• http://blog.marketo.com/ Jon Miller

    The square root rule is very insightful and useful. Our research at Marketo shows that the actual relationship between advertising spending and results varies from x^0.4 to x^0.6, where 0.5 would equal a square root.

    Once you have that data for each advertising medium (or even each keyword), it becomes very useful for allocating spending optimally across options (e.g. portfolio-based optimization) — subject, of course, to all the complexity you point out (i.e. lower and upper limits, discontinuities, etc.).