A Statistical Investigation of the Synoptic Problem

This paper presents a statistical investigation of the literary relationships among the three synoptic gospels—Matthew, Mark, and Luke—using vocabulary frequency data drawn from the Hoffmann, Hieke, and Bauer Synoptic Concordance. Word occurrence counts across nineteen synoptic categories are modeled using a Poisson distribution, and pairwise relationships between categories are tested using maximum likelihood estimation and the likelihood ratio test, with a correction for the overdispersion characteristic of word-frequency data. The analysis identifies statistically significant vocabulary affinities between specific synoptic categories, yielding evidence for Markan priority, for Luke's use of Matthew, and for a sayings source underlying the double tradition. The results are most consistent with the Three-Source Hypothesis: Mark composed first; Matthew drew on Mark and a sayings source; Luke drew on Mark, the sayings source, and Matthew. The same framework accommodates, without establishing, more speculative refinements—a proto-Mark and a proto-Luke—that are developed on literary grounds in the discussion and reserved for fuller treatment elsewhere. An extended example from Luke 14:1–6 illustrates how an alliterative Aramaic saying, preserved in Greek translation, illustrates Luke's use of all three sources.