Does the loss of purity in the church limit church growth? Churches do not grow indefinitely. There are barriers to the church’s growth. Is that growth restricted by societal factors or by church issues such as its purity in the faith?

The limited enthusiasm model of church growth has conversion driven by enthusiasts. Growth slows down as the pool of potential converts shrinks. Eventually, enthusiasts can no longer make sufficient contacts to sustain conversions and growth stops. Assume the potential effectiveness of the enthusiasts is constant, and that after a while, they become inactive believers.

What happens if that potential effectiveness depends on the balance of enthusiasts to inactive believers in the church? Enthusiasts may find it harder to be effective if a large number of inactive believers are holding them back. Maybe some inactive believers are opposed to the enthusiasts on grounds of doctrine or behaviour. Think of the enthusiasts as “pure” and the inactive as “impure”. As the church becomes more impure, conversion declines

System Dynamics Model

The model is given in figure 1. People join the church through conversion. The pool of potential converts is unlimited. Conversion occurs through contact between enthusiasts and unbelievers. The more enthusiasts, the more converts, feedback loop R1. Enthusiasts lose their enthusiasm and become inactive after some time, loop B1.

Evangelistic purity model
Figure 1: Evangelistic purity model

The evangelistic purity of the church depends on the fraction of the church who are enthusiasts. The smaller that fraction, the lower the purity. Enthusiasts are more effective if purity is increased and vice versa. Thus, the conversion rate per enthusiast is directly proportional to evangelistic purity. This process forms a second reinforcing loop R2: the more conversion, the more enthusiasts, the greater purity, thus the higher conversion rate.

However, the number of inactive believers negatively influenced the evangelist purity. The more enthusiasts, the more inactive believers after a while, resulting in lower purity, and thus lower conversion rate. This feedback is balancing, B2. The relative strength of loops R2 and B2 will determine the dynamics of the church’s growth.

The parameter, maximum conversion potential per enthusiast, is key. It measures the effectiveness of the enthusiasts in a church that is 100% pure. As the church becomes less pure, the actual conversion rate per enthusiast falls below this maximum.


The pattern of church growth depends on the effectiveness of the enthusiasts. For values of the maximum conversion rate per enthusiast below a threshold, purity falls as the church grows, blue dashed curve, figure 2. Consequently, church growth slows and reaches a maximum, solid blue curve, figure 2.

evangelistic purity result
Figure 2: Church numbers and evangelistic purity for two values of the maximum conversion rate per enthusiast, either side of the tipping point

Raise the maximum conversion rate above the threshold, then purity rises, red dashed line, and church growth continues unabated, red sold line, figure 2. In this scenario, other factors would curb church growth.

Church purity can be a barrier to growth. However, this barrier can be overcome if enthusiasts are sufficiently effective.