Findings: Route Geographic Span vs OTP

Summary

Geographic span (the maximum distance between any two stops on a route) is a moderate negative predictor of OTP within bus routes (r = -0.38, p < 0.001), but stop count remains the stronger predictor after controlling for the other. Partial correlation analysis disentangles the two: stop count predicts OTP even after controlling for span (partial r = -0.41, p < 0.001), while span's independent contribution is smaller (partial r = -0.23, p = 0.03).

Key Numbers

• Span vs OTP (bus only, primary): Pearson r = -0.38 (p < 0.001, n = 89), Spearman rho = -0.37 (p < 0.001)
• Span vs OTP (all routes, secondary): r = -0.32 (p = 0.002, n = 92) -- includes Simpson's paradox risk
• Stop density vs OTP (bus only): r = 0.04 (p = 0.71) -- not significant
• Span vs OTP | stop count (bus, partial): r = -0.23 (p = 0.03)
• Stop count vs OTP | span (bus, partial): r = -0.41 (p < 0.001)
• Span-stop count collinearity: r = 0.41

Observations

• The bus-only correlation (r = -0.38) is actually stronger than the all-mode correlation (r = -0.32). The pooled-mode result was muted by Simpson's paradox -- rail routes have moderate span but high OTP, pulling the all-mode trend line toward zero.
• Span and stop count are moderately correlated (r = 0.41), but not so strongly as to make partial correlation unreliable.
• After controlling for stop count, span still has a small but significant independent effect -- longer routes face additional challenges beyond just having more stops (longer exposure to traffic, more variance in conditions).
• However, stop count's partial correlation (-0.41) is nearly twice span's (-0.23), confirming that the number of stops matters more than the distance covered.
• Stop density (stops per km) shows no correlation with OTP at all (r = 0.04), meaning that tightly-packed stops are no worse than widely-spaced stops once total count and distance are accounted for.

Implication

Both stop count and route distance independently degrade OTP, but stop consolidation is the higher-leverage intervention. Shortening routes would help modestly, but eliminating stops on existing routes would have roughly twice the impact per unit of change.

Caveats

• Geographic span (max pairwise distance) is a crude proxy for actual route length. GTFS shape data would provide a more accurate route-length measurement.
• Routes with fewer than 12 months of data are excluded to reduce noise.

Review History

• 2026-02-10: RED-TEAM-REPORTS/2026-02-10-analyses-12-18.md — 4 issues (1 significant). Bus-only correlations now primary; Spearman added.

Methods: Route Geographic Span vs OTP

Question

Does the geographic extent of a route predict on-time performance independently of stop count? Analysis 07 found stop count is the strongest OTP predictor (r = -0.53), but routes with many stops also tend to cover more distance. Disentangling the two could clarify whether the problem is "too many stops" or "too long a route."

Approach

• For each route, collect all stop coordinates from route_stops joined to stops.
• Compute geographic span as the maximum haversine distance between any pair of stops on the route (the diameter of the stop set in km).
• Compute stop density as stops per km of span, to capture how tightly packed stops are.
• Correlate span, stop density, and stop count separately with average OTP (Pearson and Spearman).
• Use partial correlation to test whether span predicts OTP after controlling for stop count, and vice versa.
• Scatter plots for span vs OTP and stop density vs OTP.

Data

Output

• output/geographic_span.csv -- per-route span, stop density, stop count, avg OTP
• output/span_vs_otp.png -- scatter plot of geographic span vs OTP
• output/density_vs_otp.png -- scatter plot of stop density vs OTP