We continue to explore the numerical nature of the Okounkov bodies focusing on the local behaviors near given points. More precisely, we show that the set of Okounkov bodies of a pseudoeffective divisor with respect to admissible flags centered at a fixed point determines the local numerical equivalence class of divisors, which is defined in terms of refined divisorial Zariski decompositions. Our results extend Roé’s work [R] on surfaces to higher-dimensional varieties although our proof is essentially different in nature.