Exponential decay applies to a lot of physical phenomena, such as dissipation of sound for example, and interestingly the evidence suggests it is also a good model of human behavior in the aggregate. For example, people are more likely to visit a park near home, which makes sense, and they become less likely with increasing distance. And that likelihood doesn’t decline in a straight line but exponentially, which suggests to me it is better for urban quality of life to have many small decent parks rather than a few large great ones.
Urban parks are essential infrastructure for public health and environmental resilience, yet systematic comparative evidence on how distance constrains recreational access across metropolitan areas remains scarce. This study analyzes 60 million park visits across 20 U.S. metropolitan areas to establish mathematical relationships governing park visitation and their determinants. Park visitation universally follows exponential decay (V = αe-βd) rather than power law scaling, with exceptional model fits (R2 > 0.95) across diverse urban contexts. However, decay parameters vary substantially, from β = 0.090 (Minneapolis) to β = 0.211 (Detroit), creating a 2.34-fold difference in distance sensitivity. This variation produces markedly different accessibility patterns: residents in high-constraint cities experience 50% visitation decay within 3.3 km, while those in low-constraint cities maintain equivalent access to 7.7 km. Regression analysis reveals that transportation infrastructure, built environment characteristics, and sociodemographic factors collectively explain 56.3% of variation in median travel distance to parks. Transit proximity, street network design, and regional employment accessibility emerge as primary associations, while minority-predominant and car-free neighborhoods face compound disadvantages through both restricted mobility ranges and heightened distance sensitivity. These findings establish exponential decay as a consistent mathematical relationship for recreational mobility while demonstrating how local context shapes its parameters. For planning practice, uniform park service area standards may inadequately reflect actual visitation patterns, as the empirically measured half-distance at which visitation drops by 50% varies more than twofold across metropolitan areas. Calibrating park spacing to locally measured decay rates and coordinating green space provision with transportation investment could improve both the efficiency and equity of urban park systems.
I have one quibble, and I would be surprised if the authors didn’t think of it and control for it somehow. And that is the idea that car-free neighborhoods would be at a disadvantage in terms of park access. Now maybe this is true, but it seems to me the decay should be measured in travel time or cost (in the difficulty sense) rather than absolute distance. People who get around a neighborhood mostly by walking aren’t going to travel to a park three miles away, which is no big deal by car (if there is ample free parking on both ends, which is one reason the park has to be so far away!). But the people walking to a smaller nearby park might have an equally pleasant subjective experience than the ones driving. Or they might not. But my point is I can’t tell, at least just from this abstract.
