In this work we investigate under what circumstances a TV campaign should be complemented with online advertising to increase combined reach. First, we use probabilistic models to derive necessary and sufficient conditions. We then test these optimality conditions on empirical findings of a large collection of TV campaigns to answer two important questions: i) which characteristics of a TV campaign make it favorable to shift part of its budget to online advertising?; and ii) if it should shift, how much cost savings and additional reach can advertisers expect? First, we use classification methods such as linear discriminant analysis, logistic regression, and decision trees to decide whether a TV campaign should add online advertising; secondly, we train linear and support vector regression models to predict optimal budget allocation, cost savings, or additional reach. To train these models we use optimization results on roughly 26,000 campaigns. We do not only achieve excellent out-of-sample predictive power, but also obtain simple, interpretable, and actionable rules that improve the understanding of media mix advertising.