A Statistical Investigation of the Synoptic Problem

This study 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.