# LSOA exposure assumptions and mileage pilot

London • South East • South West | Frozen pilot mileage-v1 | 11 October 2026

We have implemented a conditional mileage denominator for 13,972 Lower Layer Super Output Areas (LSOAs) across 67 authorities. The panel contains 55,888 LSOA-year records for 2021–2024. It combines published major-road traffic with a modelled allocation of the remaining authority mileage across minor roads.

| Region | LSOAs | 2024 miles | Major share | Major miles routed |
| --- | --- | --- | --- | --- |
| London | 4,994 | 19.43 bn | 58.7% | 57.7% |
| South East | 5,571 | 53.60 bn | 69.4% | 58.0% |
| South West | 3,407 | 35.13 bn | 60.9% | 65.7% |

South West supplies a contrasting region with substantial rural roads. It also includes urban areas, so we retain a separate resident settlement indicator rather than treating the whole region as rural.

## What the implementation establishes

All seven allocation variants conserve each available authority-year total to within one millionth of a mile. There are 55,878 positive exposure rows, eight zero-allocation rows and two missing-exposure rows. The richer traffic model outperforms the simple benchmark on development geographic holdouts. We retain both allocations and four frost-related stress scenarios.

## What remains conditional

No LSOA denominator is independently validated. Major-road matching leaves substantial fallback allocation; minor-road absolute prediction error is high; some road functions have no count-site training support. Three frost bands fail the flow-bias check. Agreement with an authority total cannot establish the distribution of traffic within it.

The all-road frost comparison improves 2024 deviance in London and South East, but worsens it in South West. Calibration also remains weak. These results support further investigation, not insurance pricing, causal claims or a declaration that the LSOA exposure gap is closed.

# What exposure means at LSOA level

Our denominator is all-motor vehicle miles travelled on roads inside an LSOA polygon during a calendar year. A through-journey contributes mileage to every LSOA crossed. Vehicle ownership, driver residence and home postcode do not determine this denominator.

| Element | Working assumption and consequence |
| --- | --- |
| Unit | One LSOA2021 × calendar year. Miles are vehicle miles, not road miles or trips. |
| Boundary | ONS LSOA21 full-resolution BFC V10 polygons in British National Grid. The fixed UTLA23 lookup supplies authority membership. |
| Vehicle scope | DfT all-motor flow. AADF includes both directions and is used once; pedal cycles are outside the denominator. |
| Collision scope | Police-reported injury collisions with definite covered motor involvement, assigned once to the collision location. This is not claims frequency. |
| Road scope | Non-fictitious OS links excluding Restricted Local Access Road. Other mapped links are treated as a public-access proxy. |
| Population context | Fixed Census 2021 population and 2021 rural/urban classification aggregated from output areas. Resident settlement is a contextual proxy, not a classification of each road. |
| Frost context | Frozen 1991–2020 mean annual air-frost days from the public 2 km Met Office product. National road-weighted deciles stay fixed. |

The OS Open Roads April 2026 snapshot is reused retrospectively for all four years. It does not reconstruct historical openings, closures, altered access, diversions or growth within an authority. Mapped geometry is generalised; measured lengths support allocation, while published DfT section lengths determine major-road traffic totals.

Exact line–polygon intersections allocate mapped length. Tile duplicates are removed after checking identifiers, geometry and attributes. Road segments coincident with a boundary are counted once, assigned to the lexicographically first LSOA. The pilot covers 118,852 km of access-screened mapped network; 36.1 km of boundary-coincident length required this single-assignment rule.

The original frost feature uses a broader non-fictitious mapped network, including restricted roads. We preserve it and its deciles rather than silently redefining the climate feature. Exposure and frost therefore have a documented network-scope mismatch.

# Major road mileage assumptions

For each DfT major-road count point and year, we calculate section vehicle miles as all-motor AADF × published link kilometres ÷ 1.609344 × calendar days. We use 366 days in 2024 and 365 in the other pilot years. Counted and Estimated source flags are retained. A counted annual estimate is not continuous observation of every vehicle.

## Routing published sections

The Major Road Database provides section endpoints, not the true road alignment. We find a shortest connected path on OS links with the same road number. Both endpoints must be within 100 metres of network nodes, the count location within 75 metres of the path, and path length between 80% and 120% of published length. At least 99% of the routed length must lie in the recorded authority. Coordinates use their projected horizontal components.

Within an accepted section we assume constant average daily flow. The published section miles are distributed by the length of routed geometry inside each LSOA in the authority. This preserves the official section total despite differences between generalised mapped length and published length.

| Allocation result | 2021–2024 section-years | Interpretation |
| --- | --- | --- |
| Accepted route | 15,135 | Geometric rules met; traffic remains a published estimate. |
| Same road-number fallback | 7,354 | Allocate over all same-number major links in the same authority. |
| Same road-class fallback | 12 | No same-number geometry; allocate over the authority’s motorway or A-road class. |
| Unallocated section | 0 | If no compatible geometry existed, the affected authority-year would be withheld. |

Fallback is a modelling assumption, not successful matching. It spreads a section’s miles across other pieces of the same road, or in the weakest case its broad class. The authority audit reports the fallback fraction. More than 5% fallback fails the predeclared major-allocation quality gate.

## A stricter major-road comparison

For the separate collision comparison, we exclude all 1,096 section-years sharing any routed OS edge with another section. The remaining 14,039 section-years require an exact first-road number and collision position within 30 metres, with positive exposure in the assigned LSOA. Multiple-section matches are excluded. This leaves 57,351 matched collisions over four years and a balanced 6,480-LSOA subset. Displaced coordinates, junction coding and incomplete matching still limit interpretation.

# Minor road traffic model and validation

We fit minor-road flows using Counted AADF observations from 2021–2023. Sites must match the compatible B-road or other-minor class within 50 metres; B-road numbers must agree. Tied nearest links and authority mismatches are excluded. Of 4,480 counted site-year observations across 2021–2024, 4,458 pass matching.

Training contains 3,365 observations at 1,263 distinct sites in 138 geographic blocks. Repeated site observations receive inverse-frequency weights so each site has one total unit of fitting weight. The simple benchmark uses region × B/other class × resident settlement means, shrunk with 20 site-equivalents towards the class mean.

The selected alternative is a regularised Poisson mean regression with alpha 1. Predictors are region, road class, OS road function, log resident density, resident urban fraction and mean endpoint degree. Training-only scaling is used. Frost, collision counts and claims are forbidden predictors. The Poisson loss estimates a positive mean; it is not an assertion that traffic counts have Poisson sampling variance.

Selection uses five fixed geographic folds based on 20 km blocks, with all observations from a site kept together. The model’s mean development deviance is 1,658.1, against 2,054.5 for the benchmark, a 19.3% reduction. The benchmark would win if within 1% of the model.

| 2024 geographic holdout | Sites | Blocks | Mean bias | Absolute error |
| --- | --- | --- | --- | --- |
| London | 176 | 8 | 8.0% | 62.3% |
| South East | 480 | 65 | -1.4% | 63.1% |
| South West | 437 | 77 | -0.9% | 64.3% |

Every usable 2024 site was also observed in training years. The original new-site assessment is therefore unavailable. After identifying this source limitation, we documented a supplementary check: each 2024 site is predicted with its complete geographic block withheld from the 2021–2023 fit. This reuses the development block scheme; it is not an independent model-selection exercise.

All three regional aggregate biases are within ±10%, but weighted absolute error remains 62–64%. Supported groups require at least 30 sites and three blocks. D1 bias is +12.6%, D5 −12.9% and D9 +10.3%, all outside the target. Count-site performance may not represent the much larger population of uncounted minor roads.

# Annual allocation and frost stress scenarios

For authority a and year t, the minor-road balance is R(a,t) = official all-road motor miles − the sum of all published DfT major-section miles. A missing or negative balance is withheld. We do not clip it to zero or invent a denominator.

For minor fragment j inside LSOA i, its allocation weight is mapped length × predicted AADF. We sum these weights within the LSOA. Minor miles are R(a,t) × W(i) / the sum of W across the authority. Total LSOA miles equal allocated major miles plus these minor miles. The annual days multiplier would cancel from this within-authority normalisation.

The training-based relative minor shares are fixed across 2021–2024. All annual growth comes through the authority minor-road balance; no unsupported road-class or neighbourhood growth factor is invented. This preserves totals but cannot detect local redistribution of traffic. We separately refit the outcome comparison without 2021 to test sensitivity to the recovery period.

## Stress assumptions

We multiply minor weights by 1 + δ × (D − 5.5) / 4.5, where D is the fixed national frost decile and δ is −20%, −10%, +10% or +20%. Missing deciles receive neutral weights. We then normalise again inside each authority-year. Major miles are unchanged. These are assumption scenarios, not confidence intervals. Normalisation means a ±20% weight change can produce a total-mile change exceeding 20% for some LSOAs.

| Worked 2024 LSOA | Modelled vehicle miles |
| --- | --- |
| E01015519 · Swindon 001A | Frost D8 |
| Routed major-road component | 1,028,201 |
| Other major-road allocation | 58,498 |
| Selected minor-road allocation | 1,153,146 |
| Selected total | 2,239,845 |
| Simple benchmark total | 2,023,862 |
| Colder weights −20% / +20% | 2,162,249 / 2,310,476 |

Across the four stress variants, the 95th percentile of each LSOA’s largest absolute total-mile change is 6.2% in London, 19.7% in South East and 14.3% in South West. The scenarios measure sensitivity to frost-correlated allocation error; they do not estimate its probability.

# Missing exposure and quality flags

We retain every target LSOA-year, including zero collisions and missing exposure. Rates are calculated only where modelled miles are positive and the inherited authority rate gate passes. The validated-frequency flag remains false in every row.

| Condition | Treatment and implication |
| --- | --- |
| No usable authority exposure | Isles of Scilly 2022 and 2023 remain missing because the frozen authority denominator failed reconciliation. No replacement is inferred from neighbours. |
| Zero mapped allocation | Greenwich 041C (E01034195) and Newham 042G (E01034230) have zero assigned exposure in all four years. This means no usable mapped allocation, not proof of zero travel. Greenwich 041C has one assigned 2024 collision; its rate is withheld. |
| Reporting or rate warning | Avon and Somerset reporting warnings affect five authorities in 2022–2023. Buckinghamshire lacks the independent official comparison rate in all four years. These areas remain in the exposure output but are excluded from the balanced outcome cohort. |
| Unsupported road function | Local Access Road and Secondary Access Road have no matching training sites. Their unseen function indicator is zero in the fitted model; the other fitted terms still supply a prediction. This extrapolation is explicitly flagged. |
| Sparse traffic stratum | Region × road class × function groups with fewer than 30 distinct training sites are flagged. London B roads have 26 sites. Sparse support is a warning, not automatic deletion. |
| Density extrapolation | Fragments outside the global training log-density range are flagged. A plausible positive prediction does not establish coverage of that setting. |
| Frost coverage | LSOAs failing the original 99% road-climate coverage rule remain in the exposure table but cannot enter the frost comparison. |

Unsupported road functions receive 2.53 billion modelled minor-road miles in 2024, or 6.6% of the allocated minor total. Each LSOA carries its own unsupported-function, sparse-group and density-extrapolation fractions of model minor-road weight.

The balanced all-road outcome cohort requires positive exposure, eligible frost and passing inherited authority rate gates in every year. It contains 4,992 London, 5,156 South East and 2,319 South West LSOAs. This exclusion pattern changes the South West mix, especially because the Avon and Somerset reporting warnings remove otherwise available urban areas.

Polygon-assigned collision totals are audited against recorded-authority totals. Cross-boundary coding and unassigned collisions can make them differ. The authority unassigned count is repeated as context on each LSOA row and must never be summed over LSOAs.

# What the exposure assumptions do to the frost result

We fit a new exploratory LSOA mean model on 2021–2023 and assess it on 2024. M0 contains region, log resident density, resident urban fraction and major-mile share, with log modelled miles as an offset. M1 adds the fixed national frost deciles. These are separately fitted models, not transferred coefficients from phase 6. There is no fitted calendar-year effect.

| Region and denominator | Deviance gain and paired 95% interval |
| --- | --- |
| London · traffic model | 8.24% (3.67% to 12.78%) |
| South East · traffic model | 5.17% (3.25% to 9.11%) |
| South West · traffic model | -5.66% (-12.13% to -1.67%) |
| Pilot · traffic model | 5.20% (2.80% to 7.83%) |
| London · strict major subset | 7.40% (2.39% to 12.20%) |
| South East · strict major subset | 2.22% (-0.31% to 4.42%) |
| South West · strict major subset | -4.24% (-12.18% to 0.82%) |

Positive gain means M1 has lower count deviance than M0. The intervals use 1,000 paired authority resamples within regions. They condition on the fitted predictions and denominator; they exclude traffic-model, geometric-allocation and selection uncertainty. They do not establish causation or prospective performance. The study years have already been inspected elsewhere.

| Region | −20% cold weights | Selected model | +20% cold weights |
| --- | --- | --- | --- |
| London | 7.87% | 8.24% | 8.70% |
| South East | 3.04% | 5.17% | 7.65% |
| South West | -4.94% | -5.66% | -6.12% |

London and South East improve under all displayed allocations, while South West worsens. The direction persists in the stricter major-road subset, although its regional intervals are wider and South East and South West intervals include zero. The subset is selective and uses the original whole-LSOA climate feature.

Observed-to-expected collision ratios for the selected all-road frost model are 0.873 in London, 0.889 in South East and 0.970 in South West. The pooled ratio is 0.892. Values below one indicate overprediction. Better deviance than M0 does not resolve this calibration weakness or the exposure-validation failures.

Our working conclusion is that the apparent frost contribution is geographically uneven and materially conditional on exposure and omitted road context. We preserve the original phase 1–6 results. Annual frost anomalies, time on frost-affected roads, vehicle mix within LSOAs and insurance claims exposure remain unmodelled.

# How to use the LSOA output

The full compressed CSV contains one row for every pilot LSOA and year. The website lookup shows 2024 and allows searches by LSOA code, name or authority. Use the quality columns alongside every estimate; do not turn a blank rate into zero.

| Field or family | Meaning |
| --- | --- |
| lsoa, year, authority, region | Stable LSOA2021 code, calendar year, UTLA23 membership and English region. |
| population, density, urbanFraction | Static Census context; density is residents per km² and urbanFraction lies between zero and one. |
| roadFrostDays, roadDecile, roadEligible | Frozen climate normal, national D1–D10 and original road-climate eligibility. |
| minorNetworkMetres | Access-screened mapped minor-road length assigned inside the LSOA. |
| majorMiles, routedMajorMiles | All allocated major miles and the subset meeting the routing rules. Their difference is fallback major allocation. |
| preferredMinorMiles, preferredMiles | Selected traffic model’s minor allocation and total exposure. |
| benchmarkMiles, modelMiles | Total exposure under each traffic candidate. Both use identical major allocation and authority totals. |
| minus20Miles through plus20Miles | Total miles under the four decile-weight stress scenarios. The label describes the weight multiplier, not a guaranteed final-mile percentage. |
| assignedMotorCollisions, conditionalRatePer100k | Location-assigned definite-motor injury collisions; count ÷ modelled miles × 100,000 where gates permit. |
| nearBoundaryMotorCollisions | Assigned collisions within 10 metres of a boundary; positional uncertainty context. |
| majorFallbackShare | Authority-year fraction of major miles requiring fallback, repeated across its LSOAs. It is not the LSOA’s own fallback fraction. |
| unsupportedFunctionMinorShare and related shares | Fraction of model minor weight with unsupported function, sparse group or density extrapolation. |
| denominatorAvailable, rateEligible, balancedModelCohort | Authority exposure available; inherited current-year rate gate; eligible in all four years for the outcome comparison. |
| validatedFrequencyEligible, qualityReasons, qualityFlags | Always false for validated frequency; original authority reasons and explicit modelling warnings. |

Additional downloads include count-site matching and held-out predictions, per-fragment traffic estimates, source section allocations to LSOAs, road-function support, authority conservation, numerator reconciliation, model coefficients, outcome comparisons and checksums. The numeric allocations can be audited without treating the map as exact surveyed geometry.

# Evidence provenance and next validation work

## Frozen source editions

| Source | Edition or use |
| --- | --- |
| DfT road traffic downloads | Archived AADF, annual Major Road Database 2021–2024 and official authority motor miles. Both counted and estimated major sections remain visible. |
| Ordnance Survey Open Roads | April 2026 national archive; SHA256 begins bb2bbff8be3d637b. Geometry, numbers, function and topology. |
| ONS geography | LSOA2021 EW BFC V10 archive; SHA256 begins 3f9e1af25956e4e0. Fixed UTLA23 membership. |
| Census and rural classification | Existing verified OA population and rurality input; Census 2021 and RUC2021. |
| Met Office | HadUK-Grid v1.1.0.0 public 2 km 1991–2020 air-frost normal, retained from the frozen frost release. |
| DfT road safety | Frozen STATS19 collision and vehicle files, motor-scope rules and polygon assignments from the earlier study. |

Official source entry points: roadtraffic.dft.gov.uk/downloads and roadtraffic.dft.gov.uk/about; docs.os.uk/os-downloads/products/transport-network-portfolio/os-open-roads/os-open-roads-technical-specification; the ONS Open Geography Portal; and gov.uk/government/statistical-data-sets/road-safety-open-data. Exact asset URLs, full hashes and inherited input checksums are in source-register.json and the preceding frost release.

## Reproduction and checks

The repository includes the complete staged build script, geometry allocator, numerical checks, frozen design and documented assessment amendment. Raw nationwide OS and ONS archives are external prerequisites and must match the recorded hashes; a later edition is not a substitute. Geometry-derived section allocations and fragment predictions are also published. The output manifest identifies every release file.

Numerical checks cover unique LSOA-year rows, nonnegative exposure, authority conservation for every scenario, preserved missing values, unchanged major components under stress, geographic site grouping, forbidden predictor exclusions and the identical assessment cohort across scenarios. Earlier frost input hashes are unchanged. Site type checks and production build are separate implementation checks; browser interaction testing was unavailable in this environment.

## Priorities before relying on local rates

Improve matching for the major-road sections currently using fallback, then review representative urban and rural examples. Obtain count data for local-access and secondary-access functions and a genuinely new geographic sample. Validate allocation against independent segment traffic, reporting errors by frost band as well as road class. Reconstruct material historical network changes and annual local traffic redistribution. Resolve reporting and reconciliation exclusions before expanding the collision cohort.

Only after those checks should we reconsider validated LSOA frequencies. Any revised denominator needs a new version, preserved source hashes and rerun sensitivity comparisons. This pilot is suitable for assumption testing and gap prioritisation; it does not establish an insurer rating factor.