Given a Shi arrangement $\mathcal{A}_Φ$, it is well-known that the total number of regions is counted by the parking number of type $Φ$ and the total number of regions in the dominant cone is given by the Catalan number of type $Φ$. In the case of the latter, Shi gave a bijection between antichains in the root poset of $Φ$ and the regions in the dominant cone. This result was later extended by Armstrong, Reiner and Rhoades where they gave a bijection between the number of regions contained in an arbitrary Weyl cone $C_w$ in $\mathcal{A}_Φ$ and certain subposets of the root poset. In this article we expand on these results by giving a determinental formula for the precise number of regions in $C_w$ using paths in certain digraphs related to Shi diagrams.