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Say you're building a funnel where only 1-2% of traffic...
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See plansIt sharpens the reasoning rather than changing its direction. At a 1-2% positive rate, a funnel is close to strictly dominant, and it’s worth making the math explicit rather than just asserting it.
Roughly: the cost of a funnel is the router cost, plus (the fraction cleared early × the cheap-layer cost), plus (the fraction escalated × the expensive-layer cost). The cost of running one model over everything — distilled or not — is that model’s per-request cost times 100% of volume, regardless of how much difficulty actually varies.
When the escalated fraction is 1-2%, the funnel’s expected cost is dominated almost entirely by the cheap layers, and no amount of distilling the expensive model changes that much, because the expensive model still isn’t the thing running on 98% of traffic. What distillation usefully targets in that architecture is the screening layers, not the escalation layer — making the cheap-but-not-free early stages themselves cheaper or faster lowers the fixed cost paid on 100% of volume, which is a different lever than shrinking the rarely-invoked expensive model.
Worth naming unprompted: optimizing for raw accuracy is meaningless at this base rate, since a model that says “not suspicious” for everything scores 98-99% and catches nothing. The metric that governs the whole architecture is recall on the positive class, with precision treated as a cost constraint rather than the objective.