Reach curves arise in advertising and media analysis as they relate the number of content impressions to the number of people who have seen it. This is especially important for measuring the effectiveness of an ad on TV or websites. For a mathematical and data-driven analysis, it would be very useful to know the entire reach curve; advertisers, however, often only know its last data point, i.e., the total number of impressions and the total reach. In this work I present a new method to estimate the entire curve using only this last data point.
Furthermore, analytic derivations reveal a surprisingly simple, yet insightful relationship between marginal cost per reach, average cost per impression, and frequency. Thus, advertisers can estimate the cost of an additional reach point by just knowing their total number of impressions, reach, and cost.
A comparison of the proposed one-data point method to two competing regression models on TV reach curve data, shows that the proposed methodology performs only slightly poorer than regression fits to a collection of several points along the curve.