Degree distributions are widely used to characterize networks, including food webs, and play a vital role in models of food web structure. To date, there have been no mechanistic or statistical explanations for the form of food web degree distributions. Here, I introduce models for food web degree distributions based on the principle of maximum entropy (MaxEnt) and show that the distributions of the number of consumers and resources in 23 (45%) and 35 (69%) of 51 food webs are not significantly different at a 95% confidence level from the MaxEnt distribution. These findings offer a new null model for the most probable degree distributions in food webs and other networks. They suggest that there is relatively little pressure favoring generalist or specialist consumption strategies but that biological drivers or methodological bias may force the consumer distribution away from the MaxEnt form.