Historical Studies include many tools to determine the probability of a historical event being true. Regarding the historicity of Jesus and the events recording in the Bible, Richard Carrier claims that the methods used by Christian apologists to support their claims are not in keeping with accepted historical methods in other fields (see here). Carrier promotes the use of Bayes' theorem as the best method of determining the probability of an historical event occurring. Unlike other tools such as the Argument to the best explanation, Bayes' theorem is mathematically precise, thus is more valid if used properly.
Vridar has posted a detailed explanation of Bayes' theorem and its proper application to historicity of Jesus studies.
Bottom line in this discussion: It makes no difference whether or not Jesus is based on a real person. The character is effectively fictional.