The degree to which neural networks can generalize to new combinations of familiar concepts, and the conditions under which they are able to do so, has long been an open question. In this work, we study the systematicity gap in visual question answering: the performance difference between reasoning on previously seen and unseen combinations of object attributes. To test, we introduce a novel diagnostic dataset, CLEVR-HOPE. We find that while increased quantity of training data does not reduce the systematicity gap, increased training data diversity of the attributes in the unseen combination does. In all, our experiments suggest that the more distinct attribute type combinations are seen during training, the more systematic we can expect the resulting model to be.