Alternative splicing (AS) is a widespread process underlying the generation of transcriptomic and proteomic diversity in metazoans. Major challenges in comprehensively detecting and quantifying patterns of AS are that RNA-seq datasets are expanding near exponentially, while existing analysis tools are computationally inefficient and ineffective at handling complex splicing patterns. Here, we describe Whippet, a method that rapidly, and with minimal hardware requirements, models and quantifies splicing events of any complexity without significant loss of accuracy.Using an entropic measure of splicing complexity, Whippet reveals that approximately 33% of human protein coding genes contain complex AS events that result in substantial expression of multiple splice isoforms. These events frequently affect tandem arrays of folded protein domains. Remarkably, high-entropy AS events are more prevalent in tumour relative to matched normal tissues, and these differences correlate with increased expression of proto-oncogenic splicing factors. Whippet thus affords the rapid and accurate analysis of AS events of any complexity, and as such will facilitate biomedical research.