The appreciation of humor is a universal phenomenon and a key aspect of cognition. It has been studied in the context of jokes, where the incongruity in expected and observed context results in the perception of humor. The present study examines how the humor appreciation of single words relates to the humor of the whole joke – is a joke simply a sum of its parts? Using a novel dataset of single-word humor ratings, collections of jokes from the JESTER database were analyzed. A multiple regression analysis showed joke length and individual word arousal were the best predictors of joke funniness. Longer jokes with fewer individually arousing words were found funnier. Individual word humor did not contribute to the humor of the overall joke. These findings suggest the cognitive aspects of humor are likely driven by broader semantic context, whereas appreciating humor on a per-word basis links to separate factors.