Membrane protein channels employed as stochastic sensors offer large signal-to-noise ratios and high specificity in single molecule binding measurements. Stochastic events in a single ion channel system can be measured using current-time traces, which are straightforward to analyze. Signals arising from measurement using multiple ion channels are more complicated to interpret. We show that multiple independent ion channels offer improved detection sensitivity compared to single channel measurements and that increased signal complexity can be accounted for using binding event frequency. More specifically, the leading edge of binding events follows a Poisson point process, which means signals from multiple channels can be superimposed and the association times (between each binding event leading edge), allow for sensitive and quantitative measurements. We expand our calibration to high ligand concentrations and high numbers of ion channels to demonstrate that there is an upper limit of quantification, defined by the time resolution of the measurement. The upper limit is a combination of the instrumental time resolution and the dissociation time of a ligand and protein which limits the number of detectable events. This upper limit also allows us to predict, in general, the measurement requirements needed to observe any process as a Poisson point process. The nanopore-based sensing analysis has wide implications for stochastic sensing platforms that operate using multiple simultaneous superimposable signals.