The researchers introduce AgentOPSD, a critic-free, recursive framework designed to improve turn-level credit assignment in long-horizon, multi-turn agentic reinforcement learning tasks. Addressing the limitations of trajectory-level advantage estimates and sparse outcome-based rewards, AgentOPSD utilizes a privileged self-distillation approach to generate denser supervision. The method functions by aggregating token-level log-probability gaps between teacher and student models into turn-level evidence, which is then used to recursively update a Bayesian belief state within the log-odds space. This mechanism enables a principled reweighting scheme that identifies critical decision points through marginal belief revision between consecutive states. Notably, the approach integrates seamlessly with standard policy optimization without requiring additional rollouts or an auxiliary critic model. Experimental evaluations using Qwen2.5 models (3B and 7B scales) across the ALFWorld, WebShop, and Search-QA benchmarks demonstrate the efficacy of this method. AgentOPSD significantly outperforms GRPO and existing self-distillation baselines, notably achieving an 89.1% success rate on the ALFWorld benchmark when paired with the Qwen2.5-7B model. Ablation studies confirm that the performance improvements are driven specifically by the turn-level aggregation and the history-dependent recursive belief update architecture.