Were the gospels written by eyewitnesses? A statistician’s approach

What has statistics to do with the Christian gospel?  Even as a long-time Christian and professional academic statistician, I struggled with this question when challenged to relate my academic discipline to my faith. After a good deal of pondering, I reflected on how we use statistics in society as evidence for / against decisions that we make.

What is statistics?
If something always happens, then we do not need statistics.  If we do A and B always follows, we have a straightforward deterministic causal relationship.  However, most systems (especially if they involve humans) are not like that. If I have a bad headache – mercifully rare – I take paracetamol and it goes.  Another person might find that paracetamol is not very effective and prefer a different painkiller.  Both painkillers are effective on average, but not in every case, so there is uncertainty.  This uncertainty can make the patterns hard to see or suggest patterns that are not there. Statistical analysis or modelling uncovers the patterns that are there and eliminates those that are not.
Statistical literacy is the ability to understand and reason with statistics and data. It is necessary for all of us to understand material presented in newspapers, on television, and on the Internet. For scientists, statistical literacy is important in order to produce rigorous and reproducible research.
We understand that if we are not statistically literate, we can be taken in by tricks like changing the scale of graph axes to make changes seem bigger than they are, or take figures out of context, like the infamous £350m per week for the NHS on the bus.
Nevertheless, done well, statistics is a lifesaver; it can help me and my doctor decide which medical treatments are likely to be effective for my particular condition.

Statistics can:
•    Evaluate alternative hypotheses
•    Incorporate existing knowledge or prior beliefs
•    Identify if distributions are the same
•    Identify if differences are significant
•    Analyse data
•    Make use of metadata
•    Take account of the context of data collection
•    Identify and guard against bias
•    Investigate causality & correlation
•    Consider ethics, probability in court cases

The type of evidence statistics provides typically includes whether one medical treatment is more effective than another,  if life expectancy is under different circumstances, whether one policy is more effective than another, early warning systems under uncertainty (e.g. will this volcano erupt?), subgroup analysis (e.g. Herceptin is not very effective for breast cancer on average, but for HER2 receptor positive breast cancer it is very effective).

What can statistics tell us about the gospels?

Can we harness the power of statistics in relation to the Christian gospel? Let’s consider two hypotheses:

The primary source documents – the four gospel accounts, Matthew, Mark, Luke & John – are
a)    eyewitness accounts
b)    fabrications

It is important, firstly, to note that scholars agree that the four gospel accounts were not written in the locality of the events, but in Syria, Rome, Asia Minor. The book of Acts is an account of the early Christian church after Jesus’s death, which we can also examine.

How shall we test these hypotheses?  What is our data?
•    Gospels themselves
•    Other writings from the era
•    Geography
•    Botany
•    Agriculture
•    Climate
•    Archaeology

Evidence from names
Now, we all know that babies’ names go in and out of fashion.  We can often guess a person’s age by hearing their name. First, consider names given to babies in the UK between 1996 and 2017.

With this information, we can assess how likely a person is to have been born in the UK between 1996 and 2007. No one in my class at school was called by any of these names (we had more John, Charles, Sally and Susan).  Other countries have different names. In addition, the popularity of names vary by region, too. We can use known patterns to compare with new patterns and see if they are the same or different.
So what about personal names in the Bible era? There is some relatively recent research on popular names to draw on. The Lexicon of Jewish Names in Late Antiquity: Part I: Palestine 330 BCE-200 CE1 includes names from literary sources as well as those found in epigraphic and papyrological documents. The lexicon is accompanied by a lengthy and comprehensive introduction that scrutinizes the main trends in name-giving at the time. In his book Jesus and the Eyewitnesses: The Gospels as Eyewitness Testimony2, Richard Bauckham draws on this research and compares this data with data from the gospels and Acts. Here is the data showing how common names were in different sources.

Now we have this data, we can ask whether the names given in the Gospels and Acts have a similar distribution to the names we find elsewhere in the region for the same period.  

The pattern for the women’s names are less clear because there are fewer of them mentioned, but still the match is pretty good.
Now we see that we have:
•    Pattern over 4 different writers and 5 books (Luke wrote Acts)
•    Strong correlations throughout
•    Statistical significance where sample size is large enough
•    Books individually also reflect the same pattern
Perhaps this is just a reflection of Jewish culture wherever it is found.  After all, Jews have a common history, the same historic heroes, culture and other influences.  We can compare the most popular male names given to Jews in Palestine with those given to Jews in Egypt.

What do we see?
•    Some similarities
•    Significant differences
•    Writing from abroad, 4 writers of 5 books reflect the distribution of names in Palestine

The clue's in the name: disambiguation
Disambiguation also offers some evidence.  Whenever names become very popular, people are referred to with full names or nicknames so it is clear which person is being talked about.  Does this happen in the gospels?  Are the names we now know to have been popular the same as those who, in the gospels, have disambiguation applied to their names?
Simon is the most popular male name and in the gospels we see people referred to as Simon Peter, Simon the Zealot, Simon the Leper, Simon of Cyrene, Simon the Tanner and so on.  Similarly, Mary is the most popular female name and we see people referred to as Mary Magdalene, Mary the mother of Jesus, Mary the mother of James and Joseph, Mary whose brother was Lazarus, Mary wife of Clopas and so on.
There is also evidence in the way in which people are referred to by a narrator and when speech is recounted. For example, John is the 5th most popular male name.  In the account of John the Baptist’s execution, the narrator refers to him as ‘John’ but when he reports the request of Herodias’ daughter, he records her asking for the ‘head of John the Baptist on a platter’.  It was necessary for her to specify John the Baptist, as there would have been many Johns at the party and it was important to clarify whose head was being requested.
A similar pattern is observed with Jesus, the 6th most popular male name: in narration, Jesus is called Jesus, but in reported speech, Jesus of Nazareth, Jesus called Christ, etc. Other writings about these events, not included in the Bible, do not disambiguate in this way.  
What does this tell us?  We know that names are hard to remember and yet we see the gospels have the pattern of names we would expect if they are reporting what real people from Palestine said and did. This pattern is too complex for an ancient forger to reproduce (let alone four of them).  This strongly supports the hypothesis that the gospels are eyewitness testimonies.

Evidence from places
However, personal names are not all we have. Even in today’s era of Google Earth and Tripadvisor, there is nothing like having been to a place to notice some details you may not think to write in a review.  For example, on a visit to Venice, I was taken aback by the narrowness of the streets, combining with tall buildings which gave a tunnel-like feel to the route that opened up into the magnificent Piazza San Marco – “narrow streets” just doesn’t capture it.  
In the gospels there are written details about places, including the small, less important places, help to verify that the writer is writing from personal experience or under the direction of someone who with personal experience.
What do we find in the four gospels about the towns mentioned?

Other writings about these events, not included in the Bible mostly mention just Jerusalem, the capital city and therefore well known throughout the region. The mention of place names (not just towns) in the Gospels is remarkably consistent at 4.6-4.9 per 1000 words;  other writings about these events, not included in the Bible, mention places less often and with more variation. The gospels also record incidental details about locations e.g. Capernaum by the sea, the names and proximity of hills, rivers, and travel times between places – all of which can be checked.  It is also notable that the gospels mention tiny villages, not must-see places.
Using the other writings about the events in the gospels as controls we find the four Christian gospels feature the inclusion of relevant details which strongly suggests writers told things as they happened in real time and space. Forgers would find it difficult to get this pattern the same across four gospel books.
There is more, such as the record of Zacchaeus climbing a sycamore tree in Jericho (Luke 19), when the distribution of sycamore trees included Jericho, but not Turkey, Greece, Italy, Palestine, Egypt. The most natural explanation Luke went to Jericho or spoke to someone who had been there.
The four narratives of the feeding of the 5000, one in each of the gospels, each record differing incidental details, which combine to make a coherent whole.  Attention to small details suggests reliability of main details.Other incidental details in the gospels include the shape of houses, coins, social stratification, the shape of the Temple and religious settings.

If the gospels result from conspiracy or incompetence, this is not what we would expect.
If the gospels were produced on the basis of stories several steps removed from eyewitnesses, this is not would you expect.
If the gospels were based on eyewitness testimony, this is what you would expect.

Statistics helps us to assess the efficacy of medical treatments, and on that evidence, we decide to use the treatment.  If the evidence for the gospels being eyewitness testimony is so strong, shouldn’t we at least read them?

Further reading:


Can We Trust the Gospels?, Peter J Williams

1 Tal Ilan (2000) Lexicon of Jewish Names in Late Antiquity: Part I: Palestine 330 BCE-200 CE
2 Richard Bauckham (2017) Jesus and the Eyewitnesses: The Gospels as Eyewitness Testimony, Second edition
3 Peter J. Williams, New evidence the Gospels were based on eyewitness accounts (https://www.bethinking.org/is-the-bible-reliable/new-evidence-the-gospels-were-based-on-eyewitness-accounts)