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Access scoring

The BNA score answers a single question for every census block: how much of what you can reach by bicycle can you reach comfortably?

The fundamental question

Bicycle access is scored in two layers:

  • High-stress access — how many people / jobs / destinations can you reach by any bicycle route, even stressful ones along busy arterials?
  • Low-stress access — how many of those can you reach via calm, comfortable routes (stress level 1 only)?

A block scores well when the low-stress share of what it can reach is high. A neighbourhood where every school, park, and grocery store requires riding on a five-lane highway will score poorly even if it has good cycling distance to many destinations.

Population and employment access

For each block, BNA counts:

  • pop_high_stress — total population living in blocks reachable at all
  • pop_low_stress — population reachable via low-stress routes only

The ratio pop_low_stress / pop_high_stress is then run through a piecewise linear formula that rewards early gains more than later ones:

ratio = pop_low / pop_high

if ratio == 0:   score = 0
if ratio >= 1:   score = max_score (1.0)

Otherwise, interpolate linearly between:
  0         → 0
  step1=3%  → score1=0.1
  step2=20% → score2=0.4
  step3=50% → score3=0.8
  100%      → max_score=1.0

The shape is deliberately concave: going from 0% to 3% low-stress connectivity (the first few comfortable routes appearing) is worth 10% of the maximum score. Going from 50% to 100% only adds the remaining 20%. This reflects the diminishing returns of additional comfortable routes once a neighbourhood already has broad low-stress access.

Employment (emp_score) uses the same formula, with LODES WAC job counts replacing population.

Destination access

Destinations are counted as clusters (groups of nearby individual POIs), not individual buildings. A block's destination score for a type is:

  1. Count how many clusters of that type are reachable at all (high_stress).
  2. Count how many clusters are reachable via low-stress routes (low_stress).
  3. Apply a stepped formula based on the first few clusters mattering most:
if high == 0:     score = NULL  (type not present / reachable)
if low == 0:      score = 0
if high == low:   score = max_score (1.0)

Otherwise (example: first=0.7, second=0.2, third=0):
  low == 1  → 0.7
  low == 2  → 0.9
  low >= 3  → 0.9 + (0.1) × (low - 2) / (high - 2)   [linear to max]

The parameters (first, second, third) differ by destination type, reflecting how much a single accessible hospital matters vs. a single accessible park. Schools use first=0.3, second=0.2, third=0.2 because the third school adds meaningful value; hospitals use first=0.7 because reaching even one hospital comfortably is highly significant.

Standard destination parameters by type:

Type first second third
colleges 0.7 0 0
community_centers 0.4 0.2 0.1
dentists 0.4 0.2 0.1
doctors 0.4 0.2 0.1
hospitals 0.7 0 0
parks 0.3 0.2 0.2
pharmacies 0.4 0.2 0.1
retail 0.4 0.2 0.1
schools 0.3 0.2 0.2
social_services 0.7 0 0
supermarkets 0.6 0.2 0
transit 0.6 0 0
universities 0.7 0 0

Trail access

Trails are handled differently from destinations because the goal is to count qualifying recreational paths, not POI clusters. The scoring uses reverse Dijkstra rather than a forward search from each block:

  1. Build the transposed (reversed) routing graphs G_high.T and G_low.T.
  2. For each qualifying trail (path_length > 4800 m and bbox_length > 3300 m):
  3. Run Dijkstra on the reversed low-stress graph from the trail's road vertices.
  4. Any source block with a reachable vert within max_trip_distance can reach this trail via low-stress routes → increment trails_low_stress.
  5. Repeat on the reversed high-stress graph → increment trails_high_stress.
  6. Apply the destination-count formula with first=0.7, second=0.2.

The reverse approach is much faster than forward Dijkstra from each block when there are fewer trails than blocks (typically 50–300 trails vs. thousands of blocks).

Trail scores use NULL when trails_high_stress == 0 (no qualifying trail reachable at all), 0 when trails are reachable but only via stressful routes, and the piecewise formula otherwise.

Category scores

Destination scores are grouped into five categories:

Category Weight Members
People 15 population (pop_score)
Opportunity 20 employment, schools (35%), colleges (10%), universities (20%)
Core services 20 doctors (20%), dentists (10%), hospitals (20%), pharmacies (10%), supermarkets (25%), social_services (15%)
Retail 15 retail
Recreation 15 parks (40%), trails (35%), community_centers (25%)
Transit 15 transit

The category score is a weighted average of its members, with a conditional denominator: only members where at least one block has high-stress access in the city contribute to the denominator. If a city has no hospitals at all, hospitals is excluded from the core_services denominator — it cannot drag the score down.

Overall block score

The per-block overall_score (0–100) combines all category contributions:

overall_score = 100 × (
    people_weight × pop_score
  + opportunity_weight × opportunity_contribution
  + core_services_weight × cs_contribution
  + retail_weight × retail_score  [if any retail reachable]
  + recreation_weight × rec_contribution
  + transit_weight × transit_score  [if any transit reachable]
) / (
    people_weight
  + opportunity_weight  [if any school/college/university reachable]
  + core_services_weight  [if any core service reachable]
  + retail_weight  [if any retail reachable]
  + recreation_weight  [if any park/trail/cc reachable]
  + transit_weight  [if any transit reachable]
)

The conditional denominator is the key design: categories with zero high-stress destinations in the entire city are excluded from both numerator and denominator. A rural city with no transit stops is not penalised for lacking transit — it is scored on what it has.

Blocks with no connectivity at all (isolated road network) receive a score of 0.0 (not NULL) because people always contributes to the denominator.

Implementation notes

All scoring is a single vectorised pandas GROUP BY over connectivity_df: one O(pairs) pass through the connectivity table, computing every destination type at once.

Relationship to brokenspoke-analyzer

The SQL scripts this stage replaces — and any points where the output intentionally differs — are catalogued in the Differences from brokenspoke-analyzer section.