FPGA-based designs dominate many applications for their faster implementation, configurability, and low design cost. These applications need a root of trust to be secured against malicious activities. Physical unclonable functions (PUF) are promising security primitive that can be used to identify silicon dies. To effectively distinguish between different dies, PUF should satisfy a set of quality metrics. FPGA-based PUFs are susceptible to parameters such as systematic variation and placement and routing. In this work, we conduct a statistical analysis to quantify the effect of physical layout on the randomness of multiple copies of the same PUF structure that deployed relatively close on the same FPGA die. As a case study, we have adopted an FPGA-based ring PUF structure known as bistable ring PUF. The results show that only 2 out of the 64 PUFs structure can show good randomness behavior. Even by considering 40%-60% randomness as an acceptable range, only 10 out of 64 PUFs can pass this criterion. Moreover, most of the rest PUFs are extremely biased toward a single state. As a result, 84.4% of PUFs under test end up non-functional PUFs due to the physical design of the FPGA.