We assess the variability of protein function in protein sequence and structure space. Various regions in this space exhibit considerable difference in the local conservation of molecular function. We analyze and capture local function conservation by means of logistic curves. Based on this analysis, we propose a method for predicting molecular function of a query protein with known structure but unknown function. The prediction method is rigorously assessed and compared with a previously published function predictor. Furthermore, we apply the method to 500 functionally unannotated PDB structures and discuss selected examples. The proposed approach provides a simple yet consistent statistical model for the complex relations between protein sequence, structure, and function. The GOdot method is available online (http://godot.bioinf.mpi-inf.mpg.de).