The wide distribution of polyploidy among plants has led to a variety of theories for the evolutionary advantages of polyploidy. Here we claim that the abundance of polyploidy may be the result of a simple ratcheting process that does not require evolutionary advantages due to the biological properties of organisms. The evolution of polyploidy is a one-way process in which chromosome number can increase but not decrease. Using a simple mathematical model, we show that average ploidal level within a plant lineage can continually increase to the levels observed today, even if there are ecological or physiological disadvantages to higher ploidy. The model allowed us to estimate the average net speciation and polyploidy rates for ten angiosperm genera. Based on these estimates, the model predicts distributions of ploidal levels statistically similar to those observed in nine of the 10 genera.