Wireless sensor networks WSNs usually consist of many tiny sensor nodes and a sink. Problems and characteristics like resources' severe constraints, low reliability and fault tolerance, low throughput, and insecure operational environments, significantly degrade their overall performance. One significant solution against these problems is multipath routing. However, the existing multipath routing protocols have weaknesses like high overhead and algorithmic-computational complexity, security vulnerabilities, low scalability, and permanent usage of optimal paths and resources' severe exhaustion. As a result, this paper proposes a statistical distributed multipath routing protocol for homogeneous WSNs, called SDMR. It is different from other existing multipath routing protocols in terms of statistical-mathematical nature, criteria and procedure of routing score calculation, routes' selection process and traffic load distribution technique. The performance of SDMR is compared with the performance of secure and energy-efficient multipath routing protocol called SEEM; results of algorithmic-complexity and statistical-simulation analyses show that the SDMR is improved in terms of energy consumption, throughput, accuracy, average rate of packet loss, scalability and fault tolerance, average delay and routing overhead in the route discovery process.