IEEE 802.11ax uplink orthogonal frequency division multiple access (OFDMA)-based random access (UORA) is a new feature for random channel access in wireless local area networks (WLANs). Similar to the legacy random access scheme in WLANs, UORA performs the OFDMA backoff (OBO) procedure to access the channel and decides on a random OBO counter within the OFDMA contention window (OCW) value. An access point (AP) can determine the OCW range and inform each station (STA) of it. However, how to determine a reasonable OCW range is beyond the scope of the IEEE 802.11ax standard. The OCW range is crucial to the UORA performance, and it primarily depends on the number of contending STAs, but it is challenging for the AP to accurately and quickly estimate or keep track of the number of contending STAs without the aid of a specific signaling mechanism. In addition, the one for this purpose incurs an additional delay and overhead in the channel access procedure. Therefore, the performance of a UORA scheme can be degraded by an improper OCW range, especially when the number of contending STAs changes dynamically. We first observed the effect of OCW values on channel efficiency and derived its optimal value from an analytical model. Next, we proposed a simple yet effective OBO control scheme where each STA determines its own OBO counter in a distributed manner rather than adjusting the OCW value globally. In the proposed scheme, each STA determines an appropriate OBO counter depending on whether the previous transmission was successful or not so that collisions can be mitigated without leaving OFDMA resource units unnecessarily idle. The results of a simulation study confirm that the throughput of the proposed scheme is comparable to the optimal OCW-based scheme and is improved by up to 15 times compared to the standard UORA scheme.