Methodology

TripRisk implements an evidence-based, probabilistic risk-assessment framework for surface transportation. Rather than relying on heuristic proxies for danger, the system ingests authoritative federal crash records, traffic-volume telemetry, and real-time environmental data to produce a continuous, per-segment fatality-probability estimate for every route it evaluates.

The modeling pipeline combines exposure-normalized crash rates, empirical Bayesian shrinkage estimation, temporal and meteorological adjustment factors, and constrained multi-objective route optimization to surface the trade-off between travel time and fatality risk in a form that is both statistically rigorous and immediately actionable.

This document describes each stage of the pipeline in detail. Where appropriate, we reference the underlying literature and data sources. Certain implementation specifics of the routing algorithm are proprietary and are described at a conceptual level.

Data Foundation

The risk model is grounded in four primary data sources, each contributing a distinct dimension to the overall hazard estimate.

FARS — Fatality Analysis Reporting System[16]

Maintained by NHTSA, FARS is a census of every motor-vehicle crash on US public roads that results in at least one fatality within 30 days. We ingest the 2019–2023 multi-year file, yielding approximately 190,000 geo-located fatal-crash records. Each record carries precise coordinates, time-of-day, weather conditions at time of crash, road functional classification, and vehicle/person-level detail. This three-year window balances statistical stability against currency of infrastructure conditions.

HPMS — Highway Performance Monitoring System[17]

Published by FHWA, HPMS provides annual average daily traffic (AADT) counts and geometric attributes for over 8.7 million road segments nationwide. AADT serves as the denominator in our crash-rate calculation: without exposure normalization, high-volume roads would appear disproportionately dangerous simply because more vehicles traverse them. HPMS segments are linked to FARS crash locations via a spatial join using a KD-tree nearest-neighbor index projected into an equal-area coordinate system (EPSG:5070, Albers Equal-Area Conic).

OpenStreetMap[18]

The routable road network is derived from OpenStreetMap (OSM) via continental PBF extracts. OSM supplies road geometry, connectivity, speed limits, turn restrictions, and functional classification tags that are essential for graph-based pathfinding. Each OSM edge is matched to its corresponding HPMS/FARS risk score during graph construction.

Open-Meteo[19]

Real-time and forecast weather conditions are obtained from the Open-Meteo API, which aggregates multiple national meteorological services. We sample conditions at regular spatial intervals along the route to detect localized weather events (e.g., a snow band crossing a mountain pass) that may not be present at the origin or destination.

Risk Quantification

The core risk metric is the fatality rate per 100 million vehicle-miles traveled (VMT). This exposure-normalized measure is standard in transportation safety research and allows meaningful comparison across road segments with vastly different traffic volumes.[16]

Crash-rate estimation

For each HPMS segment, we compute a raw fatality rate by dividing the count of FARS-matched fatal crashes (within a configurable snap radius) by the segment’s annual VMT derived from AADT and segment length. Because many segments — particularly low-volume local roads — observe zero fatal crashes in the study period, naïve maximum-likelihood estimation would assign them a risk of exactly zero, which is clearly an underestimate.

Empirical Bayesian shrinkage[26,27]

To address the zero-crash problem and stabilize estimates on low-exposure segments, we apply an empirical Bayesian framework. Each segment’s observed crash count is treated as a draw from a Poisson process whose rate parameter is itself drawn from a prior distribution. The prior is constructed at the functional-system level (e.g., interstate, principal arterial, minor collector), reflecting the well-documented relationship between road classification and crash severity. Segments with little data are “shrunk” toward their functional-class mean, while segments with substantial crash history retain estimates close to their observed rate. This yields smoothed, defensible estimates even where crash counts are sparse.[26,27]

Log-normalization and calibration

The resulting fatality rates span several orders of magnitude. To produce a bounded risk score suitable for route optimization, we apply a logarithmic transformation calibrated to the 95th percentile of the positive-rate distribution. This mapping compresses extreme outliers while preserving rank-ordering and relative magnitudes across the bulk of the distribution. The final score lies on a continuous [0, 1] scale where 0 indicates negligible historical fatality risk and 1 indicates risk at or above the 95th-percentile threshold.

Temporal Adjustment

Fatality risk is not uniform across the diurnal cycle. NHTSA and IIHS data consistently show that nighttime driving carries substantially elevated fatality rates per VMT relative to daytime driving, due to reduced visibility, higher prevalence of impaired and fatigued drivers, and lower seatbelt-use rates.[20,21]

We partition the day into three lighting regimes — day, twilight (civil twilight), and night — using solar-position calculations based on the departure time and geographic coordinates.[22] The raw NHTSA/IIHS fatality ratios (day = 1.0, twilight ≈ 1.5, night ≈ 2.75) are then decomposed against VMT-weighted exposure fractions from the 2017 National Household Travel Survey to remove the baseline temporal mix already embedded in the annual HPMS crash rates.[22]

The resulting adjusted multipliers represent the marginal change in risk attributable to lighting conditions above or below the annual average. Daytime trips receive a multiplier below 1.0 (i.e., below-average risk), while nighttime trips receive an elevated multiplier, faithfully reflecting the empirical day/night disparity without double-counting the temporal component already present in the base rates.

Weather Integration

Adverse weather — rain, snow, and fog in particular — is a well-documented contributor to crash frequency and severity.[23] We integrate weather effects through a two-stage process:

  1. Multiplier derivation. Using FARS 2021–2023 crash records stratified by atmospheric condition at time of crash, we compute condition-specific fatality multipliers normalized by exposure. Exposure fractions are estimated from temporal prevalence data (fraction of hours in each weather state), not from crash-involvement fractions, to avoid conditioning on the outcome. The resulting multipliers quantify the proportional increase in fatality risk relative to clear-and-dry conditions, broken out by road functional classification.
  2. Spatial sampling. At route-computation time, we query the Open-Meteo forecast API at regular spatial intervals (approximately every 10 km) along the route for the user’s specified departure time. Each sample yields a weather condition (clear, rain, snow, or fog) which is mapped to the corresponding multiplier and applied to the risk scores of edges within that sample’s coverage zone. This spatial approach captures localized weather variation — a critical feature for mountain-pass and lake-effect corridors.

Vehicle Profiling

Fatality risk varies substantially by vehicle type. NHTSA and IIHS data show that motorcyclists face fatality rates an order of magnitude higher than passenger-car occupants per VMT, while occupants of larger vehicles (SUVs, pickup trucks) experience modestly lower rates attributable to greater crashworthiness and mass differential advantages.[24,25]

TripRisk supports vehicle-category selection, applying a multiplicative adjustment factor derived from NHTSA fatality-rate tables disaggregated by vehicle body type. The adjustment is applied to the final fatality probability rather than to individual edge weights, preserving the routing graph’s independence from vehicle choice and enabling instant client-side recalculation when the user switches vehicle types.

Supported categories include sedan, SUV, pickup truck, van/minivan, and motorcycle. Motorcycle selection triggers a prominent safety advisory given the approximately 29× elevated fatality rate per VMT relative to passenger cars.

Route Optimization

The routing engine solves a bi-objective shortest-path problem over a large-scale road network graph, simultaneously minimizing travel time and cumulative fatality risk. This is fundamentally a multi-objective optimization problem: the fastest path is rarely the safest, and the safest path may impose an unacceptable time penalty.

Strategy decomposition

TripRisk presents three canonical strategies to the user:

  • Fastest: Minimizes travel time without regard to risk. This serves as both a user-facing option and the reference benchmark for the balanced strategy’s time budget.
  • Safest: Minimizes cumulative distance-weighted fatality risk without regard to travel time. This represents the Pareto-optimal solution at the extreme risk-minimization end of the frontier.
  • Balanced: Identifies the most risk-minimizing path that remains within a time-budget constraint relative to the fastest route. This is the solution most users should prefer, as it captures the majority of available risk reduction with modest time cost.

Constrained optimization via Lagrangian relaxation[28]

The balanced strategy is computed using a Lagrangian relaxation approach. We introduce a multiplier that scalarizes the two objectives — risk and time — into a single composite edge weight. By varying this multiplier across a structured search, we trace out a family of efficient paths along the Pareto frontier. The algorithm selects the solution that achieves maximal risk reduction subject to the constraint that total travel time does not exceed a fixed proportion of the fastest route’s duration.

This formulation avoids the pitfalls of naïve weighted-sum approaches (where poorly scaled objectives cause one term to dominate) and provides provable bounds on solution quality. The specific implementation details, including the search strategy, convergence criteria, and edge-weight construction, are proprietary.

Risk in Perspective

Human intuition is notoriously poor at evaluating low-probability events. To aid interpretation, TripRisk places the computed fatality probability alongside a curated set of familiar risks drawn from authoritative sources. The following table lists annual per-person fatality odds for various events in the United States, ordered from rarest to most common.

EventOdds (annual)Explanation
Plague1 in 309MThe US averages roughly 1 plague fatality per year among 330 million residents, making it one of the rarest causes of death in the country.[1]
Powerball jackpot1 in 292MThe probability of matching all five numbers plus the Powerball in a single ticket. Often cited as the benchmark for "essentially impossible" events.[2]
Earthquake1 in 165MAnnual fatality risk from earthquakes in the contiguous US, averaged across all regions including low-seismicity zones. Risk is highly concentrated in specific fault corridors.[3]
Meteor strike1 in 128MEstimated individual annualized fatality risk from bolide impacts. Dominated by the extremely rare but catastrophic large-body events; the per-year expected deaths are small.[4]
Vending machine1 in 112MApproximately 2–3 deaths per year result from toppling vending machines, typically during attempts to shake free a stuck product.[5]
Botulism1 in 80MRoughly 3–4 deaths per year from botulinum toxin poisoning in the US, most commonly from improperly home-canned foods. Case fatality has declined markedly with modern antitoxin therapy.[6]
Shark attack1 in 66MAnnual US fatality risk from unprovoked shark encounters. Despite media attention, fatal attacks average fewer than 5 per year nationwide.[7]
Snake bite1 in 60MRoughly 5–6 deaths per year from venomous snake bites in the US, principally from rattlesnakes in the southeastern and southwestern states.[8]
Commercial flight1 in 11MPer-flight fatality risk for US commercial aviation, reflecting the extraordinarily low accident rate of modern air transport.[9]
Tornado1 in 5.7MAnnualized individual fatality risk from tornadoes. Risk is concentrated in the Great Plains and Southeast during spring convective season.[10]
Lawn mower1 in 4.8MApproximately 69 deaths per year from riding and push mower incidents, including rollovers, contact with blades, and struck-by debris events.[5]
Lightning strike1 in 1.2MBased on a 10-year average of approximately 270 fatalities per year. Risk is strongly seasonal (June–August) and highest in Florida.[11]
Falling out of bed1 in 755KPrimarily affects elderly adults; CDC WISQARS data show roughly 440 bed-fall fatalities annually, driven by head trauma and hip fracture complications.[12]
Train accident1 in 413KIncludes both occupant and trespasser fatalities at railroad crossings and along track rights-of-way.[13]
Drowning1 in 94KApproximately 3,500 unintentional drowning deaths per year. Children 1–4 and males are disproportionately represented.[12]
House fire1 in 88KRoughly 3,700 civilian fire deaths annually, predominantly in residential structures. Cooking equipment and heating systems are the leading ignition sources.[14]
Choking1 in 66KAbout 5,000 choking deaths per year; food aspiration in adults over 65 accounts for the majority of fatal cases.[15]
Gun violence1 in 17.8KEncompasses all firearm-related fatalities including homicide, suicide, and accidental discharge. The US rate is substantially elevated relative to other high-income countries.[12]
Falls (all types)1 in 9.2KThe leading cause of injury death among adults 65 and older. CDC WISQARS estimates approximately 36,000 fall fatalities annually across all age groups.[12]

Note that the driving fatality probability reported by TripRisk is a per-trip estimate, not an annual aggregate. To compare with the annual figures above, one would multiply the per-trip probability by the number of similar trips taken in a year.

Limitations & Caveats

  • Fatal crashes only. FARS records only crashes with at least one fatality. Non-fatal injury and property-damage-only crashes — which outnumber fatal crashes by roughly 200:1 — are not captured. This means the model estimates fatality risk specifically, not overall crash risk.
  • HPMS coverage gaps. HPMS does not report AADT for all local roads, particularly unpaved rural roads and private roadways. Segments lacking AADT data receive a global imputed rate based on aggregate national statistics, which may over- or under-estimate true exposure.
  • Weather: forecast vs. observation. Weather multipliers are applied using forecast data at departure time. Actual conditions may differ, particularly for longer trips where weather can change substantially en route.
  • Intersection risk. The current model attributes crashes to road segments, not to specific intersections. Intersection geometry, signal timing, and turning-movement volumes — all significant crash predictors — are not modeled explicitly.
  • Temporal stationarity. The model assumes that historical crash rates (2019–2023) are representative of current conditions. Road improvements, new construction, or changes in traffic patterns after the data window may not be reflected.
  • Driver behavior. Individual risk factors — speeding, impairment, distraction, seatbelt non-use — are not modeled. The reported probabilities reflect population-average risk for a given route, time, and weather.

References

  1. Centers for Disease Control and Prevention. "Plague in the United States." CDC, 2023.
  2. Multi-State Lottery Association. "Powerball® Game Rules and Odds." Powerball.com, 2024.
  3. U.S. Geological Survey. "Earthquake Hazards Program: Deaths from Earthquakes in the United States." USGS, 2024.
  4. Morrison, D. "The Hazard of Asteroid and Comet Impact on Earth." NASA Ames Research Center / Tulane University Environmental Studies, 2023.
  5. U.S. Consumer Product Safety Commission. "CPSC Injury and Fatality Statistics." CPSC, 2023.
  6. Centers for Disease Control and Prevention. "Botulism: Epidemiological Overview for Clinicians." CDC, 2023.
  7. International Shark Attack File. "Yearly Worldwide Shark Attack Summary." Florida Museum of Natural History, University of Florida, 2024.
  8. Centers for Disease Control and Prevention. "Venomous Snakes: Clinical Management." CDC NIOSH, 2023.
  9. National Transportation Safety Board. "Aviation Accident Statistics." NTSB, 2024.
  10. National Oceanic and Atmospheric Administration. "Storm Prediction Center: Annual US Tornado Fatalities." NOAA SPC, 2024.
  11. National Weather Service. "Lightning Fatalities by State and Activity, 2006–2023." NWS, 2024.
  12. Centers for Disease Control and Prevention. "Web-based Injury Statistics Query and Reporting System (WISQARS)." CDC NCIPC, 2024.
  13. Federal Railroad Administration. "Highway-Rail Grade Crossing Safety & Trespass Statistics." FRA, 2024.
  14. National Fire Protection Association. "Fire Loss in the United States." NFPA, 2024.
  15. National Safety Council. "Preventable Deaths: Choking and Suffocation." NSC Injury Facts, 2024.
  16. National Highway Traffic Safety Administration. "Fatality Analysis Reporting System (FARS)." NHTSA, 2019–2023.
  17. Federal Highway Administration. "Highway Performance Monitoring System (HPMS)." FHWA, 2023.
  18. OpenStreetMap Contributors. "OpenStreetMap." openstreetmap.org, 2024.
  19. Zippenfenig, P. "Open-Meteo: Free Weather API." open-meteo.com, 2024.
  20. National Highway Traffic Safety Administration. "Traffic Safety Facts: Nighttime Traffic Fatalities." NHTSA DOT HS 813-305, 2022.
  21. Insurance Institute for Highway Safety. "Fatality Facts: Darkness." IIHS, 2024.
  22. Federal Highway Administration. "National Household Travel Survey (NHTS)." FHWA, 2017.
  23. National Highway Traffic Safety Administration. "Traffic Safety Facts: Weather-Related Crash Statistics." NHTSA, 2023.
  24. Insurance Institute for Highway Safety. "Fatality Facts: Vehicle Type." IIHS, 2024.
  25. National Highway Traffic Safety Administration. "Fatality and Injury Reporting by Vehicle Category." NHTSA NCSA, 2023.
  26. Robbins, M. M., and Srinivasan, S. "Empirical Bayes Method for Estimating Safety Performance of Roadway Segments." Transportation Research Record, vol. 2083, pp. 41–48, 2008.
  27. Hauer, E. Observational Before-After Studies in Road Safety. Pergamon Press, 1997.
  28. Boyd, D. T. "Multi-objective Optimization in Transportation Network Design." Journal of Transport Geography, vol. 46, pp. 12–22, 2015.
TripRisk is a free, independent project built and maintained by Mark S.. If you find it useful, consider supporting the project.