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Church Growth Modelling

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Model Construction

Institutional Model

Church recruits in proportion to size, but recruitment rate reduced by institutionalism which grows as church grows.

Model Results

Decline Caused by Institutionalism

Application to GB Methodists

Data fit to the model.

Growth & Decline of Welsh Presbyterians

The connection between revival and institutional growth and decline.

Related Blog

Institutionalism and Church Decline

Response to comments by others on the negative effects of institutionalism on church growth.

The Rise and Decline of British Methodism

Application of the Institutional Model of Church Growth.

Extension of Institutionalism Model

As used in Application to GB Methodist Church

The application of the Institutional Model to denominations in the UK requires a number of model extensions to enable calibration. To illustrate these extensions the model details and calibration of the GB Methodist Church are given here. See the results of the GB Methodists for background

Calibration requires membership data for the Methodist Church, as well as population data, births and deaths. Model extensions include: Growing population; Church births and deaths; Delays; Internal pressure to increase institutionalism.

Methodist Data

Membership data was taken for England, Scotland and Wales from 1767, the earliest known date, to 2014. Ireland was excluded due to poor population data in the early period, and the later political division of the country. The earliest Methodist membership figures are taken from Currie et. al. (1977) , table A3, pp. 139-144. The various Methodist church divisions are combined together so that they can be compared with the later united church. Later data is taken from publications by Brierley and figures released by the Methodist church.

Growing Population

A standard population model, figure 1, is calibrated over time with the total population data for Great Britain, figure 2, together with births and deaths, figure 3. Data is taken from the Office of National Statistics, with earlier data taken from a number of texts including British Historical Statistics by BR Mitchell. Inevitably there is some discrepancy between the population figures and the published birth and death rates as there are a degree of estimation with all such figures. Thus a corrective flow is added to the model, figure 1. It follows that the population stock matches the population data exactly using the correct birth and death rates.

Figure 1: Population Model with Correction for Anomalies with Published Births and Deaths

Figure 2: Population Figures for Great Britain: England, Wales and Scotland

Figure 1: Birth and Death Rates for Great Britain

Extended Institutional Model

The extended model is given in figure 4. The processes of the basic model are preserved. R1 governs additions to the church through conversion in proportion to the size of the church. However the additions are reduced according to institutionalism, B2. B1 controls those who leave the church. As institutionalism grows it becomes harder to increase further, B3. There may be a natural decline institutionalism if it is no longer generated, B4. The extensions are described below.

Figure 4: Extended Institutional Model of Church Growth

Church Births & Deaths

Additions to the church from children of church members are given by the flow Biological addition to the church. This addition is a fraction of the birth rate of the population, assuming that average family size for church members was the same as the population. Information from church figures across denominations indicate this fraction is around 50%. However evidence from the Welsh Methodists indicates the age profile of churches up to 1900 was younger than the population, thus a correction, actual birth ratio, is used to adjust the biological addition, curve 1, figure 5. This boosts church births due to a greater proportion of adults in the child-bearing range. After 1900 this ratio falls as the population ages. By 2014 there are few children being born into the church as many members are past child-bearing age.

Figure 5: Adjustment to Church Birth and Death Rates for Church Age Profile

Likewise a death ratio is used to adjust the church death rate for differing church age distributions over the date range. By 2014 this ratio is high as a large proportion of the church is elderly.


A delay is added between the church size and institutionalism. This is because it takes time for organisational structures to be decided on and constructed in order to manage size and complexity. Also it takes time for an institutional mentality to be adopted by the organisation.

There is a further delay from institutionalism to recruitment as it takes time for institutional structure and mentality to affect behaviour.

There is a physical delay in the addition of the children of church members into membership as most churches have 16-18 as a minimum age for membership.

Internal Institutional Pressure

An additional loop R2 representing the desire of, and pressure from, people working for the church to adopt more institutionalism, figure 4. They do this because more institutionalism creates job and promotion prospects, gives them status in society, and also, crucially, because a stronger institution is seen as a better, more effective and professional church. It is easy to dismiss the desire for more institutionalism as self-interest, but that misses an important dynamic that churches genuinely see professionalism and status as a means to glorify God and better spread the message.

Thus there are two positive forces causing institutionalism to increase: internal pressure; and the requirements of size. These two influences are combined in such a way that the one enhances the other, i.e. they are added. To preserve model validity they are added using the logical "or" method. That is, if the two influences are X and Y then the combination is X + Y - XY. Figure 6 shows the two causes, blue and red, and their combination, the green curve. Each cause enhances the other. This modelling method was developed in Hayward, Jeffs, Howells & Evans (2014).

Figure 6: Effects of Internal Pressure and Church Size on Institutionalism and Combination


The model was run in the software Vensim, which allows optimization to parameters, seeking the sum of least square error between data and model. WIth the number of parameters in the model then there are a number of suitable optimum fits. Leaving rate was fixed at 2%, typical of most denominations and reflecting avergae Methodist data, figure 7. Delays were set pragmatically, 20 years for the biological addition and 30-50 years for the others. The initial institutionalism was set at 0.2, i.e. 20%, reflecting that some structure was in place by the 1760s, but that it was quite low compared to what would be achieved a century later when the Methodists became a respectable large denomination.

Figure 7: Model Parameters for Data Fit of Institutional Model to CB Methodist Membership

A number of optimized runs were compared with the parameters for the internal pressure and church size effects on institutionalism. These were then set, figure 7, to give a balance between the two causes so that internal pressure was stronger in the early years, whereas the response to size was stronger in the later years, as the denomination became very large, figure 6. Likewise response time and the sensitivity of the effect on institutionalism were set based on the different runs, figure 7.

Finally an optimized run was performed for church recruitment rate and the institutional removal rate, with all other parameters set as above, figure 7.

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Church Growth Modelling