Application of the Limited Enthusiasm Model with Demographics

Membership data for the Southern Baptist Convention (SBC) in the USA from 1980 to 2012 was fitted to the Limited Enthusiasm Model of Church Growth. The results showed that the denomination had been growing up to the 21st century in revival growth mode. However, since 2006, it has declined in a way inconsistent with its previous growth. That is, the decline cannot be described as a natural consequence of its prior growth, such as the overshoot phenomena that can happen with revival growth. At least one of the parameters must have changed since 2006 for the data to fit the model. Either the enthusiasts have become less effective, with fewer conversions; or people are leaving in greater numbers, perhaps to other types of churches; or society is becoming more hardened to the SBC. Although birth rates are falling, this is not sufficiently fast enough to explain the drop in membership as a cohort effect alone.

Membership 1980-2012

Membership figures for the SBC from 2004 were obtained from the Southern Baptist Annual Reports. Earlier data were obtained from the now-defunct who use a variety of published sources. From 1950 membership has increased until 2006, although that increase had been slowing since the mid-1980s (figure 1). Since 2006 the membership has declined sharply.

Figure 1: SBC Membership 1950-2012

Given people attend church for some time before joining, and stay on membership roles for some time after they stop attending, the membership figures probably reflect an attendance pattern of a few years earlier.

The USA population data were obtained from the US Census. As a fraction of the total population, the SBC peaked in the 1980s (figure 2). Since then, it has not kept pace with demographic changes. The falling birth rate would work against it, whereas the rising immigration rate is unlikely to help as immigrants may not be a large source of recruitment for most SBC churches which lie outside of big cities.

Figure 2: SBC Membership as Percentage of USA Population 1950-2012


The data was compared with the General Limited Enthusiasm Model, which assumes growth is driven by a subclass of church members, called enthusiasts, who eventually lose their potential to reproduce themselves through the conversion of unbelievers. Data was fitted from 1980 to prevent earlier trends dominating over later ones. Some of the changes from previous decades may reflect societal changes. Such changes are outside the scope of the model. Data fitting was stopped in 2006 so that the model’s membership predictions for subsequent years could be compared with what actually happened.

A best-fit between model and data gives a value for the reproduction potential and the two thresholds of extinction and revival growth. Many such “best fits” were obtained for a variety of initial values of enthusiasts and hardened unbelievers, as their values cannot be measured. From that range of “best fits” the distance between each threshold and the reproduction potential was examined.

Other parameters are determined as follows:

  • Birth and death rates were taken from figures published by the US Census. Changes in these rates over the period are built into the model. Migration has not been accounted for as it is unclear what fraction of immigrants would be potential converts for the church.
  • The leaving (reversion) rate was estimated at 5% per year, typical of figures that were obtained by data fitting to a variety of churches (see A General Model of Church Growth and Decline). It should be noted that small variations in this figure have little effect on the likelihood of extinction or survival.
  • Retention of children born to church members was taken as 50%. This figure was deliberately set higher than the 30% estimate for the UK as Christian family life in the USA appears stronger than that in the UK.
  • The average time taken for a leaver to be open to returning to church again was taken as 20 years, same as the UK as there is no reason to believe this process is radically different between the two countries given the similarity of cultures.


All the best fits show the church well above the extinction threshold and above the revival-growth threshold for at least the 1980s. However most best fits show that revival growth had stopped by the first decade of the 21st century. Subsequent behaviour shows the growth of the church slowing leading to a small decline due to overshoot. The church membership numbers would eventually settle to an equilibrium value but on a timescale much longer than the validity of the parameters, and the simulation. Thus the growth of the SBC was expected to come to an end by 2006 which confirms a similar result in A General Model of Church Growth and Decline.

A pessimistic data fit, where the SBC ceased revival growth in 1990, can be compared with an optimistic fit, where it only just ceased revival growth in 2006. Figure 3 compares two such fits with the data. There is little to choose between the two scenarios based on the data from 1980 to 2006. However extrapolating from 2006 onwards the optimistic scenario shows growth continuing, due more to demographics than revival growth. The pessimistic fit shows the decline due to the overshoot caused by the earlier growth, an effect due to people continuing to leave the church in large numbers when growth has slowed. Even the pessimistic fit is well above the actual data.

Figure 3: Best Fit to SBC Membership 1980-2012

Comparing the data with the pessimistic fit (figure 3) it can be seen that the actual decline in membership after 2006 is much faster than the rise before 2006. The data is not symmetrical, which implies another effect has been increasingly important from 2006 that is causing the decline. Variations in birth and death rates can be excluded as these are built into the model. They do not change fast enough to account for such a decline. Including immigration would only make the difference between the data and the model greater.

Three explanations are suggested:

  1. The leaving rate from the church has been increasing since 2006. If the rate steadily increased from 5% in 2006 to 5.8% in 2012, then this is sufficient to explain the data. A higher leaving rate could be due to people switching to more contemporary churches, or even to more liberal churches. As contemporary churches are growing and liberal churches are declining faster than the SBC, changing to the contemporary is more likely.
  2. There has been a fall in reproduction potential from 2006. This could be due to a lack of confidence among members of the SBC undermining their witness, or an increasing sense of intimidation by non-Christian society.
  3. An increasing number of the non-SBC population (society), has become more hardened to the SBC. This might be potential converts from unbelievers or potential switchers from other Christian churches. Either way, a greater proportion of non-SBC people are hostile to the SBC.

The decline could be a combination of all three effects.

If the reproduction potential continues to drop at the rate suggested by the recent data, then the effect on the SBC membership figures will be dramatic (curve 2. figure 4). The church will drop to under 12 million by 2025, well below its 1980 membership. If the decline is due to a rising leaving rate (curve 1, figure 4), or an increasing hardening rate of potential converts (curve 3, figure 4) the decline is likewise dramatic. Thus, if the SBC is not to see a serious decline, the source of its drop in membership figures needs to be identified and dealt with.

Figure 4: Scenarios to Explain SBC Decline


Figure 5 compares the reproduction potential (line 3) with the extinction threshold (line 2) and revival growth threshold (curve 1), for the pessimistic scenario. The revival growth threshold rises as the numbers of potential converts fail to keep pace with demographics, due to conversion, and due to people becoming hardened to the Christian message. After 1995 the reproduction potential is under the revival growth threshold, and growth then slows to a halt. Up to 2006, the reproduction potential is well over the extinction threshold (line 2).

Figure 5: Reproduction Potential compared with Extinction and Revival Growth Thresholds

If the parameters do not change, then stability would be achieved with revival growth threshold matching the reproduction potential. However, the data from 2006 suggest one or more parameters have changed.

  1. If the leaving rates continue to rise, the extinction threshold will increase, and the church’s decline will be one that will eventually head to extinction (figure 6), similar to the more liberal denominations in the USA. (Note curve 2 is rising towards line 3, thus the gap to extinction narrows.)
  2. If the decline is called by falling reproduction potential, then it will eventually fall below the extinction threshold, and the same scenario for the SBC will result but quicker (figure 7). (Note curve 3 drops dramatically, towards curve 2.)
  3. If the scenario is that society is becoming more hardened (figure 8), then although extinction is technically avoided, the stable level for the church is very small, in the thousands across the USA. In reality, issues with the low density of the denomination and small congregations (not in the model) would reduce the reproduction potential and the church would become extinct.

The timescales of these events go past the end of the 21st century. Although this is outside the model’s time horizon, it gives a flavour of the seriousness of the decline.

Figure 6: Reproduction Potential & Thresholds, Increasing Leaving Rate Scenario
Figure 7: Reproduction Potential & Thresholds, Decreasing Reproduction Potential Scenario
Figure 8: Reproduction Potential & Thresholds, Increasing Hardening Rate of Society Scenario