During a trapping study interval, each target insect is either caught or not caught. Therefore, the current analysis treats trapping as a binomial process. Data from a binomial calculator, along with computer simulations of random walkers, documented that the inherent variance associated with estimates of absolute population density generated by a single catch number in a pheromone-baited monitoring trap becomes very high when catch probability averaged across the trap's sampling area falls below 0.02, as is the case for most insect trapping systems operating in the open field. The imprecision associated with interpretations of single catch numbers renders many current pest management decisions risky and unsatisfactory. Here we reinforce how single-trap, multiple-release experiments can and should be used to measure catch probability, plume reach, and trap sampling area. When catch probability lies in the danger zone below 0.02, steps are suggested for how multiple traps might be deployed to raise composite catch probability to a level where estimates of absolute pest density become reliable. Heat transfer is offered as an appropriate conceptual model for the mechanics of trapping. A call is made for a radical rethinking in the designs of insect monitoring traps in light of their significant current deficits highlighted by this study.