Comparing Armies

Dungeon Overlord's creature combat can be a complex and costly endeavor, but its rewards can greatly outweigh the risks if you choose your battle correctly. The first step is to somehow scout your opponent's army. This is usually accomplished with something like a Level 1 Thief. You won't be able to determine the layout of their dungeon, but you will know the content of their army. Of course, their army will usually have different numbers of creatures at different levels, so how does it compare to your army?

The first step is to attempt to compare apples to apples. In this case, I'm going to look at the simplified battle of the same type of creatures at different levels; so say 4 level 1 Dark Elves vs a level 16 Dark Elf. There's a particular reason I chose this example. As you level your creatures, its Hit Points and Damage each increase by +20% of the base value. This means at level 11, your creature has a base +300% bonus to damage and Hit Points, or four times the damage and hit points. That looks a lot like 4 level 1 creatures.

There is a slight difference, however. As combat progresses, those level 1 creatures will die and overall do less damage, while the level 11 creature continues to do its full damage.

To avoid getting into other aspects like Attack vs Defense and resistances, let's imagine to hypothetical creatures called Groo (plural and singular). We'll say a level 1 Groo hits, on average (once we account for misses from Attack vs Defense) for 10 points of damage per round and has 200 Hit Points. Thus, a level 16 Groo will hit for 40 points on average and have 800 Hit Points. Clearly, the level 16 Groo will kill the four level 1 Groo after it deals 800 damage, which will take 20 rounds. The level 1 Groo would kill the level 16 Groo after 800 damage as well, but after 20 rounds they will only have dealt 500 damage.

The reason why is because after 5 rounds, one of the level 1 Groo dies, and now it's 3 level 1 Groo vs 1 level 16 Groo. Another 5 rounds later and it's 2 vs 1, and then 1 vs 1. Every 5 rounds the number of opponents, and this the total damage, decreases. The total damage dealt will be 5*(4+3+2+1)*10=500 damage. If you had 5 level 1 Groo instead, then they would deal 5*(5+4+3+2+1)*10=750 damage over 25 rounds, while the level 16 Groo deals 1000 damage (killing all the Groo). It thus takes 6 level 1 Groo to kill a level 16 Groo. These will do 60 damage for 5 rounds, then 50 damage for 5 rounds, then 40 damage for 5 rounds, then 30 damage for 2 rounds for a total of 810 damage. and leaving 3 Groo alive (though one of them is down to 120 Hit Points).

Can we generalize this? How many level 1 Groo does it take to kill a level Z Groo? Or, more generally, for any creature?

WARNING MATH AHEAD

Let N = Number of level 1 creatures (4 or 6 in the previous examples). Let R = number of Rounds before a level 1 creature dies (5 in the previous example). Let d = damage a level 1 creature deals on average per round (10 in previous example). Let b = base hit points of a level 1 creature (200 in the example above). Let X = the multiplier the higher level creature gets over the lower level creature (4 in the example above... note that X = (level+4)/5). Let D1 = Damage that the level 1 creatures do in the entire combat (500-1050 in the examples above... note it exceeds opponent HP). Let D2 = Damage that the higher level creature does in the entire combat (800-1200 in the examples above). Let HP1 = Hit Points of the level 1 creatures, total (800-1200 in the examples above). Let HP2 = Hit Points of the higher level creature (800 in the example above).

Okay, so that's probably confusing at first, but what we want to do is look at the total damage that the level 1 creatures do, set it equal to the total hit points of the higher level creature, then take the total damage the higher level creature does and set it equal to the total hit points of the level 1 creatures. Then, any N larger that that situation will mean the level 1 creatures deal more damage.

Also, note that (N+(N-1)+(N-2)+...+3+2+1)=0.5*N*(N+1). This is used for how you have N creatures attacking, then one dies so you have N-1 attacking, then one dies, etc. to give the total number of attacks.

Total damage dealt by level 1 creatures = (Rounds each creature is alive for)x(Total number of attacks)x(damage per round) D1=R*0.5*N*(N+1)*d

Total hit points of the higher level creature = (base hit points)x(multiplier) HP2=b*X

Total damage dealt by higher level creature = (Rounds each creature is alive for)x(Number of level 1 creatures)x(damage per round) and (damage per round)=(damage per round for level 1 creature)x(multiplier) D2=R*N*d*X

Total hit points of the level 1 creatures = (Number of level 1 creatures)x(base hit points of a level 1 creature) HP1=N*b

Now, by setting the damage dealt equal to the hit points (D1=HP2 and D2=HP1), and doing a little algebra (solve for R and substitute) you get the final result: The number, N, of level 1 creatures needed to kill a single creature of multiplier X, where X=(level+4)/5, satisfies: N*(N+1)>2*X^2

Now, there are two great things about this equation. Because of the multiplier X, you can actually use this to compare non-level 1 creatures. So if they have a bunch of level 10 Orcs against your level 25 Orc, you just calculate each ones multiplier relative to level 1, and take the ratio of the two to get their relative multiplier. In the above example it would be 29/14, or roughly 2:1, which means it would take 3 level 10 Orcs to kill a level 25 Orc.

Second, if there are multiple units on each side, break it down to a ratio of several low level units to the 1 high level unit. For example, 9 level 1s versus 3 level 10s is just three separate battles of 3 to 1. While this is not true to the math, it is more true to the actual play of the game (you don't get all 9 attacking one creature).

This brings us to one of the overlooked aspects: the Tank ability of the creature... which is how many creatures can attack it at once. But in general your army will be more complicated than this analysis allows. In addition to number and level, there are also different compositions (which would affect resistances and range vs melee) as well as traps as well as the biggest factor: the randomness inherent in the a.i. This analysis is meant as a general guideline, but should help you know when battles are expected to be blowouts, and when they might be close.