Hmm, I think you mean calculate the diversity of the minion average, not take the average of minion diversity. If we calculate the average minion damage vector and compare its diversity to a particular minion we could see if the group was composed of different vectors or not that averaged out. But if we average the diversity of the minions itself, we are averaging scalars: we lose the damage typing. In other words, a group with all minions doing nothing but smashing damage has the same average diversity as a group with eight different minions, each doing just one type of damage, because each of those minions has the same diversity: all one type.
That's intentional. The diversity of the average minion shows as the highest in that case, but each minion shows as the lowest diversity. But if each minion tended towards a mix of damage types, then the average of the scalars will be much higher. It is a way to check if the diversity we see within the minions individually matches the overall diversity of the group.
I have a separate question. You seem to be taking it as an axiom that if you have two minions, one that does all smashing and one that does all lethal, that group is in some ways weaker than one that has all minions doing an equal amount of smash/lethal. I have a hunch that is true myself in at least some cases. But do you have a way to demonstrate that? I'm not 100% convinced that those two situations are distinguishable in a way I would *want* to distinguish.
Yes, I'm taking it somewhat axiomatically. If we assume for the moment that diversity of damage types has intrinsic value, then it would stand to reason that the integrity of that damage diversity also has value.
A quick example. Suppose you have 50% resistance to fire, but no resistance to psionic. You face two minions that each do 10 DPS, 5 each of fire and psionic. You are thus facing 15 effective DPS. Defeat either one of the minions, and you now face 7.5 DPS. But suppose you next face two minions, one of which does 10 DPS of fire, the other of which does 10 DPS of psionic. The diversity of the spawn's damage registers as the same in this case, and the initial effective damage is still 15 DPS. But you have the opportunity to focus fire down the psionic enemy, and once you do so the incoming damage drops to 5 DPS. By segregating the damage types into individual minions, the result is that the threat of the enemy spawn, while initially the same, is concentrated in a way that it can be reduced with more ease.
The counter-argument, I suppose, is that the second situation introduces a new possibility: a spawn entirely composed of psionic damage dealers. To some extent we're concerned with the worst case scenario, since a player is generally going to choose a difficulty that they expect to be able to manage routinely, and you go through enough spawns that this is not unlikely scenario. At least, I think it's not. How does CoH generate the composition of a spawn?
At least though if you settled on the belief that damage diversity existing within the group is what matters, and individual diversity is a wash, then one aspect of the problem is removed.
Specific to CoH, I don't think it works. Or rather I don't think it does what you were intending it to do. I understand you reserve the right to tweak numbers, but consider the case of a critter that does 25% smashing, 25% lethal, and about 8.3% of each of the other types. This is a critter that is basically engineered to do 50% s/l damage, and 50% everything else spread out among all the other types. It has an extremely low score: 0.408. This critter's score is only marginally higher than the "perfect diversity" critter that deals 12.5% of everything. So when I go from 25% s/l to 50% s/l, the diversity score barely budges. That doesn't seem intuitively "right." And here's something interesting: this system judges a critter that does 50% s/l and equal amounts of the rest to have the same diversity score as something that does *no* s/l damage at all, and equal amounts of the rest. Both have very low (numerical) scores, implying very high diversity. But I don't think those are actually equivalent in what I would colloquially consider to be "diverse damage."
I hadn't noticed that last particular oddity, and I agree that's a significant issue. One possibility could be to explore the p-norm more generally to effectively attach greater weight to damage types of larger proportion.
I had a niggling thought in the back of my mind that the simplest thing to do might be simply to count up how many damage types go over a particular threshold, but I need to think about that more.
Then there's the question of coupling. Consider that a critter that does 50% smashing and 50% lethal has the same score as a critter that does 50% fire and 50% psi. Smash/lethal resistances and defenses are closely coupled: if you have a lot of one you likely have a lot of the other. Fire and psi are not closely coupled: it is not easy to build for both. A fire/psi critter is, in CoH, a much more dangerous critter than a s/l critter even before you account for the fact that s/l resistances are somewhat more common. This suggests to me there would be some need for either affinity weighting or type collapsing to make this work in CoH.
And then there's the last question about normalization. Pretty much all the standard critters in CoH have very bad diversity scores. And yet we consider them to be "normal" in difficulty. We don't assign reward penalties to them even in the architect. So if an all s/l critter has no reward penalty when the devs create it, should we be applying a severe penalty to them if they are player-created? Shouldn't the system be designed to roughly approximate what the normal content does?
In the general case, would a system like this work? I'm skeptical. I think if you designed the game around the system it would not have some of the problems that it would have in CoH, but something about the basic function seems insufficiently "discriminating." When I reduce the problem to the two-dimensional case, the curve seems insufficiently frontloaded to be decisive. I'll have to think about it more to judge it less arbitrarily.
The smashing/lethal issue is one that I've been pondering. One possibility is just to lump them together as one type; the game nearly does this to begin with.
I had to clarify for myself why this issue is an issue in the first place. S/L damage is so ubiquitous in the game that you just take for granted that it will be present. How many enemy groups don't do significant S/L damage? But other types are relatively rare. They are treated as
exotic, and it's extremely rare to see high concentrations of those types, and when you do the developers had the option of determining appropriate rewards. As such, there is little apparent issue in providing very high resistances to exotic damage types in thematic mitigation sets. Fiery Aura Brutes can have 90% resistance to fire, Electric Armor Brutes can have 90% resistance to energy, and so on. But AE allows one to invert this basic premise, to create content that doesn't approximate normal content. Exotic damage types can be brought front and centre, and as we so often comment on, the way resistance works in CoH means that mitigation sets can now become several times more effective than what's expected. The intersection of treating the exotic as still exotic, while actually making the exotic commonplace, is where the problem originates.
Perhaps, then, an option to explore is to only measure diversity of the "exotic" types, and what proportion of the overall damage falls into these types.
