No, rather, I just didn't type "HP/supply" * "DPS/supply".
x/supply is a pretty decent approximation (ignoring AOE) of what a critter would be if you scaled it down to a 1 supply unit. I could do it /100 supply, or /150 supply, or whatever if you'd prefer. I just figured scaling it down to /1 supply makes the number smaller.
The product of your HP and DPS is a useful quantity when comparing two units. Suppose (ignoring AOE) you built a column of each type of unit that fought each other one on one.
If you double the amount of HP a unit has, it would kill twice as many of the enemy as it lost. If you double the DPS of a unit, it would kill twice as many of the enemy as it lost. I call this "linear power".
Now, if you throw two of an identical unit against one of them, with no micro you end up with two living units with half a unit's HP lost. If you had a two-wide column on one side, and a one-wide column on the other, of identical units, you end up with 4 of the one column units dieing for every 1 of the two column units dieing. So doubling numbers (assuming engagement surface area is sufficient) quadruples your linear power.
Linear power isn't all that useful, because you rarely fight units in a line. However, as you can see above, linear power grows quadratically with unit count -- so if we take the square root of linear power, we get a practical measure of power (quadratic power).
Note that when the unit count is low, this approximation fails. A unit with twice as many HP and damage beats two single strength units by killing one, then the other, and ends up with ~25% HP left. But when you have significantly greater than one unit, this effect fades in significance. (Feel free to double check).
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So what I did was I scaled the unit down to a "1 supply version", then calculated their linear power of the "1 supply version", so I could compare them. I could have taken the square root, but I just wanted to see ordering.
My apologies for not dividing by supply twice.
And yes, like all abstractions, it is imperfect. But it does validate my own experience, that Void Rays, while powerful, simply lose to marine balls. The marine is so strong that in order to beat it, you basically have to exploit area damage dealing, or win on economy, or the like (out range, out economy, out aoe, out maneuver, etc).
There are a handful of T3 units that beat Marines in a strait out supply-for-supply fight. I'm surprised Battlecruisers pulled it off, even before factoring in armor -- but that does explain how annoyed I get when someone actually does tech to BCs in a multiplayer game.
Does that help?
Got my ass handed to me. I'll post the replay later.
