Base editors are dedicated engineered deaminases that enable directed conversion of specific bases in the genome or transcriptome in a precise and efficient manner, and hold promise for correcting pathogenic mutations. A major concern limiting application of this powerful approach is the issue of off-target edits. Several recent studies have shown substantial off-target RNA activity induced by base editors and demonstrated that off-target mutations may be suppressed by improved deaminases versions or optimized guide RNAs. Here, we describe a new class of off-target events that are invisible to the established methods for detection of genomic variations and were thus far overlooked. We show that nonspecific, seemingly stochastic, off-target events affect a large number of sites throughout the genome or the transcriptome, and account for the majority of off-target activity. We develop and employ a different, complementary approach that is sensitive to the stochastic off-target activity and use it to quantify the abundant off-target RNA mutations due to current, optimized deaminase editors. We provide a computational tool to quantify global off-target activity, which can be used to optimize future base editors. Engineered base editors enable directed manipulation of the genome or transcriptome at single-base resolution. We believe that implementation of this computational approach would facilitate design of more specific base editors.