History in the Bible Podcast

How Fast Did Christianity Spread in the Roman Empire?

Podcast Episodes: Season 3.

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On this page I present my one and only original contribution to biblical studies. Everything in my podcast rests on the scholarship of many, many others; who are all way smarter than I am. Now I get my own chance at academic fame. Wish me luck!

The issue is: how fast did the Christian population grow in the Roman empire?

I say the historians have it all wrong. I am here to show them the error of their ways.

Christian Growth in the Roman Empire

Many scholars have made rubbery estimates of the population at various times in the empire. Some examples from two sources are presented in the table below. One is a formal estimate by Rodney Stark, who was an influential sociologist of religion. The other is an informal estimate by Bart Ehrman, a scholar in New Testament studies at the University of North Carolina at Chapel Hill.

I have converted absolute numbers to proportions/percentages of the imperial population using the common scholarly educated guess that the Roman empire contained about 60 million people, from about 100 to about 400 AD/CE.

These estimates are as good as any, so let's roll with them. Given this data, how fast did Christianity grow?

Year Stark's Estimate of Number of Christians Proportion of the Roman empire Christian Ehrman's Estimate of Number of Christians Proportion of the Roman empire Christian
100 8,000 1 in 10,000
150 40,000 7 in 10,000 36,000 6 in 10,000
200 220,000 35 in 10,000 155,000 26 in 10,000
250 1,170,000 2% 680,000 1%
300 7,500,000 12% 3,000,000 5%
315 10,200,000 17%
400 29,500,000 49%

The Historians Get It Wrong: Exponential Growth

All scholars, including Stark and Ehrman, take it for granted that the growth of the religion can be modeled by an exponential growth function.

We all know what exponential growth is. It's what happens to your money in the bank: compound interest. Say you start with $1000 in the bank, and the bank gives you 10% interest each year (lucky you!). Then at the end of year one, you will have $1,100. At the end of year two, you will have $1,100 plus 10% of $1,100 ($110), for a total of $1,210. That's exponential growth.

A great thing about exponential growth is that it needs only two numbers to describe how something grows over time: the amount there is now, and the growth rate. In the human world, growth rates are often defined as annual rates, but you can use any time period you like. Growth rates of bacteria could be defined as per hour or per day.

After much humming and hawing, Stark thought that the growth of the Mormon religion in modern times could provide estimates for Christianity's growth in the Roman era. He decided that, like the Mormons, Christianity grew at a rate of about 3.5% per annum in the Roman empire.

The chart below shows Christian growth according to Stark, at a rate of 3.5% per annum.

For reasons that will become clear soon, the y-axis is not absolute numbers of people, but proportion of the population that is Christian. Stark's figure of 3.5% refers to growth in absolute numbers, not growth in proportion of the population. I designed the chart to fit Stark's estimate of about 12% of the Roman population as Christians in the year 300 (from the table above).

The wrong way to investigate the growth of Christianity is by using the common exponential growth model.

The wrong way to investigate the growth of Christianity is by using the common exponential growth model. This curve is constructed to fit Stark's data point of about 12% of the Roman population as Christians in the year 300.

An aside: The curve looks the same everywhere

Before we move on, have a look at the growth from the 100 to 320, in the green box in the chart above. Looks very different to the rest of curve, right? That is only an illusion! In the chart below I zoom in. The curve is the same shape as the long term curve. One of the properties of an exponential curve is that, no matter how much you zoom in, the curve always looks the same.

Zooming in on the early years of growth. The curve is the same shape.

Zooming in on the early years of growth. The curve is the same shape as the curve above.

The big problem: the exponential model leads to stupid results

You can see the big problem from the first chart. With a simple exponential growth model, Christians end up as 110% of the Roman population by the year 370, and 1,600% of the population by the year 470. Ooops! The historians admit it all gets rather silly, but then brush if off. Ehrman makes a heroic effort to avoid awkwardness by juggling his hypothetical growth rates over time.

Garry Gets It Right: Innovation Theory's Model of Logistic Growth

I can fix the silliness. The historians are simply using the wrong model for Christian growth.

A much better model comes from innovation diffusion theory, which uses what we call a logistic model. This has only been around for 60 years. This may explain why biblical scholars have missed it.

As its name implies, innovation diffusion theory attempts to explain how new ideas and technologies spread. The logistic model used provides excellent descriptions of many phenomena, such as the adoption of mobile phones or dishwashers. It is also widely used in biology. Here are some examples from the USA.

It is obvious to me that the logistic model is the one to use for the spread of the religious innovation that was Christianity.

A logistic curve looks like a lazy-S, as shown below.

The logistic model has several differences to a simple exponential growth model:

  • Growth is expressed as a proportion of the population, not as absolute numbers.
  • Growth has a natural upper limit (called the carrying capacity). This may be less than 100% of the population (but never more!). Not everyone wants a mobile phone, or a dishwasher, or to become a Christian. The logistic equation prohibits growth from becoming more than the carrying capacity. That immediately eliminates the embarrassments of the historians.
  • Growth begins as exponential. As an innovation spreads and climbs towards the population's carrying capacity, growth slows down, and becomes linear. Finally, growth becomes a negative exponential curve. This produces a lazy-S curve.
  • A logistic growth curve cannot be described by a single number. In a logistic model, it makes no sense to say that a population is growing at so-and-so per cent per annum.

Here are some examples of technologies spreading through the US economy. They all show logistic growth.

Examples of logistic growth in innovations.

Examples of logistic growth in innovations.

Christians did not grow like money in a bank account. Christianity was an innovation, and diffused in the Roman population much as predicted by innovation diffusion theory.

First attempt: Using Stark's data

In the chart below, I fitted a logistic curve to Stark’s estimate of about 12% of the Roman population as Christians in the year 300. I guessed that at most 90% of the Roman population was susceptible to Christian conversion. This becomes the Christian carrying capacity of the empire.

In this model from Stark's estimates, the empire is about 50% Christian by the year 330, 20 years after it was legalised. Christianity hits saturation about the year 400.

Logistic curve to fit Stark's data point.

The right way to investigate the growth of Christianity is by using a logistic growth model. This curve is constructed to fit Stark's data point of about 12% of the Roman population as Christian in the year 300.

Second attempt: Using Ehrman's data

Let's have another go. This time I make a curve to fit Ehrman's estimate of an empire that is 50% Christian in the year 400. In this model, Christianity hits saturation about the year 500.

Logistic curve to fit Ehrman's data point.

This curve is constructed to fit Ehrman's data point of about 50% of the Roman population as Christian in the year 400.

Conclusion: Logistic Is The Way To Go

You can choose your data points and growth rates as you wish. We have so little actual data to work from. But regardless, the best way to model the growth of Christianity in the Roman empire is to use the logistic growth model from innovation theory.

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