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Statistics And The "Jesus Family Tomb"

In late February, 2007, Simcha Jacobovici and Charles Pellegrino launched a new book titled The Jesus Family Tomb: The Discovery, the Investigation, and the Evidence That Could Change History. They followed it up with a documentary shown a few days later on the Discovery Channel.

It was a fascinating and controversial book. I grabbed it as soon as I could and read it carefully to see what the case is. I'll say right away that I came to like Simcha Jacobovici very much while reading the book. His intellectual curiosity launched this investigation, and he clearly loves a great puzzle. There are folks who want to make Simcha the bad guy here, as if he somehow set out to demolish Christianity by cooking up some evidence. I don't get that impression from reading his story or watching him on video. He's clearly passionate about this story and interested in getting at the truth.

It had the potential to be a BIG story. A bone/box had been found in 1980 in a rock/cut tomb in Jerusalem with the name "Jesus son of Joseph." In the same tomb were nine other bone/boxes. Five of them had names on them, and those names included Mary twice, Joseph, Judah, and Matthew. We know that Jesus had two brothers named Joseph and Judah and his grandfather was named Matthew. Furthermore, two of his disciples were also named Judah and one was named Matthew. Isn't that an awfully big coincidence? What if this Jesus is the REAL Jesus of Nazareth? Simcha Jacobovici wondered why the archaeologists didn't pursue this with a little more interest.

After reading the book carefully, I knew there were some serious problems with the case that the authors had made. No need to comment here on the archaeological or linguistic issues. Those have been discussed already by various scholars. I'll refer you to the blogs and various articles listed at the bottom of this page.

In this article, I'll focus on the statistical analysis described in the book The Jesus Family Tomb. [Note added: This is the first of several articles that I published in 2007/2008, each more detailed than the last. This article was very widely read, so for historical reasons, I've left it almost identical with the original, with a few tweaks to the text and some comments inserted in red to point out things that have changed since 2007.] In The Jesus Family Tomb, the authors explained why they believe that the odds are 600 to 1 that the tomb they found contained the bone/boxes of Jesus of Nazareth, his mother Mary, his "wife" Mary Magdalene, his "son" Judah, his brother Joseph, and one other person named Matthew who might be either a disciple or a family member. The book describes a "Jesus Equation" that defines this probability.

I believe that the statistical calculations need to be done differently. This is not the place to cast aspersions on Mr. Jacobovici or Mr. Pellegrino or the statistician they asked to do their calculations, Dr. Andrey Feuerverger. Name-calling solves nothing. What I want to do is to redo the calculation in a way that I believe answers the fundamental question more accurately.

And what is the fundamental question? That's very important. In science, getting the right answer is a whole lot easier when you start with the right question. Years ago, when I wrote a book on the alleged Bible code, I found time after time in which the Bible coders had asked the wrong question and then answered it correctly. They concluded that they had found powerful evidence that God encoded secret messages in the Bible. But I believe they were wrong, because they asked the wrong question.

The Fundamental Question

Here is the fundamental question: We have found a bone-box containing a man named "Jesus son of Joseph." We have found with it five other bone-boxes containing two women named "Mary" and three men bearing the names of brothers or disciples of Jesus of Nazareth. One of the bone-boxes contains the son of the Jesus of the tomb. Based on this information, what is the probability that the Jesus of this tomb is Jesus of Nazareth?

I'll explain later why this is the correct question to ask. I'll also explain why it's a better question to ask than the ones that Simcha Jacobovici and Charles Pellegrino asked their statistician.

First, let me show how to answer the question. As much as possible, I'll use the same numbers as those used in The Jesus Family Tomb, because part of their calculation is quite reasonable.

Those numbers, in fact, can be found in another book that appeared a few years ago, The Brother of Jesus, by Hershel Shanks and Ben Witherington III. Hershel Shanks is the editor of Biblical Archaeology Review. Ben Witherington III is a well/known scholar of the historical Jesus, and is the author of Jesus The Sage, among other books.

On page 56 of The Brother of Jesus, a table is listed showing how common various men's names were in first/century Jerusalem. The table is based on data from Rachel Hachlili's article, "Names and Nicknames of Jews in Second Temple Times," published by the Israel Exploration Society in 1984 in volume 17 of Eretz/Israel. [Note added: there is a second source of names which I had no access to when I wrote this article originally, and it is generally considered more accurate--the list published by Dr. Tal Ilan. In an article published a few weeks after this one, I considered the results of using Ilan's numbers.] 

Here is the table, using the usual English equivalents for the Hebrew and Aramaic names:
Name Percentage
Simon 21%
Joseph 14%
Judah 10%
Yohanan (John) 10%
Eliezer 10%
Jesus 9%
Jonathan 6%
Matthew 5%
Hanina 3%
Yo/ezer 3%
Ishmael 2.2%
Menachem 2%
Jacob (James) 2%
Hanan 2%
Levi 0.2%
Isaac 0.2%
Gamaliel 0.2%
Hillel 0.2%

The interpretation of this table is the following. If you were in ancient Jerusalem and walked up to some randomly chosen man on the street, the probability is 14% that his name would be the Hebrew or Aramaic equivalent of Joseph. The probability is 9% that his name would be the Hebrew or Aramaic equivalent of Jesus in one of its forms. (There are several different forms for many Hebrew names, just as there are for English names. For example, Robert, Rob, Robby, Bob, and Bobby are all different forms of the same name.)

So if you walked up to a random man in Jerusalem, the probability that his name would be Jesus and that his father's name would be Joseph is about 1.26%. You get this number by multiplying 9% by 14%.

We know that these bone/boxes were used in Jerusalem for only a short stretch of time in history -- roughly from 20 B.C. to A.D. 70. One can then estimate the total number of men in Jerusalem who lived during that time. That number is estimated in the book The Brother of Jesus, page 58, to be about 80,000 men. This is a reasonable number and we'll use it in our estimates. [Note added: this number is at the high end of the reasonable range. I would put the low end of the range at around 30,000 men.]

So now we can estimate the number of men in Jerusalem who would have been named "Jesus son of Joseph". The number is 1.26% of 80,000 men, which works out to 1008. Remember, this is an estimate. How good is this estimate?

That is easy to answer. We would expect the true number of such men, using the usual laws of statistics, to be between 900 and 1100 men. (We compute the "standard deviation" of our estimate to be the square root of 1008, which is about 32. With extremely high probability, the true number of men should be within 3 standard deviations of our estimate of 1008. So, in round numbers, we can be VERY confident that there were between 900 and 1100 men in Jerusalem named "Jesus son of Joseph" or some variation of that name. [Note added: in making this error estimate, we are assuming that our estimate of the number of men in Jerusalem was accurate and that Rachel Hachlili's name frequencies were accurate. As I learned after writing this article, neither of these assumptions is perfect, so the actual number of men named "Jesus son of Joseph" in Jerusalem was probably less than 1000.]

The next step is a little more complicated. We know that all 1008 of those men died and were buried somewhere. Some were put in bone-boxes, some were tossed to the wolves, some were laid to rest in other ways. We know that at least one of them ended up in a tomb in Jerusalem in the company of five other named bone-boxes, and those bone-boxes bore some extremely interesting names. There were two women named Mary! (Of the women close to Jesus of Nazareth, at least three were named Mary: his mother, Mary Magdalene, and Mary of Bethany.) Three of the bone-boxes bear the names of brothers or disciples of Jesus of Nazareth. Coincidence or not?

The standard way to answer this question in statistics is as follows: Let's imagine that all 1008 of the men named "Jesus son of Joseph" were buried with 2 women and 3 men. Compute the probability that the 2 women would both be named Mary AND that the 3 men would have names of Jesus' brothers or disciples.

The first part of the question is very easy. Mary was an extremely common name in Jerusalem. Approximately 21.4% of all women in Jerusalem bore some variation of this name. So if a man were buried with two female relatives, the probability is about 4.6% that BOTH would be named Mary. (We get this number by multiplying 21.4% by 21.4%, once for each of the two Marys.) So of the 1008 men named "Jesus son of Joseph" whom we are burying with 2 females, we would expect that 46 of these men would be buried with two Marys.

Now we have to calculate the second part of the question. If we ALSO bury all 46 of those men with 3 males, how many of them will be buried with 3 men whose names are either the brothers of Jesus of Nazareth or one of the twelve disciples? This is a little more complicated, and we can actually ask it in three different ways. Two of the three men in the tomb bore names of the BROTHERS of Jesus (Judah and Joseph). Two of the three men in the tomb bore names of the DISCIPLES of Jesus. (Judah and Matthew). All three of the men in the tomb bore names that were EITHER brothers of Jesus OR disciples of Jesus. What are the odds of each of those three cases?

Let's make some tables that add up the probabilities for the names of Jesus' brothers and for his disciples:
Brother's Name Percentage
Simon 21%
Joseph 14%
Judah 10%
Jacob (James) 2%
Total 47%
What this means is that if you went up to a random man on the street in ancient Jerusalem, the odds are 47% that his name would be the same as one of the four brothers of Jesus!

Disciple's Name Percentage
Simon 21%
Judah 10%
Yohanan (John) 10%
Matthew 5%
Jacob (James) 2%
Levi 0.2%
Other disciples Very low
Total 48.2%

What this means is that if you went up to a random man on the street in ancient Jerusalem, the odds are 48.2% that his name would be the same as one of the twelve disciples of Jesus!

Disciple or Brother Percentage
Simon 21%
Joseph 14%
Judah 10%
Yohanan (John) 10%
Matthew 5%
Jacob (James) 2%
Levi 0.2%
Other disciples Very low
Total 62.2%

So if you went up to a random man on the street in ancient Jerusalem, the odds are 62.2% that his name would be the same as one of the twelve disciples of Jesus or one of his brothers!

Now let's return to our questions. We'll answer them each in turn. (The calculations use the "binomial distribution" from probability theory, and I am not going to explain that here. I'll just say that any statistician would apply this distribution to solve this problem when it's set up this way.)

  • If we have 3 men in bone/boxes, what is the probability that at least 2 of those 3 men have names of the brothers of Jesus? Answer: 45.5%. (The odds are 35.1% that 2 of them match, and the odds are 10.4% that all 3 match.)
  • If we have 3 men in bone/boxes, what is the probability that at least 2 of those 3 men have names of the disciples of Jesus? Answer: 47.3%. (The odds are 36.1% that 2 of them match, and the odds are 11.2% that all 3 match.)
  • If we have 3 men in bone/boxes, what is the probability that all 3 men have names of either disciples of Jesus or brothers of Jesus? Answer: 24.1%.
Now we can answer our main question. Remember, we had 46 men named "Jesus son of Joseph" who are buried with a pair of Marys. If we bury all of those with 3 randomly chosen male family members and friends, we expect the following:

  • About 21 will be buried with at least 2 men whose names match the brothers of Jesus.
  • About 22 will be buried with at least 2 men whose names match the disciples of Jesus.
  • About 11 will be buried with 3 men whose names match either the disciples of Jesus or the brothers of Jesus.
The conclusion then is that one would expect at least 11 men to be buried with a set of other people that meets or beats the "amazing coincidence" found for the Jesus of the tomb. Obviously, not all of those 11 men were buried in family tombs, not all of them were buried with 2 named women and 3 named men, and not all of the tombs have been discovered. But we know that one of those men was buried in those conditions and his tomb was discovered. But any one of those 11 men COULD have been buried and found. The purpose of the above statistical argument was to take all the evidence we had and estimate how many men would be expected to fit the profile of the Jesus of the tomb. Now we know the answer.

We expect at least 11 men of ancient Jerusalem to fit the profile of the Jesus of the tomb. [Note added: After I wrote this article, it became clear that most of the assumptions were open to challenge. We don't know how many men lived in Jerusalem in this time period. We don't know the exact frequencies of the names of the brothers and disciples of Jesus. The "Judah" in the tomb is clearly not the brother of Jesus, so it's not really necessary to include him in the calculation. And the known family of Jesus had only one Mary, not two, so it's only necessary to include one of them in the calculation. As you change the assumptions, you change the results. In a later article, I analyzed the effect of changing the assumptions. I ultimately decided that the assumptions made above were probably too favorable for the "Jesus family tomb hypothesis" which means that probably there were more men in ancient Jerusalem who fit the profile of the Jesus of the tomb.]

Is It Jesus of Nazareth?

The next question is the really explosive one: What are the odds that the Jesus of the tomb is Jesus of Nazareth?

You might be tempted to say: There are 11 candidates and Jesus is 1 of those 11, so the odds are 1 out of 11. In other words, the probability is about 9%. That is the naive number, but it is wrong, because there is one more piece of evidence to consider.

Let's remember one very important thing. The Jesus of the tomb had a son. One of the bone-boxes bears the name "Judah son of Jesus." Most of the men in Jerusalem would have had sons. It's hard to estimate the exact probability, but most Jewish men married and most of them had children. Lacking birth control, and believing that children were God's gift, most Jewish men had lots of children. It's a very strong bet then that most of our 11 men would have had at least one son.

But what about Jesus of Nazareth? The authors of The Jesus Family Tomb argue at some length that this tomb shows that Jesus must have had a son. But the argument doesn't work that way. You have to first demonstrate that the Jesus in the tomb IS Jesus of Nazareth based on the evidence you have. And the evidence we have is that Jesus of Nazareth very likely didn't have a son.

Remember that the family of Jesus was very important in the earliest Jewish-Christian community in Jerusalem. For about 30 years after Jesus died, his brother James was the acknowledged leader of the Jewish Christians. James was killed about the year A.D. 62, and then his cousin Simon son of Clopas took over the job. The book of Jude in the New Testament is attributed to Judah, the brother of Jesus. These facts tell us that the male relatives of Jesus formed a strong dynasty in the early Jewish-Christian community. If Jesus had a son, that son would have been an important member of the community. There is a very strong case that we would know about him.

But no ancient source ever mentions such a son! Based solely on the historical record, one has to argue that the probability is VERY low that Jesus had a son. (Some folks might want to make a theological argument that Jesus could not have had a son, but such arguments simply won't wash. There is no theological reason Jesus could not have married and had children. The earliest Jewish-Christian community would not have been embarrassed by a wife and children for Jesus. Wives and children were considered good gifts from God, not sinful.)

Let's emphasize the point: The HISTORICAL record shows no evidence of a son. Had there been a son, the odds are EXTREMELY high that history would mention him, because he would have been part of the Jesus dynasty.

We must conclude that the probability is VERY low that Jesus of Nazareth had a son. One could poll historians and ask them the odds that Jesus had a son. That's a fuzzy question that depends on historical judgment, so you wouldn't get the same answer from everyone. Answers might range from "1 in 1000" or maybe "1 in a million" up to "it's impossible."

Now we can get back to the question about whether the Jesus in the tomb is Jesus of Nazareth. We have 11 candidates for the Jesus of the tomb. 1 of those candidates is Jesus of Nazareth who almost certainly didn't have a son. The other 10 are men who probably had sons.

If you want a probability estimate, here is mine. I would say that the odds are FAR LESS than 1 in a 1000 that Jesus of Nazareth had a son. That works out to .1%. So you should multiply that factor by the naive probability that Jesus is one of the 11 candidates, which we computed as 9%. The result is going to be less than .01%.

Based on that estimate, the odds are MORE THAN 10,000 to 1 against Jesus of Nazareth being the Jesus of the tomb. [Note added: Shortly after I published this article, Gary Habermas, a well/known Christian apologist, called me to talk about my calculations. I explained each step of the process. Gary told me that he agreed that it seemed unlikely that Jesus had a son, but that he would be comfortable with a probability higher than 1 in 1000. This would of course change my estimate above, so in my later articles I've radically increased my probability estimate that Jesus had a son. The important point is that the "Judah son of Jesus" inscription REDUCES the probability that this tomb belongs to Jesus of Nazareth.]

It is possible to make refinements of the estimates I've given above. However, in my opinion, I don't believe any revisions of the calculation will change the basic result. It is EXTREMELY UNLIKELY that the Jesus of the tomb is Jesus of Nazareth.

Why The Different Results?

If you have read The Jesus Family Tomb, then the obvious question is: How come they got a different answer than I did?

The answer is that they asked a different set of questions than I did. Let me review for you the questions they asked, and then I'll explain why I believe they weren't the correct questions to ask. I'll make the case that the question I asked is better.

Let me reiterate one thing here: Let's keep the issue of biases out of this, shall we? That gets really old really fast. It is tempting to say, "Simcha Jacobovici and Charles Pellegrino are just trying to disprove Christianity," or to say, "Randy Ingermanson just wants to defend Christianity." Having read Simcha and Charles' book, I don't believe they're trying to wreck Christianity. I think they're just pursuing an interesting question the best they can. That's what I'm trying to do, too. The final question is not who's biased. The final question is who makes the best mathematical case.

Let's review the first calculation that the authors of The Jesus Family Tomb call "The Jesus Equation." The calculation is found in Chapter 4, which Charlie Pellegrino wrote, so I'll refer to the author as Charlie in what follows. But Simcha clearly agrees with him on this.

Charlie started out exactly the same way I did. Following Shanks and Witherington's book, he estimated 80,000 men in ancient Jerusalem. Then he multiplied the probability of a "Joseph" (14%) by the probability of a "Jesus" (9%) and got 1008 men named "Jesus son of Joseph." That is identical to the number I got.

From that point on, our calculations are different. Recall that I then calculated the probability for finding 2 "Marys", each having a probability of 21.4%. That is not what Charlie did.

He noted that the 2 "Marys" took different forms. One was spelled "Maria" and the other was "Mariamne". Both of these are variant forms of "Mary." (Just as Rob, Robby, Bob, and Bobby are all variant forms of Robert.)

Charlie then looked up the frequencies in ancient inscriptions for those EXACT spellings. Here is what he found (p. 75/76):

Disciple's Name Percentage
Maria 4.17%
Mariamenon 0.518%

I will argue that this is not the right procedure. The reason is quite simple. What was the reason Simcha felt surprise when he first heard about the bone-box with "Jesus son of Joseph" inscribed? He was surprised because there was another bone-box discovered nearby with "Mary" on it. And Mary was the mother of Jesus.

Note that there are several variant forms of Mary that could have been found on the tomb: Maria, Mariam, Mariamme, Mariame, Mariamne, Mariamenon, etc. ANY one of those variant forms would have been cause for surprise. Any one of those could well be the actual name used by Mary the mother of Jesus. There is no way to know for sure what name she went by. In fact, the real Mary could have gone by several of them simultaneously. (For example, my legal name is "Randall" so I use that when I'm dealing with the government. But most of my friends call me "Randy." A few of them call me "Ran." And occasionally, one of them will call me "Ran the Man." I've even had a friend call me "Ranbert" in honor of the cartoon character Dilbert. I've had my name misspelled by various people as "Randal," or "Randell," or "Rancy." So any of these names can apply to me, but I'm still only one person.)

Likewise, we can't know for sure what was the usual name used by the Mary whose name was spelled "Maria" on the bone/box. Any variant of "Mary" could have been chosen and they would all apply to the same woman. Any of them. But when the stonemason went to write the name on the box, only one was actually written. It doesn't matter which variant was written. And the odds for finding one of those variant forms is 21.4%. It is irrelevant that the actual form found was Maria. Had Simcha found the name Mariam instead, he would have been just as surprised and would have pursued the investigation with the same vigor. Any form of Mary is as good as any other. That is why you MUST use the probability of finding ANY of the various forms. Because they all count. The family could have asked the stone mason to write any of those forms on the bone/box.

The same goes for the second form of Mary, the diminutive form Mariamenon (in the genitive case, Mariamenou). This is a rare form of the name, but it's still a Mary.

In The Jesus Family Tomb, Simcha goes to great lengths to "prove" that this is somehow the name that Mary Magdalene went by. He is incorrect on numerous counts. His argument hinges on the fact that Mary Magdalene is called Mariamne in the late 4th century Gnostic text The Acts of Philip. Simcha learned this from the works of Dr. Francois Bovon of Harvard University. Simcha's entire argument requires that Mary Magdalene be named Mariamne, and that Mariamne be a rare name that is only ever applied to Mary Magdalene.

The problems are the following:

  • As Dr. Bovon has said publicly, the "Mariamne" in the Acts of Philip is a literary figure, not a historical figure.
  • The Acts of Philip is nearly four full centuries after the time of Jesus, and it has no historical value. It's fiction.
  • The "Mariamne" in the Acts of Philip is ALSO identified at the same time as Mary of Bethany. But Mary of Bethany is an entirely different historical person than Mary Magdalene.
  • "Mariamne" is in fact a fairly common variant form of Mary. King Herod the Great had a wife whose name is spelled both "Mariamne" and "Mariamme" in different sources.
  • The name on the ossuary is in fact "Mariamenon", not "Mariamne".
  • In the New Testament, Mary Magdalene's name is spelled "Maria", exactly the same spelling as Mary the mother of Jesus, and Mary of Bethany. There is no reason to believe that "Mariamenon" was a unique identifier for Mary Magdalene.
In the "Jesus equation" of The Jesus Family Tomb, the whole reason for computing the probability of finding "Mariamenon" is that this is supposed to be a sure sign that they'd found Mary Magdalene. But it isn't. Mary Magdalene was no more and no less likely to have gone by "Mariamenon" than was any other Mary on the streets of Jerusalem.

The result is that in my calculation, when I estimated the probability of finding 2 Marys to be the product of 21.4% and 21.4%, which is 4.6%, Charlie estimated the probablity to be the product of 4.17% and .518%, which is .0216%. This drastically reduced his estimate for the number of men named "Jesus son of Joseph" who might have been buried with the 2 Marys. His prediction for this number of men is .2 men. My prediction was 46 men.

The final stage of Charlie's calculation was to ask for the probability of finding a man named Joseph in the tomb. That probability is 14%, and he multiplied that into his equation to get a final computation that .032 men should be predicted to live in Jerusalem. Or in his way of putting it, the probability of finding such a man is 1 in 2.5 million. (If you divide the 80,000 men in Jerusalem by 2.5 million, you get .032 men.)

Charlie was unsure how to handle the evidence for the Matthew inscription or the Judah inscription, so he stopped at this point. Please note that this not the final answer given in the book The Jesus Family Tomb. If this were the stopping place, then they would have quoted odds of 30 to 1 that the Jesus of the tomb is Jesus of Nazareth. (1 divided by .032 is about 31. A probability of 1/31 means odds of 30 to 1.) On page 82 of the book, Charlie incorrectly quotes his preliminary estimate as 2.5 million to 1, because he forgot to divide by the 80,000 men. But if you divide 2.5 million by 80,000, you'll find that what he really meant was odds of 30 to 1.

At some point, the authors consulted a statistician, Dr. Andrey Feuerverger, who did more calculations for them. Dr. Feuerverger added in the data for the Judah inscription and his final answer was 600 to 1 that the Jesus of the tomb is Jesus of Nazareth. I'll describe his calculations and explain why I disagree with them. [Note added: The calculations described below are those that were made public in the book The Jesus Family Tomb and in the web site for the associated documentary. These calculations are very different from those that Feuerverger ultimately published in The Annals Of Applied Statistics, but that article only became public a year later. So for most of the year 2007, nobody knew that Feuerverger's calculations were much more sophisticated than those that Simcha and Charlie were making public.]

To begin with, let's note that Simcha and Charlie apparently convinced Dr. Feuerverger that the second Mary inscription is definitely a reference to Mary Magdalene. Dr. Feuerverger is a statistician, not a historian, and he accepted their claim that the 4th century apocryphal document, "The Acts of Philip," could be relied on as proof that "Mariamenon" is Mary Magdalene. They attribute this conjecture to Dr. Francois Bovon of Harvard University, but they misunderstood him. The Acts of Philip tells of the timid disciple Philip and his bold sister Mariamne who is identified with BOTH Mary Magdalene and Mary of Bethany. (A historical impossibility, since these were two different women. Furthermore, Philip was from Bethsaida, which is several miles from Magdala, Mary Magdalene's home village. The Acts of Philip is an extremely poor source for historical data.) And note that "Mariamne" is not "Mariamenon". There is just no good reason to say that an inscription labeled Mariamenon MUST be Mary Magdalene.

As a result of this assumption that "Mariamenon" meant "Mary Magdalene", Dr. Feuerverger assigned a probability of the "Mariamenon" inscription as .625%, slightly larger than the .518% that Charlie had previously computed. The reason for the difference is not clear, but let me point out that both of them are far smaller than the correct number, which is 21.4%. This inscription "Mariamenon" is one of many forms of "Mary," just as "Ran" is one of the many forms of my legal name "Randall."

For the "Joseph" bone/box, Dr. Feuerverger used a probability of 5% (which was lower than Charlie's estimate of 14%). The reason for this was that the tomb uses the form "Yose," which is a less/common nickname for Joseph. In Charlie's original calculation, he used 14%, the probability of finding any form of "Joseph." Charlie's first guess was right. It's more correct to use 14%, since "Joseph" has a number of variants in Hebrew, including "Yehosef," "Yosef," "Yose," and others. Any one of them could refer to the brother of Jesus. In English texts of the book of Mark, this brother is called "Joses" which is an English form for "Yose". But in Matthew, this same brother is called "Joseph". It's very likely that the brother went by both names in different contexts. Just as Matthew and Mark each had to choose one of the forms of the name for this brother, so the stonemason had to choose one of the variant forms to inscribe on the bone/box. It is irrelevant whether he chose a common form or an uncommon form. It's still the same man inside the box! [Note added: This is a similar mistake to that made years earlier by Bible code enthusiasts, who inflated their odds when finding rare spellings of names like "Hitler" in their "codes." I had seen this mistake many times, so it was obvious to me when I saw it in the context of the Jesus family tomb.]

At this point, Dr. Feuerverger correctly noted that we need to have some way to quantify the fact that some of the names of the brothers of Jesus are found on the bone-boxes and some aren't. In The Jesus Family Tomb, Charlie calls this the "surprise factor." When Simcha saw that there was a bone-box with "Mary" on it, he said "Wow!" because Mary was the mother of Jesus. When he saw a box with "Judah" on it, he again said "Wow!" because Judah was a brother of Jesus. The box with the name "Yose" on it got another "Wow!" because Yose was another brother of Jesus. But Jesus had two other brothers, James and Simon. There was no box with "Simon" on it and none with "James," but Simcha did not say a negative "Wow!" when he learned that those were missing. Nor did Simcha say a huge negative "Wow!" when he saw that "Judah" was a son of "Jesus" instead of being a brother. So Dr. Feuerverger asked for some way to account for the missing "Wows". In the end, he added in a factor of 4 in his probability estimates to offset things. This factor is not explained in the book, so it's hard to analyze. However, it is similar in spirit to my computations in which I asked, "What are the odds of finding 2 out of the 3 males with names that are brothers of Jesus?" [Note added: This strange factor of 4 appears nowhere in Dr. Feuerverger's published article, which appeared a year later, so it's even more puzzling. I don't know where Simcha and Charlie got it, but they attribute it to Feuerverger. I have no compelling reason to think he had anything to do with it. But there was no way to know that when I originally wrote this article.]

In the end, Dr. Feuerverger and I came to similar estimates on the probability of finding those brothers who were actually found. He computed a 20% probability. I computed three different scenarios, and wound up using the smallest of the three, which was 24.1%. So on this issue, our conclusions are nearly identical.

There is one very important point at which my calculation differs from that of Dr. Feuerverger. I used a factor of 80,000 (the number of men in Jerusalem who might be candidates for the Yeshua of the tomb). Dr. Feuerverger used a factor of 1000 (the number of tombs in Jerusalem that might contain groups of buried people.) This is a very significant difference!

It seems clear to me that 80,000 is the correct number. We are asking how many men named Jesus lived in Jerusalem who could have conceivably had a father named Joseph and who could have been buried with five persons with a given set of names related to Jesus of Nazareth (2 Marys, 3 males with names chosen from the known brothers and disciples of Jesus).

My calculation answers the question "How many such men might have existed?" Feuerverger answers the less relevant question: "How many such men might have existed and then been buried in family tombs of the type we've found?"

But the issue of burial type is beside the point. In the words attributed to Dr. Feuerverger, we are looking for the surprise factor -- features that are known to be true of Jesus but are not true of all men. In fact, we might better call these "Jesus factors". The "Jesus factors" are those features that help us decide if the buried man might be Jesus of Nazareth. Here is a list of the various "Jesus factors" we have studied:
  • Being named Jesus
  • Being the son of Joseph
  • Having multiple close female relatives and friends named Mary
  • Having brothers James, Simon, Judah, and Joseph
  • Having disciples named Simon, Judah, Matthew, etc.
Charlie's equation and Dr. Feuerverger's equation and my equation have all tried to account for these "Jesus factors" in one way or another. We've had our differences, but we've all agreed that these are features of Jesus that are not common to all men.

In my calculations, I was interested first in asking which of the 80,000 men in Jerusalem might meet all the "Jesus factors" listed above. I found that at least 11 of them might.

I also found that the Jesus of the tomb had one "not-Jesus factor" that made it unlikely he was Jesus of Nazareth -- namely, he had a son. A "not-Jesus factor" is a feature that most men have that Jesus very likely did NOT have.

Not all features are "Jesus factors" or "not-Jesus factors." There are some features that are simply irrelevant, such as being left-handed, or being taller than six feet. We have no knowledge about Jesus that says he was either left-handed or right-handed. We have no knowledge of him that says he was tall or short. If we found that the Jesus of the tomb were left-handed or six feet tall, that would not change our calculations at all, because these are features that do not DISTINGUISH between Jesus and other men. We can call these "neutral factors" because they can't enter in the calculation at all.

Please note that "being buried in a family tomb" is neither a "Jesus factor" nor a "not-Jesus factor." We have no information on whether the family of Jesus was more or less likely to have a family tomb than other families in Jerusalem. So this is a "neutral factor" and can not possibly change the probability of whether the Jesus of the tomb is Jesus of Nazareth. [Note added: After I published this article, archaeologist Jodi Magness posted an article on the Biblical Archaeology Society web site arguing that in fact, being buried in a rock-cut tomb is a "not-Jesus" factor. Assuming that Jesus's body was removed from the temporary tomb provided by Joseph of Arimathea, Magness argues that it is unlikely to have ended up in a rock-cut tomb. I find her argument reasonable, so in my later articles I took account of this.]

In Dr. Feuerverger's calculations, he has effectively added a factor that is irrelevant -- being buried in a family tomb. There is no reason to believe that the family of Jesus of Nazareth was more likely to have a family tomb than other families. There is no reason to add this extraneous factor.

Finally, I will note that Simcha and Charlie and Dr. Feuerverger have not accounted for the historical implausibility of Jesus having a son. Simcha tried to make a case that Jesus MIGHT have had a son. He made some interesting arguments, and I have to admire his creativity. For example, he argued that "the disciple whom Jesus loved" mentioned in the gospel of John was actually this "Judah, son of Jesus."

That's very interesting, but it can't possibly work. John 21:20-24 makes clear that "the disciple whom Jesus loved" was a man who outlived Peter and the other disciples and who ultimately was the authority behind the gospel of John. The gospel of John is dated by virtually all scholars, liberal or conservative, to AFTER A.D. 90. The problem is that "Judah, son of Jesus" died and was buried BEFORE A.D. 70 and wound up in the family tomb. He could NOT have been "the disciple whom Jesus loved."

It is interesting to note that Dr. Feuerverger has posted comments on his web site that make it clear he makes no claims to be a Biblical scholar and merely used the linguistic data he was given at face value. [Note added: These comments are no longer on his web site.]  It's clear that he puts far less stock in the results of the calculation than do Simcha and Charlie. From his point of view, they gave him certain assumptions and he made the calculation based on those assumptions.

I've said this before, and I'll say it again right now. It is silly and counterproductive to throw accusations of bias at Simcha and Charlie and their coworkers on the book and documentary. They've shown a great deal of courage and tenacity in pursuing an interesting question far longer than most people would have. I believe their conclusions on the identity of the Jesus of the tomb are incorrect. But I wish everyone showed as much interest in Jesus of Nazareth as these folks have shown. Whatever you may believe theologically about Jesus of Nazareth, he was a great man, a man worth studying. [Note added: The above comments reflect my opinion of Simcha Jacobovici in 2007, after reading his book. I'm quite a bit less charmed by him now after seeing his responses to the many problems that people have pointed out in his tomb hypothesis over the years.]  

The bottom line is this: Jesus of Nazareth is EXTREMELY UNLIKELY to be the Jesus found in the family tomb. My estimate is that the odds are at least 10,000 to 1 AGAINST Jesus of Nazareth being the man found in the tomb. [Note added: As I've mentioned above, in my later calculations, I've changed some of my assumptions. So I would amend this estimate to say that I consider it hard to get a probability of more than about 2% that this is the authentic tomb of Jesus.]

If you liked this article, you may enjoy reading the sequel, Bayes' Theorem and the "Jesus Family Tomb", in which I refine the calculations using Bayes' Theorem. I wrote this article on March 26, 2007, after some weeks of intensive discussions with Jay Cost and a number of other experts around the web.

Useful Links

If you want to read more about the alleged Jesus family tomb, check out these pages, which I have listed in roughly chronological order:

  • The web site created by Simcha Jacobovici and company to provide evidence alongside the documentary and book.
  • The "Tomb Evidence" PDF file that was originally posted on the web site of the Discovery Channel, summarizing Simcha Jacobovici's evidence for the tomb. This PDF file contains a page title "Statistics Overview" that claims to represent the calculations of Dr. Andrey Feuerverger. A year later when Feuerverger's article was published in The Annals Of Applied Statistics, it became clear that Jacobovici had badly misrepresented Feuerverger's work. 
  • Prof. Ben Witherington's blog. Dr. Witherington is a New Testament scholar who wrote the book on the famous ossuary that reads "James, son of Joseph, brother of Jesus".
  • Prof. Mark Goodacre's blog at NT Gateway. Dr. Goodacre is a well/known New Testament scholar and he's done a fair and even/handed treatment of the subject.
  • Jack Poirier's article on "The Statistics Behind The Tomb"
  • Randy Ingermanson's first simple spreadsheet analysis of the statistics of the tomb, which appeared on March 3, 2007
  • An article by Dr. Jodi Magness, "Has the Tomb of Jesus Been Discovered?," arguing that the family of Jesus of Nazareth is unlikely to have owned the family tomb in East Talpiot that has been called the "Jesus family tomb. Prof. Magness teaches at the University of North Carolina, Chapel Hill, and specializes in Early Judaism.
  • Dr. Michael Heiser's web site. Mike wrote a paper on the Jesus family tomb ossuaries back in 2003, when few other people were looking at the subject. Mike has a Ph.D. in Biblical Hebrew and Semitic Studies and I've known him since the bad old days when the Bible code was hot.
  • Prof. James Tabor's blog. Dr. Tabor is another well/known Biblical Studies scholar, and he's argued strongly that the evidence in favor of this being the tomb of Jesus of Nazareth is a lot stronger than most people are giving credit.
  • Randy Ingermanson's second, more complicated spreadsheet analysis of the statistics of the tomb, which appeared on March 26, 2007
  • The technical article by Jay Cost and Randy Ingermanson using Bayes' Theorem to analyze the tomb, posted on March 26, 2007
  • Stephen Pfann's article on "The Improper Application of Statistics In The Lost Tomb of Jesus"
  • Stephen Pfann's article "How Do You Solve a Problem Like Maria" analyzing how often the New Testament writers use the names Maria and Mariam.
  • Stephen Pfann's article "Yoseh Can You See?" analyzing the occurrences of Yoseh and Yehosef in the original sources.
  • The Codex blog of Prof. Tyler Williams has been following the story with interest and has a good collection of links. At the time the controversy erupted, Dr. Williams was the chair of the Religion and Theology Department at Taylor University College in Edmonton.
  • Francois Bovon has posted a short article on the SBL web site clarifying his position on the identification of Mariamne with Mary Magdalene.
  • Jay Cost has written a nice summary article on the Jesus family tomb. Jay was the first to bring in Bayes' Theorem to the discussion.
  • Dr. William Dembski, famous for his work on Intelligent Design, has written an article on "The Jesus Tomb Math" which you can find on his Design Inference web site. The article is co/authored with Robert J. Marks II.
  • Kevin Kilty and Mark Elliott have written an article using Bayes' Theorem that analyzes the tomb using a simple model. Their probability estimate ranges from about 6% to about 48%, depending on which assumptions they make.
  • Prof. Andrey Feuerverger's article in The Annals of Applied Statistics summarizing his original calculations.
  • Randy Ingermanson's discussion article in The Annals of Applied Statistics responding to Feuerverger's article.
  • The other referees' discussion articles in The Annals of Applied Statisticsresponding to Feuerverger's paper.
  • Feuerverger's response to the referees in The Annals of Applied Statisticsin which he said clearly that he does not believe that his original calculations are statistically significant.
  • Randy Ingermanson's calculations posted as a supplement on the web site of The Annals of Applied Statistics estimating that the tomb has less than a 2% probability of being authentic.

I'm sure I've forgotten (or missed) some of the important sites around the web, but the above will get you rolling in your quest for more info.

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