Multi-FPGA boards are being used for logic emulation, rapid prototyping, custom computing and low volume subsystem implementation. A key feature which characterizes these boards is their routing architecture(RA). Inter-FPGA connections in an RA can be of two types, namely fixed connections through direct wires and programmable connections through intermediate Field-Programmable Interconnect Devices. This paper presents an analytical approach for evaluating routing performance of an RA employing both types of connections . Our approach consists of two steps: 1) Generation of random interconnection requirement matrix for modeling real circuits with an orientation towards the available interconnection architecture. 2) Checking the routability of the generated matrix on the given RA.The evaluation experiments for many RAs demonstrate that our methodology matches in results with purely experiment based approaches. However, it is more versatile in that it can evaluate new RAs. Also it provides more observability and controllability of architectural, circuit and performance parameters.