Locust vs aa analyse

when Locusts brawl vs AA (pure damage vs hp)

define brawl value (dps*hp) (BV) of a cluster of units, whose amont determines win lose directly

define brawl factor square (BF_sq) is that a cluster of units cost C has BV = BF_sq*Cost*Cost

BF_sq = dps/Cost * hp/Cost

define (standard) brawl factor is BF = sqrt(BF_sq)

so BV = (BF*Cost)^2

A unit with Cost/BF_A vs B unit with cost Cost/BF_B draw when brawl, we say brawl ratio of unit A,B is BF_A:BF_B

brawl factor: Locust 1.0082, Gremlin 1.5996, Toad 1.4257, Tarantula 1.1638, Ettin 1.1224, Reaver 2.2406, Razor 2.3877, Stardust 3.7344.

glaive 2.3907, trident 0.8606, raptor 1.1055.

assume brawl ratio Locust vs AA is 1:1.4

Assume locust has overwelming speed, so that:

AA must spread evenly across the front line, which is normally map width.

Locusts attacks and pass thorugh AA range immediately so we dont calculate damage that AA can done before locust attack.

AA range can affect how much AA can attack Locusts.

When rich ( players expanded enough and have frontline):

1 unit is 512 elmo(iirc) ( width x height of map's description).

assume typecal AA range 900

for width 14 map, when locusts attack, only (900*2) / (14*512) ~= 0.25 of AA unit can actually attack locusts.

So overall locust advantage ratio is Locust vs AA 2.85:1. You must cost 2.85x locust value on AA to defent them properly.

This calculation varies depends on map width, the wider the map the more advantage air have.

This calculation didnt take riots in count, which only affects when locust want to attack a regular army.

And the calculation may not be correct.

When expanding:

assume players expands as a circle, they need AA forces to cover then edge of circle.

define expand cost: cost they need to spend on army to protect area / area

more idea is required

The overwhelming speed assumption is a poor approximation, particularly the corollary that Locusts don't take significant damage closing with AA units. AA can shoot down Ravens that don't need to stick around to apply their damage, and in modest quantities can do so while the Ravens are inbound. But as a more fundamental problem, if Locusts really were that fast, the perimeter defense scheme you describe would be pointless, because the Locusts would only take trivial amounts of damage for flying past the perimeter into the undefended inner economy.

Your AA suffers from an assumption in the other direction that AA only moves while Locust raids are not underway, yet has efficiency closer to mobile AA than static AA. Use the numbers for Razors in your perimeter defense instead of static Toads and the Locusts' calculated advantage almost disappears. Or maneuver the AA units defensively while you're under attack by Locusts, moving them into range of your anti-ground defenses and thus violating the assumption that riots don't matter.
Finally, you seem to be ignoring AoEv, which where present is a practical limit on Locusts' ability to scale up.

Between these various assumptions, you've crippled every single AA option. An Artemis must wait for the Locusts to start hitting it, then pick them off one at a time. Anglers are stuck plinking away at a rate of one missile every three seconds, with a pair of them taking six seconds' worth of incoming Locust damage before scoring a single kill. Crashers cannot group up under fire, nor can they run for the apathetic support of any nearby Rippers because riots do not care unless they themselves are under attack. And Razors need to slow down their DPS to match the mobile options.