In our previous work, a random-sampling-based footstep planner has been proposed for global biped navigation. Goal-probability threshold (GPT) is the key parameter that controls the convergence rate of the goal-biased nonuniform sampling in the planner. In this paper, an approach to optimized GPT adaptation is explained by a benchmarking planning problem. We first construct a benchmarking model, in which the biped navigation problem is described in selected parameters, to study the relationship between these parameters and the optimized GPT. Then, a back-propagation (BP) neural network is employed to fit this relationship. With a trained BP neural network modular, the optimized GPT can be automatically generated according to the specifications of a planning problem. Compared with previous methods of manual and empirical tuning of GPT for individual planning problems, the proposed approach is self-adaptive. Numerical experiments verified the performance of the proposed approach and furthermore showed that planning with BP-generated GPTs is more stable. Besides the implementation in specific parameterized environments studied in this paper, we attempt to provide the frame of the proposed approach as a reference for footstep planning in other environments.