Homepage Density Optimizer
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How many items should your homepage have? Too few and you leave traffic on the table; too many and conversion collapses under choice overload. There's a closed-form answer.
The model
Utility is traffic times conversion: U(n) = T(n) · P(n), where n is the number of items on the page.
- Traffic grows with more indexable content but with diminishing returns: T(n) = a·ln(n+1).
- Conversion decays as choices pile up (Hick's Law / choice overload): P(n) = c·e−λn, where λ is how fast conversion falls per added item.
Maximizing U(n) — set dU/dn = 0 — gives (n*+1)·ln(n*+1) = 1/λ, whose closed-form solution uses the Lambert W function:
n* = eW(1/λ) − 1
An alternative model where extra items also dilute traffic (SEO cannibalization at rate μ), T(n)=a·n·e−μn, gives the simpler n* = 1/(λ+μ). The only input either needs is your conversion-decay rate λ — measured from two data points, or estimated (a page's Cognitive Load score is a rough proxy).