A growing body of research documents that the size and growth of an industry in a place depends on how much related activity is found there. This fact is commonly referred to as the "principle of relatedness". However, there is no consensus on why we observe the principle of relatedness, how best to determine which industries are related or how this empirical regularity can help inform local industrial policy. We perform a structured search over tens of thousands of specifications to identify robust -- in terms of out-of-sample predictions -- ways to determine how well industries fit the local economies of US cities. To do so, we use data that allow us to derive relatedness from observing which industries co-occur in the portfolios of establishments, firms, cities and countries. Different portfolios yield different relatedness matrices, each of which help predict the size and growth of local industries. However, our specification search not only identifies ways to improve the performance of such predictions, but also reveals new facts about the principle of relatedness and important trade-offs between predictive performance and interpretability of relatedness patterns. We use these insights to deepen our theoretical understanding of what underlies path-dependent development in cities and expand existing policy frameworks that rely on inter-industry relatedness analysis.