Detector delay as a useful detector timing feature is often recommended for minimizing disruptions on major movements caused by one or more minor movements. However, this benefit of detector delay is not always certain because the applicability of detector delay is subject to a combination of gap demand, gap availability, critical gap acceptance, follow-up headways, and other factors. The improper use of detector delay could be costly to traffic on minor streets. With little literature on the subject, the complex relationship between detector delays and different critical factors has not been fully understood. An analytical model that estimates the probability of clearing right-turn-on-red queues within the period of detector delay is presented. This probability is the first step toward an understanding of how this detector feature affects an intersection's operational efficiency. The gap-finding process of multiple right-turn-on-red vehicles is divided into several realistic cases and analyzed in detail. Insights about the process described in each case are applied to derivation of a probability model. Validation of the model is conducted with more than 4,000 simulation runs. A close fit is found between the computed probability and the simulated data with errors no larger than 5.7% of the targeted values. The method for deriving the probability model provides a stepping-stone toward deriving the delay distributions for right-turn-on-red traffic.