The attack-rate hump @ Tracks

The attack-rate hump

The red team's win probability against how often it attacks, decomposed into its two terms. Attack rarely and a decisive attack attempt may never occur (Term B small); attack often and the pool dilutes with worse, more-visible opportunities (Term A falls) — so the optimum is interior.

Opportunity cutoff — attack only when quality > thisattack 11.3% of problems

The two terms, and their product, vs attack rate

Per attack attempt, averaged over the pool above the cutoff:

Caught by monitor c

45.4%

Successfully deployed s

21.1%

Attack rate r

11.3%

Problems N

5,000

s/(s+c)31.7%×1-(1-r(s+c))^N>99.9%=P(\text{red wins})31.7%