The training efficiency of Variational Quantum Algorithms (VQAs) is fundamentally dictated by the geometry of their cost function landscapes, which can be formally analyzed by mapping these functions to random fields on manifolds. Instead of VQAs we can then directly study the corresponding random fields, in our case the Wishart Hypertoroidal Random Fields (WHRFs). We are especially interested in the distribution of critical points (especially local minima) of WHRFs. For this purpose, the Kac-Rice formula is presented, reformulated and simulated. The findings identify phase transition in the distribution of local minima. Beyond a specific threshold, local minima concentrate near the global minimum in function value, meaning that even local minima are good approximators of the global one. The threshold is governed by the ratio between the problem Hamiltonian degrees of freedom and by the number of independent parameters in the VQA. Since the degrees of freedom parameter scale exponentially we propose symmetry reduction operations to lower degrees of freedom and subsequently also the threshold for better trainability.