Several scholars, including Martin Hengel, R. Alan Culpepper, and Richard Bauckham, have argued that Papias had knowledge of the Gospel of John on the grounds that Papias’s prologue lists six of Jesus’s disciples in the same order in which they are named in the Gospel of John: Andrew, Peter, Philip, Thomas, James, and John. In “A Note on Papias’s Knowledge of the Fourth Gospel” (JBL 129 : 793–94), Jake H. O’Connell presents a statistical analysis of this argument, according to which the probability of this correspondence occurring by chance is lower than 1 percent. O’Connell concludes that it is more than 99 percent probable that this correspondence is the result of Papias’s copying John, rather than chance. I show that O’Connell’s analysis contains multiple mistakes, both substantive and mathematical: it ignores relevant evidence; overstates the correspondence between John and Papias; wrongly assumes that, if Papias did not know John, he ordered the disciples randomly; and conflates the probability of A given B with the probability of B given A. In discussing these errors, I aim to inform both Johannine scholarship and the use of probabilistic methods in historical reasoning.