Decay Functions and Offender Spatial Processes

Although it is now well established across diverse samples that the frequency of offending ‘decays’ as distance from the home/base increases, it remains unclear what form of decay function best characterises this relationship. Different forms of decay function refl ect different patterns and rates of decrease in the likelihood of offending as distance from the home/base increases. These different patterns imply rather different underlying psychological processes. Therefore, considerations of the particular function characterising distance decay elucidate explanations of offender spatial behaviour. To bring to light the possible psychological and behavioural processes inherent in offending distance decay, the present study examined the fit of logarithmic, negative exponential, and quadratic decay functions to the distribution of the distances travelled to offend by a sample of 70 prolific burglars from the UK. It is argued that these functions are consistent with the operation of perceptual processes of magnitude estimation, friction or effort effects, and the influences of cost-benefit assessments, respectively. The results indicate that offending distance decay patterns most closely fit the logarithmic function, consistent with Stevens’ perceptual processes of distortion in magnitude estimation, whilst not ruling out additional processes relating to the increased effort required in travelling greater distances to offend. Because most geographical profiling systems are built upon the distance decay function, the impact of utilising the different forms of function on the accuracy of geographic profiles was also assessed utilising ‘search cost’ calculations. The results showed little impact of applying different decay functions. Thus, whilst the decay function does have important theoretical implications for understanding offender spatial behaviour, it is noted that the particular variant used does not significantly impact on the effectiveness of geographical profiling systems as they currently exist.