small, and the encounters felt similarly difficult, which I think vindicates my scaling here.
Aetrimonde 
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