Tuesday, 27 June 2017

Church Growth Limited by Evangelistic Purity

Limits to Church Growth 4

In three previous blogs I have looked at congregational growth being limited by:
      I.     Demand from society [1];
    II.     Supply by the church [1];
  III.     Lack of enthusiasts [2];
  IV.     Inadequate resource production [3].

When congregational growth stalls and appears to hit a limit, the obvious question is to ask “why?”. In particular, has growth ended because of factors within the church, or factors in society? If there are no internal limits to growth then society will always eventually hinder growth, limit (I) above. However churches often cause their own growth barriers, not evangelising enough, (II); have enthusiasts, the evangelisers, who cease to be effective, (III); or not generating enough resources in the church to attract, disciple and retain people, (IV).

Church congregations are a mixture of people, some are enthusiasts, wanting to reach people and see them converted. However some are inactive in conversion, preferring to spend their time on other aspects of church life, worship, socials, good works and the like. The balance of people in the church determines its culture. Thus I will put forward the hypothesis:

The balance of enthusiasts and inactive believers in the church determines the evangelistic effectiveness of the church.

I will call this effectiveness the church’s evangelistic purity, and propose the conjecture:

Falling evangelistic purity will limit the congregation’s growth, regardless of the size of society.

The Model

The model to represent this situation is given in figure 1. People are converted to church from outside. The cloud in the left hand of the diagram represents and unlimited supply of potential converts [4]. The reinforcing loop R1 captures the action of the enthusiasts, the more enthusiasts the more converted, thus even more enthusiasts. I have assumed all new converts become enthusiasts first. Enthusiasts do not stay active in evangelism indefinitely, thus they become inactive after a fixed duration, balancing loop B1.

Figure 1: Evangelistic purity model of church growth

Following the hypothesis, the conversion rate for each enthusiast depends on the evangelistic purity of the church. If the number of enthusiasts increases then the evangelistic purity of the church also increases. This reinforces the growth of enthusiasts, R2. However the more inactive believers the lower the evangelistic purity; a balancing loop resisting the growth of enthusiasts B2. If B2 is large enough then church growth will stop.


A simulation of the model, for a given conversion rate, duration enthusiast, and ratio of enthusiasts to inactive in the church, is given in figure 2 [5]. Church numbers are the sum of the enthusiasts and the inactive believers.
Figure 2: Falling evangelistic purity results in a limit to church growth

 A church of 30 people grows rapidly over 40 years, but is limited to just over 200 people as its evangelistic purity has fallen, figure 2. This limit is reached even though the pool of potential converts is infinite. It is a purely church induced limit, not affected by society.  Looking at the two types of believers, it can be seen that although the number of enthusiasts rises, their growth eventually slows as they become increasingly ineffective in a church becoming dominated by believers with no interest in evangelism, figure 3. Enthusiast numbers peak and afterwards fall away.
Figure 3: Falling evangelistic purity results in enthusiasts who are unable to reproduce themselves indefinitely

Analysing the cause of the changes in enthusiast numbers shows that it is the impact of the loop B2 that causes their numbers to fall and eventually halts church growth. Impact is a measure of the extent to which a feedback loop influences the curvature of the graph [6]. Figure 4 shows the regions of loop dominance on the enthusiasts.

Figure 4: Periods of loop dominance on enthusiast numbers

Enthusiast growth initially accelerates due to R1, their rising numbers, and R2, the influence of the enthusiasts on evangelistic purity, figure 4, first phase. The growth slows due to the generation of inactive believers, B1, and their negative effect on evangelistic purity, B2, second phase. Loop B2 becomes so powerful it causes the number of enthusiasts to change from growth to decline as conversions fall below the loss of enthusiasts. This is the third phase.

The decline in enthusiasts becomes faster, reinforced by falling conversions R1 and R2, the fourth phase. Decline finally slows as the remaining enthusiasts drain away, loop B1.

Thus the conjecture is demonstrated, falling church purity limits church growth, because the negative effect of inactive believers limits the generation of enthusiasts.

Tipping Point

So what can be done to remove this barrier to growth? There are three possible strategies:
1.     Increase the effectiveness of the enthusiasts;
2.     Increase the duration new converts remain enthusiastic;
3.     Have a church that has a greater balance of enthusiasts to inactive.

Applying any of these three strategies raises the limit to the congregation’s growth, due to a larger generation of enthusiasts. Figures 5 and 6 show the effect of increasing the initial purity of the church, the ratio of enthusiasts to inactive. Purity 1 is the lowest; Purity 5 the highest. Thus the more evangelistically pure churches are able to reach a higher limit to growth than the impure ones.

Figure 5: Effect of increasing initial church purity on church growth
Figure 5: Effect of increasing initial church purity on growth of enthusiasts

There comes a point if the purity is increased further, church growth continues indefinitely, curve Purity 5, figure 5, because enthusiasts continue to be generated, figure 6. Thus a sufficiently pure congregation can remove this barrier to church growth, and concentrate on the other barriers that come into play, not included in this model. It is good to know some growth barriers can be removed.

One way to raise church purity is to allow the inactive to leave. It sounds counter-intuitive, but if church leaving increases, church growth increases, as long as it is the evangelistically inactive that leave. This is an example of Kelley’s hypothesis that a stricter church is stronger and thus more likely to grow [7].

The principle of evangelistic purity encouraging growth can apply across all churchmanships, not just conservative or evangelical ones, as purity refers to participation in the mission and recruitment to the church, rather than theology as such. It may be possible to show that certain theologies are more likely to encourage evangelistic purity, particularly ones that see the need for personal salvation. But that takes us beyond this simple model, which shows that having enough people in the church committed to evangelism can remove a barrier to church growth.

References & Notes

[1] Limits to Church Growth – Part 1.  Lack of Supply & Lack of Demand.

[2] Limits to Church Growth – Part 2. The Reproduction of Enthusiasts.

[3] Limits to Church Growth – Part 3. Inadequate Resource Production

[4] An overview of system dynamics is given by the System Dynamics Society

[5] It is normal to use computer simulation to produce results of system dynamics model, though not always essential. The results of the evangelistic purity model can all be proved mathematically. In this blog the graphs were produced By the Stella Architect software, ISEE systems, https://www.iseesystems.com/

[6] The concept of loop impact is related to the concept of force in Newtonian mechanics. See:
Hayward J. (2015). Newton’s Laws of System Dynamics. Presented at the 33rd International Conference of the System Dynamics Society, Cambridge, MA, July 2015.
Hayward J. & Boswell G.P. (2014). Model Behaviour and the Concept of Loop Impact: A Practical Method. System Dynamics Review, 30(1), 29-57. DOI: 10.1002/sdr.1511  

[7] Kelley D. (1986). Why Conservative Churches are Growing: A Study in the Sociology of Religion. Mercer University Press.

Monday, 29 May 2017

Church Growth and the Perils of Second Order Feedback

Feedback is the process where an action has an effect, which in turn changes the original action. Either it magnifies it ­– reinforcing feedback; or it corrects it – balancing feedback. In the last blog I showed how such feedback loops affect the growth and decline of the church, where changes in the size of people groups within the church feed back on its growth and decline processes [1].

For example, consider the enthusiasts – those responsible for recruiting new people to church. The more enthusiasts, the more converts recruited, thus even more enthusiasts – reinforcing feedback with accelerating growth. This is an example of first order feedback – that is, it only involves one stock – the enthusiasts in this case. A stock is an accumulation – taking time to increase or deplete. Populations are stocks, and first order feedback means they directly change themselves: short-term changes, those up to a couple of generations. Church growth and decline is mainly governed by such first order feedback [2].

Second Order Feedback

Second order feedback involves two stocks. A change in a population stock, like church, affects another stock, before it comes back to change the original population through accumulation or depletion. The “peril” of this second order effect is that the feedback process has inertia, meaning that there is a delay in the feedback process, either magnifying, or regulating, the population changes. This feedback introduces long-term changes that are very hard to control [3]. The following example from church dynamics will illustrate this.


When a new church or movement starts, it is normally quite small, free of centralised control, and spiritually lively. They are often in the hands of people where growth and spiritual purity are to the fore, and they grow rapidly, generating many people who operate in the same unfettered manner.

However, as church gets larger, there is a growing need for organisational structures to regulate church life, train ministers, construct and maintain buildings and finance salaries. These are some of the traits of institutionalism. The bigger the church, the more institutionalised it becomes. It leads to an institutionalised mindset, where maintenance and acceptance by society become a higher priority than growth and spiritual issues.

Institutionalism is a stock, figure 1. It takes time to accumulate, and is hard to remove once it is there. Institutional inertia is well known. Second order feedback, balancing loop B3, happens because institutionalism undermines the conversion process, the first order reinforcing loop R1. The institutional shift moves the bulk of the church from mission to maintenance, thus conversions, loop R1, fall to a value under the church leaving rate and deaths, loop B2. Thus church declines. But the second order effect means that by the time the decline becomes really noticeable, the church is not able to act fast enough to remove the institutionalism to increase conversion, thus decline continues [4].

Figure 1: Institutional Model of Church Growth

Overshoot and Decline

Figure 2 shows the effects of this second order institutional loop on church numbers. There is a long period of rapid growth, helped by the delays in the loop as institutionalism takes so long to build. This is the good side of second order feedback – it takes ages to have an impact. The bad side – the peril of the second order feedback – is that by the time institutionalism has turned growth to decline it has become too large to deal with. There is some natural depletion of institutionalism, (loop B4, figure 1), but it requires deliberate action by the church to dismantle it. Unfortunately, institutionalism is also a mindset, and that action is too little, too late, and the church heads for extinction, figure 2.  

Figure 2: Overshoot and Decline Behaviour of Church Growth and Institutionalism

The result is the institutional lifecycle of figure 2. This is the current state of most of the older denominations in the UK and other Western countries. The revivals of the 18th- 19th centuries have transitioned to organisations with much wider concerns than just saving souls. The timescale of this second order effect, about 300 years in this case, is much longer than that of the revival growth dynamics.

Thus the current decline in church is not primarily due to events happening now, or from the immediate past, but events of a hundred or more years ago being naturally worked out.  I have blogged before how the UK church reached its peak around the 1870s, about 140 years after the commencement of revival [5]. Institutionalism was too high, stifling revival, spiritual life and doctrinal orthodoxy. Decline followed, and 140 years further on again, the churches are in the same declining phase, but much nearer the end.

A Way Forward?

When one church lifecycle is ending, there is more space for another to start. The Methodist movement came out of the decline of a previous church lifecycle that had started at the reformation and, with much political turmoil, had run its course by the end of the 1600s. Methodism started as a renewal movement in the Church of England in the 1730s, then eventually separated in the late 1700s, allowing both to flourish, along with the other denominations also caught up with the revival. Separation allowed Methodism to free itself of the stock of institutionalism of the established church, especially the parish system, thus breaking the effect of the second order feedback loop – at least for the next 100 years before it developed its own institutionalism.

Perhaps now is the time for those who have been part of the evangelical and Charismatic renewal of the last 60 years to separate from the declining denominations. Just tinkering with effects of second order feedback will not turn decline into growth, instead denominations will continue to head to extinction.  The more radical approach of separation is needed.

Such separation is not a recipe for division. The division is already there as is seen in the fights between the biblically orthodox and liberal wings of the older denominations. A separation now would allow both camps to concentrate on what they see as their missions, rather than battles for control of organisations that have run their course. Recently, Free Church minister David Robertson has suggested this strategy for the Church of Scotland, but it really applies to all existing institutional churches – those that have been around for 150 years or more [6].

Some of the older denominations will no doubt wither away. Others may indeed save themselves from that fate, once the internal dynamics have changed. Hopefully, in the new separated churches, it would allow the revival work that has been simmering away since the start of Pentecostalism to flourish and result in many conversions. This is a controversial solution to church decline, but the history of the church is full of such separation. This year is the 500th anniversary of Luther and his objections to the Catholic Church that led to a major parting of the ways [7]. The time may well be right for another parting of the ways in the Christian denominations.


[1] Feedback and Church Growth, Church Growth Modelling Blog

[2] The Limited Enthusiasm Model is largely a model with first order loops

In a population, birth and death precoesses are first order, as are some capacity issues

[3] Overshoot and Collapse is archetypal behaviour caused by a second order loop. See the interaction of a deer population with its environment

[4] The Institutional Model of church growth and decline is described more fully elsewhere:

and applied to the GB Methodist Church:

[5] The connection between revival and church growth and decline is illustrated from the history of the Welsh Presbyterian Church:

[6] Lessons from the Disruption – How a Church Split Can be Positive! The Blog of David Robertson, 19/5/17,

[7] The Quincentenary of the Reformation, Lutheran Council of Great Britain

Sunday, 14 May 2017

Feedback and Church Growth

Feedback in a system that changes over time is the mechanism where an action results in an effect, which then in turn influences the original action. The action literally “feeds back” on itself.

Reinforcing Feedback

For example, if a population grows through births, the more in the population, the more people are born, thus even more are added to the population and it grows faster. This is a reinforcing feedback loop; the result is exponential growth, that is growth that speeds up [1].

Sometimes church leaders think that churches grow the same way. The larger the church becomes, the more people are added to the church, thus the church grows even faster, figure 1. People may be added through births and through conversion. The rectangle “Church” is called a stock. It is an accumulation of people. The pipe “add to church” is called a flow and represents the addition of people in a fixed period of time. Figure 1 is an example of a system dynamics model.

Fig 1. Reinforcing feedback (R) applied to church growth

It is true that the early phase of a church’s growth is often exponential. However, with a bit more thought, not everyone in a church is engaged in the process of adding people to the church. Some are inactive in church altogether. Others may be active in church life but may have never brought anyone new to church. Others may have invited new people in the past but are no longer doing so. For many of the churches I have studied I have estimated that at any one time less than 5% of church members are active in adding people to their church.


As an alternative to the hypothesis in figure 1, I have proposed an alternative feedback hypothesis where only a subset of the church actively adds people to the church [2]. I call these people enthusiasts, after the nickname given to the Methodists in the 18th century – people who were very active in evangelism. Figure 2 expresses this hypothesis as a reinforcing feedback loop

Fig 2. Reinforcing feedback (R1) and enthusiasts

Those from outside the church who are made enthusiasts are also added to the church, and make more enthusiasts – the feedback effect. In addition, enthusiasts convert others who, although added to the church, are not enthusiasts themselves, converting no one. This latter mechanism has no feedback loop. The feedback of figure 2 is weaker than that of figure 1, however it is the mechanism seen in revival, evangelistic campaigns and courses such as Alpha, and can result in considerable exponential growth in the church.

Balancing Feedback

Balancing feedback is the process where the effect of an action attempts to restrain rather than reinforce the action.  For example when a population is declining through deaths, the more deaths, the less people in the population, thus deaths are reduced. The result is the exponential decay of the population, decline that slows down [3].

Limited Enthusiasm

There is good evidence that enthusiasts do not remain so indefinitely. Some run out of people to invite to church, others get taken up with other aspects of church life and forget evangelism. John Wesley complained that his converts went on to become much better people as a result of the Holy Spirit in their lives, so good they became prosperous, and lost their zeal for religion! This is often called Wesley’s law of the decline of pure religion [4], and can be expressed as balancing feedback:

Fig 3. Balancing feedback (B2) and enthusiasts

Limited Population Size

Of course converting people and making them enthusiasts does not occur in a population of an unlimited supply of people. Populations are finite and as people are made enthusiasts, this pool of unbelievers declines, and it becomes harder to make enthusiasts. This is balancing feedback on unbelievers:

Fig 4. Balancing feedback (B3) and unbelievers

Because unbelievers become enthusiasts, then the effect of the balancing feedback on unbelievers, slowing its decline, is mirrored in its equal and opposite effect on enthusiasts, slowing their growth. Feedback loops exert forces on the population, speeding them up or slowing them down, and this mirroring effect is the equivalent of Newton’s third law of motion. Some readers may remember that from high school physics.

Balance of Forces

It follows that the stock of enthusiasts is subject to three forces from the three feedback loops. The action of the enthusiasts themselves, R1, accelerates their growth; the decline of unbelievers, B3, slows the enthusiasts’ growth, turning growth to accelerating decline; the loss of enthusiasts, B2, eventually slowing their decline to zero, figure 5. Growth in enthusiast numbers eventually turns to decline because the effect of the unbelievers reduces the production of enthusiasts to a level below their losses.

Fig 5. The effects of feedback on the growth and decline of enthusiasts (percentage of population)

The effect of enthusiasts’ activity is that the total church, enthusiasts and inactive Christians, follows S-shaped growth, figure 6.  The final level of the church falls short of the total population. The enthusiasts have burnt out before they reach all people, just under 40% of the population in this example, the result of the three competing feedback loops.

Fig 6. Church growth resulting from feedback (percentage of population)

Other Feedback Loops

Over time people leave the church and people die, both balancing feedback. However new are born into the population, replenishing the pool of potential converts, a reinforcing loop. Thus enthusiasts never quite go to zero and a stable balance of church numbers is possible, despite losses and deaths. Nevertheless if conversions are not sufficient, both enthusiasts and church can head for extinction, the situation currently faced by many UK denominations.

Second Order Feedback

This “limited enthusiasm” model described here works well for a couple of generations, but over longer periods the effectiveness of churches in conversion changes for other reasons, usually resulting from “second order” loops.

All the feedback described above is “first order”, that is, only one stock is involved in the loop, see figures 1-4.  First order feedback means that its effect on increasing or decreasing a population is immediate, and thus relatively easy to follow. Not so for second order feedback, which involves two stocks. Its effects are often delayed and counter intuitive.

To give an example of  second order feedback, consider the case of loops R1, figure 2, and B3, figure 4, acting together, figure 7. Although B3 is first order on unbelievers as only one stock is involved, figure 4, the combination is second order on enthusiasts, figure 7. As enthusiasts increase, more people are taken from unbelievers, thus unbelievers falls, thus less are made enthusiasts and their numbers eventually slow – a balancing effect with two stocks. The result, with B2 (figure 3) added, is growth of enthusiasts changing to decline, figure 5, a type of behaviour that cannot occur in a stock that only has first order feedback.

Fig 7. Combining feedback loops B3 and R1 is a “second order” effect.

Jay Forrester, the founder of system dynamics, suggested that our “life and mental processes have been conditioned almost exclusively by first order negative feedback loops” [5].  By contrast second order feedback takes us by surprise and we tend not to respond to it effectively. This is so true for church growth and decline – but that is the next blog!


[1] Reinforcing feedback is also called positive feedback.

Martin, LA. 1997. An Introduction to Feedback, Road Maps, MIT System Dynamics in Education Project, D4691.

Also on the Creative Learning Exchange, Road Maps

[2] Hayward J. 1999. Mathematical Modeling of Church Growth, Journal of Mathematical Sociology. 23(4), 255-292.

Hayward J. 2005. A General Model of Church Growth and Decline. Journal of Mathematical Sociology, 29(3), 177-207.

[3] Balancing feedback is also called negative feedback. See [1] above.

[4] Kelley D. (1986). Why Conservative Churches are Growing: A Study in the Sociology of Religion. Mercer University Press.

Wesley's Law of the Decay of Pure Religion

[5] Forrester, JW. 1969. Urban Dynamics,  p.109. MIT Press.