Natural language understanding depends heavily on assessing veridicality -- whether the speaker intends to convey that events mentioned are actual, non-actual, or uncertain. However, this property is little used in relation and event extraction systems, and the work that has been done has generally assumed that it can be captured by lexical semantic properties. Here, we show that context and world knowledge play a significant role in shaping veridicality. We extend the Fact Bank corpus, which contains semantically driven veridicality annotations, with pragmatically informed ones. Our annotations are more complex than the lexical assumption predicts but systematic enough to be included in computational work on textual understanding. They also indicate that veridicality judgments are not always categorical, and should therefore be modeled as distributions. We build a classifier to automatically assign event veridicality distributions based on our new annotations. The classifier relies not only on lexical features like hedges or negations, but also structural features and approximations of world knowledge, thereby providing a nuanced picture of the diverse factors that shape veridicality.