The Statistics behind “The Tomb”

The world of New Testament studies was abuzz during the week of February 25 to March 3, 2007, with advance critiques of a documentary that aired on the Discovery Channel on March 4, 2007, entitled, The Lost Tomb of Jesus. The documentary followed the efforts of a team, led by director Simcha Jacobovici, to determine whether the Talpiot tomb discovered in 1980 might be the tomb of Jesus’ family. The show was so sensationalistic that even its own statistics were not allowed their proper weight. For example, in one scene, Jacobovici and an unnamed team member came upon an ossuary in the IAA (Israel Antiquities Authority) warehouse on which they find the inscription “Jesus son of Joseph.” “Quite amazing, isn’t it?” the team member remarks. “Amazing is not the word for it,” Jacobovici replies. With that I would agree, but in what way is “amazing” the wrong word? The show itself revealed that the odds of a given patronymic inscription reading “Jesus son of Joseph” are one in only 190, and I would suggest that “amazing” is the wrong word simply because it is far too strong.

Really, just about anyone who is aware of the very limited pool of names that we might expect to appear on a first-century ossuary, and who notices how many of the names found in the Talpiot tomb do not match up with the family members listed in the gospels, should have no difficulty seeing that the odds of this being the tomb of Jesus’ family are rather remote. (While a royal flush might be impressive under normal rules, it is not at all impressive when the rules are bent to allow multiple draws and when deuces, treys, and one-eyed jacks are all wild. It is even less impressive when wildcards can be set after a hand has been dealt.) The documentary effectively screens this problem by treating the names serially rather than as a group, making excuses for those names that don’t fit, or arguing that they really do fit somehow although they are not known from the gospels.

Director, Jacobovici, outside the tomb

In the end, in order to make their statistics work, we even have to accept that Jesus was married to Mary Magdalene and that the couple secretly had a child named “Judah.” Rather than being treated as liabilities to a statistical study, these details are turned into historical givens and are even factored in as a positive match. Consequently, most of the connections made in the documentary fall under the heading of “special pleading.”

The Data and the Odds

The tomb in question at one time contained ten ossuaries, but the whereabouts of the tenth is now a matter of contention. The field, however, is defined by the number of inscribed names—eight total (six male and two female), of which half of the male inscribed ossuaries are given in patronymic form (viz. in the form “so-and-so son of so-and-so”): “Yehudah son of Yeshua,” “Yeshua son of Yoseph,” “Maria,” “Matia,” “Yose,” and “Mariamene [who is also called] Mara.”

In what follows, I handle the masculine and feminine names as two discrete sets, a consideration brought on by the disparity in how often each of these sets is manifested. The inscriptions that are statistically interesting are “Yeshua son of Yoseph,” “Maria,” and “Yose” (a form of “Joseph”), which the documentary claims to represent Jesus, Mary, and Jesus’ brother Yose (see Mark 6:3). I will use the anglicized names below.

What are the odds of those names appearing separately, and what are the odds of them appearing together, and within the form of the appropriate patronymic? Tal Ilan provides tables of the 20 most popular male names and the 10 most popular female names in Jewish Palestine for the period 330 BC to 200 AD in her Lexicon of Jewish Names in Late Antiquity.^[1] Based on her tables, it is easy to figure the odds of a number of names and combinations of names occurring.

For example, she tells us that out of 2509 “valid” male names in her catalog, 231 are of a form of “Joseph,” so that the odds of a given Jewish male from late antiquity being named “Joseph” is about 9.21% (or 231 divided by 2509). Similarly, the odds of him being named “Jesus” are 4.11%, “Judah” 7.13%, “Simeon” 10.24%, and “James” 1.79%. Multiplying the odds of one being named “Jesus” by the odds of one being named “Joseph,” one finds that the odds of a given male patronymic being “Jesus son of Joseph” is about .38%.

Since there are two patronymic ossuaries in the Talpiot tomb, the odds of one reading “Jesus son of Joseph” is about 0.75%.^[2] Similarly, Ilan tells us that there are 80 occurrences of “Mary” within a field of 317 “valid” female names, so that the odds of “Mary” appearing in a single shot are 25.24%, and the odds of that name appearing on at least one of two female ossuaries (as found at Talpiot) are 44.10%.^[3]

What then are the odds of one of the remaining inscribed ossuaries containing a form of “Joseph”? The single shot odds are 9.21%, and the formula given above yields odds of 25.16% in the case of three shots (as afforded at Talpiot).

At this point, it is necessary to address the “after the fact” nature of many of the statistical studies made in connection with this tomb. That is, what obtains in this tomb’s sampling is sometimes being treated as the only combination of names that could foster the suspicion that this is the tomb of Jesus’ family, when in fact a number of other combinations of names could do so just as impressively.

For example, instead of “Yose” we could have had the name of any of Jesus’ other brothers. In such a case, the same arguments that have been made in connection with the appearance of “Yose” would then have been made in connection with “Judah,” “Simeon,” or “James.” A more meaningful approach would calculate the odds of finding one patronymic relation known to obtain within Jesus’ family, together with one other male family name and one known female family name, within a sampling of ossuary inscriptions featuring two patronymic male inscriptions, two non-patronymic male inscriptions, and two female inscriptions.

Since “Joseph” (or “Yose”) is a constant in every known patronymic relation in Jesus’ family, our search for patronymics will take in the pairing of “Joseph” with the names of Jesus and each of his brothers. The same pool of brothers’ names will be applied to the other three tombs (allowing, in this instance, that one of the names could appear as the father in the unmatched patronymic and still satisfy the search).

In other words, we need to determine the odds of finding “Jesus son of Joseph,” “Mary,” and the name of any one of Jesus’ brothers. Now the odds of finding one of Jesus’ brothers’ names on one of the three remaining male ossuaries can be calculated^[4] to yield a probability of 63.26%, or odds of one in 1.6.

Multiplying that figure by the above-determined figures for finding “Jesus son of Joseph” and “Mary,” we arrive at a probability for the full package of 0.21% (that is, 63.26% x 0.75% x 44.10%), or, more precisely, of odds of one in 475.1. Considering that there are some 1,000 tombs similar to “the Tomb,” it should hardly be surprising that one should yield this cluster of names. On average (and holding the number of inscribed ossuaries to be typical), we might actually expect to find two or more.

Yet the show claimed that there was only a 1 in 600 chance that this is not the tomb of Jesus’ family, and it referred to that figure as conservative. If the above considerations are all there is to it, how did the figures on the documentary grow so large? The team essentially set the search for a larger cluster of names. Unfortunately, that cluster is hardly statistically meaningful (because everything beyond the three items we included is so obviously “after the fact”), and the arguments for including the other inscriptions within the cluster are in every instance a case of special pleading.

Consider, for example, the team’s rationale for identifying one of the ossuaries with Mary Magdalene. One ossuary from the tomb is inscribed in Greek with the name “Mariamne (who is called) Mara.” First, instead of understanding “Mara” as a diminutive form of “Mariamne,” the documentary suggests that “Mara” is actually a transliteration of the Aramaic “Mara” (Lord). No explanation is given for why we should prefer this very unnatural interpretation to the simple reading of “Mara” as “Mary.”

But that’s not all: noting that the full form “Mariamne” is rare among ossuaries, the team searched for the association of this name with Mary Magdalene within Christian tradition, and found it within the fourth-century Acts of Phillip. (In the follow-up program hosted by Ted Koppel, James Tabor stated that it is also found in the second-century writings of Hippolytus.) Yet it can scarcely be doubted that, had the form of the name on the ossuary matched that which the gospels use for Mary Magdalene, then the team would have pressed that conjunction of identifiers. In other words, we are dealing with a clear case of “after the fact” data mining.

The case for this being the tomb of Mary Magdalene is extremely weak, yet the limited odds of finding the form “Mariamne” (rather than all forms of “Mary” in general) was made a part of the statistical burden. Nothing within the formulation of odds acknowledges the hurdles that we must leap over to justifiably include Mary Magdalene, of which the tallest is the sheer notion of expecting to find her in Jesus’ family album in the first place. (I really thought we were past that nonsense after the way scholars panned The Da Vinci Code.)

But there’s more: building on this identification of Mary Magdalene as Jesus’ wife, the team suggests that “Judah son of Jesus” is the couple’s son, a son who (it is speculated) was kept secret for fear that the Romans might seek to crucify him (as Jesus’ heir). This, of course, is another rather strenuous hurdle, but, once again, its problematic nature is inverted in such a way that it pads the statistics rather than detracts from them.

Conclusion

Statistics can be tricky. There’s hardly anyone who hasn’t been fooled by them in one way or another. Unfortunately, the use of statistics in biblical studies has often not been any more reliable or transparent than its use in, say, politics or environmental activism. The Discovery Channel’s presentation of “The Tomb” is arguably one of the best examples of how padded statistics can hide the truth rather than reveal it.

• ^[1] Tal Ilan, Lexicon of Jewish Names in Late Antiquity Part 1:Palestine 330 BCE—200 CE (Tübingen: Mohr-Siebeck, 2002) 56-57. Unfortunately, there are a few errors within her tables—e.g., sometimes the number of valid male inscriptions is put at 2505 instead of 2509. ↩
• ^[2] This is found by the formula 1 – (1 – (xy))², where x is the single shot odds of finding “Joseph” and y is the single shot odds of finding “Jesus.” ↩
• ^[3] The formula for finding the odds in this case and those following is 1 – (1 – x)^y, where x equals the odds of one occurrence in one shot and y equals the number of shots. ↩
• ^[4] The calculation is: 1 – (1 – .1024 – .0921 – .0713 – .0179)³ ↩