There are many approaches to model building. The following was used with church leaders in order to construct the Discipleship model.

Collecting Initial Thoughts

Participants were asked to consider how they might categorise people in the church in terms of the effect they have on the growth and life of the church. They were further asked why people join and leave the church. See handout sheet 1. Although a number of these responses have not been used the main aim was to get people thinking about how different elements are identified and how one may cause another. Later in the process, these questions were made more specific. See July Issues.

System Dynamics Elements Used in Modelling

Participants were shown how one particular model, loosely based on the Limited Enthusiasm Model, was built. This also introduced them to the concepts of stocks, flows, converters and connectors. The full presentation can be downloaded, with the four elements in System Dynamics. Essentially there are:

  • Stocks. Also called accumulations. These measure quantity. What is accumulated stays there unless there are processes that change its quantity. For example, the number of people who belong to a church at any given time could be a stock. It is a static view of the system – what is there now, rather than what happens over time.
  • Flows. Also called rates. These measure change. How many people are converted per year could be a flow. It is a dynamic view of the system, that is, how things change over a period.
  • Connector. These control change, though linking one element to another. Connectors capture the process of cause and effect. If the people who belong to church cause (that is they are involved in the process of) conversion, then there is a connector from church to conversion. The more in the church, the more conversions
  • Converter. These convert one type of quantity into another so that elements of different types can be linked together. Thus they can appear in causal chains. There are special converters that interface with the boundary of the model and have values that are set from outside. These are the parameters.

It is important to understand that any system has a static view (the stocks – what is there now), a dynamic view (the flows – how things are changing) and a causal view (the connectors – what causes what). People possess these three views of a system, but often they are in conflict with each other without them realising it. One purpose of a system dynamics model, and its simulation, is to highlight these conflicts and guide people to a resolution and a better understanding of the system.

Calibration and Parameters

The first model described in some detail was the discipleship model. With the basic stocks of the system constructed from discussions over three meetings the group assigned values to the stocks and to the parameters that control the flows, based on realistic guesses. Thus a static and dynamic view of the system was identified. The causal view was left on hold. A worksheet was constructed with the initial guesses for the parameters. The first guess gave a wide discrepancy between static and dynamic views – note the big difference between the first guess and the second which is where the stocks are calibrated to the flows (attached sheet). Participants were either overestimating the number of spiritually mature people in the church, or underestimating the process to spiritual maturity, or both.

A blank parameter worksheet is available.


Once there are satisfactory calibrations of a model, various experiments can be conducted, in the form of “what ifs”. For example, for the discipleship model, one experiment could be “what if there were a sudden influx of converts?”. How would the balance of new converts to “discipled” to “mature” behave? How long would it take to settle back down?

Feedback Loops

With a better understanding of how a model behaves, various control issues can be investigated. This is where causal loops become important, where making a change has an effect which in turn affects the original change. In the case of the discipleship model, there are at least two loops of interest.

  • How does the lack of mature Christians affect the resourcing of the church programme, in particular those resources that help generate mature Christians? Does there need to be a minimum number of mature people for a church to avoid a downward spiral in its numbers?
  • How does the number of discipled Christians affect the church’s quality and the perception of that quality by potential joiners? Could a church achieve a critical mass, so that by increasing its fraction of discipled believers, it would have such a positive impact that an upward spiral of growth would result?

Soft or Unquantified Variables

Soft variables are those for which no clear or easy measures exist. In that sense, they are unquantified, even though they have an informal sense of measure. For example, the quality of the church is a soft variable. There is no easy way to measure it, but people have a sense of what is a great church, good church, mediocre and poor. There is quantity but without specific numbers. Most models require such variables.