Opportunity-Normalized Residence-Workplace Matching and the Scale-Sensitive Structure of Urban Commuting

Urban spatial structure is commonly evaluated through the spatial distribution of homes and jobs or through aggregate commuting outcomes. Yet these approaches do not reveal how the opportunities created by urban form are selectively transformed into actual residence-workplace connections. This study introduces opportunity-normalized residence-workplace matching by comparing observed commuting distance distributions with opportunity-based distributions constructed from all within-city residence-workplace pairs weighted by residential and employment mass. Using Output Area-level data for nine British cities, we show that realized pairings are systematically more concentrated at shorter distances than the urban opportunity structure alone would predict. After normalization, matching intensity declines with distance in a recurrent but heterogeneous pattern that is approximately linear in log-log space in many cities and can be summarized by a city-specific distance-decay coefficient. London further reveals that this regularity is scale-sensitive: a comparatively flattened citywide pattern separates into consistently negative but heterogeneous relationships across employment-centered subsystems. Supplementary evidence from New York and Chicago shows similar attenuation patterns. These findings identify realized residence-workplace matching as a distinct layer of urban structure and suggest that, in complex metropolitan systems, meaningful spatial regularities may reside in coherent matching fields rather than in aggregate city boundaries.