In this paper, we propose, implement, and evaluate a simple yet powerful estimation method for the quality of service of a large-scale Wi-Fi network, which is achieved using our passive and low-complexity measurements. Specifically, our proposed method estimates a time-varying frame error rate at an access point (AP) by counting null function data frames, which are emitted periodically by stationary user equipments (UEs), such as mobile phones and tablets. We implemented our method as a user-level script and a production-level firmware. Our real-world measurements in an uncontrolled 1500-seat hall demonstrated that our method exhibited high scalability against the increase in the numbers of APs and UEs with the aid of its simple structure and was capable of detecting the quality-of-service loss induced by an unexpected dynamic frequency selection. INDEX TERMS IEEE 802.11, Wi-Fi, passive estimation, quality of service (QoS), frame error rate (FER), large-scale network. D. RETRY-RATIO-BASED THROUGHPUT ESTIMATION [20], [22] YASUHIRO OHISHI (M'19) received the B.E.