We present a new metric for braiding intensity to characterize multi-thread systems (e.g., braided and anastomosing rivers) called the Entropic Braiding Index, eBI. This metric is a generalization of the widely used Braiding Index (BI) which is simply the average count of intercepted channels per cross-section. The co-existence of diverse channels (widely different widths and discharges) within river cross-sections distorts the information conveyed by BI, since its value does not reflect the diversity and natural variability of the system. Moreover, the fact that BI is extremely sensitive to resolution (BI increases at higher resolution as smaller scale channels can be resolved) challenges its applicability. eBI, addresses these main drawbacks of BI. eBI is rooted in the concept of Shannon Entropy, and its value can be intuitively interpreted as the equivalent number of equally important (in terms of discharge) channels per cross-section. Thus, if the channels observed in a multi-thread system are all carrying the same amount of discharge, eBI has the same value of BI. On the other hand, if a very dominant channel in terms of discharge co-exists with much smaller channels, eBI would take a value slightly larger than 1 (note that the actual value would depend on the number of small channels and their relative size with respect to the dominant channel). We present a comparative study of BI and eBI for different multi-thread rivers obtained from numerical simulations and remote-sensing data and for different discharge stages. We also provide evidence of the robustness of eBI in contrast to BI when a given river system is studied under different resolutions. Finally, we explore the potential of eBI as a metric to characterize different types of multi-thread systems and their stability.