A new method for calculating average molecular weights is presented for nonlinear polymers. In contrast to the previous methods of Flory and Stockmayer which first calculate the distribution of all species and then use the distributions to calculate average properties, the new method calculates these properties directly. In contrast to the method of Gordon, probability generating functions are not required. Starting with elementary probability and utilizing the recursive nature of network polymers, property relations can be developed more simply. We illustrate the method for calculations of [formula omitted], [formula omitted], and the gel point for a wide variety of polyfunctional polymerizations.