You can price it with four numbers: monthly visitors, the share who search, the conversion rate of search sessions, and average order value. Multiply them for current search revenue, then model the same figures with search usage and search conversion moved to healthy levels. The gap is the cost of bad search.
Search revenue is visitors × search usage × search conversion rate × average order value. Only two of those four inputs are affected by search quality — usage and conversion — which keeps the model honest and the claim narrow.
A store with 50,000 monthly visitors, 3% search usage, 4% search-session conversion and a ₹2,000 order value earns ₹1,20,000 a month from search. Move usage to 20% — a visibility and suggestion-quality change, not a relevance change — and the same store earns ₹8,00,000. The delta is the cost of a search bar nobody uses.
Run the model on your own inputs rather than these; the point is the structure, not the numbers.
This model deliberately excludes support tickets caused by unanswered questions, retargeting spend on shoppers who bounced from a dead end, and the paid traffic landing on a site that cannot answer it. Those are real and harder to attribute, so they stay out of the headline figure.