Probability distribution of the infrastructure risk score

Each year, accidents lead to injuries and even fatalities on the roads. Potentially, these serious events could happen anywhere. But in reality, their location is not random.
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#intro

Accident risk is unevenly distributed

SAMRoute models the statistical distribution of the risk of accident on roads

For example, intersections, crossings, or level crossings are known to be more hazardous, as are busy roads that, mechanically, will have more accidents.

Accidents are not uniformly distributed along roads at random. The idea, therefore, is to measure the accident risk of roads based on their characteristics, such as the type of road, the number of lanes, the presence of median dividers, or lighting.

Ideally, this risk estimate would result in a meaningful figure that everyone can understand. Such a figure could simply be the probability of a road segment having an accident over 12 months, which some call the incidence rate.
Video: Understanding the visualization and the distribution
#distribution

Parameters

#/y
km
90.0%
10.0%

Calculations

#
%
x
x

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#perspectives

By estimating, based on road infrastructure characteristics, the probability of a 100-meter road segment to have an accident within 12 months (incidence rate)

SAMRoute opens new perspectives of pre-diagnostic

First, systematic scoring of roads allows segments to be ranked by risk, distinguishing those that are more dangerous from those that are less so. But now, ratios can also be calculated.
  • Between segments, a ratio quantifies how many times one segment is riskier than another.
  • Compared to a reference value, such as the population average, these ratios allow segments to be compared to this same baseline.
  • And between groups of segments, ratios enable comparisons using statistics like the average for each group.
#parameters

Parameters of calculation and conception of graphic

Number of events, network length, thresholds, and road user

1️⃣ Number of events. We indicate 3,402 as the number of road fatalities in France in 2023 (ONISR), but we could also include the number of severe, minor injuries, or uninjured cases.

2️⃣ Road network length. Here, we can specify 1 or 2,300,000 km of roads, depending on the official count or that of OpenStreetMap. We could also focus on the entire network or a specific part (department, region).

3️⃣ Thresholds. Next, we specify the upper quantiles in red for high-risk roads and lower quantiles in green for safe roads. We use 90 and 10%, but 99 and 1% are also possible.

4️⃣ Road user. Since the accident probability varies by user type, we can also change the user to among car driver, motorcyclist, cyclist, and pedestrian.

Then we derive the number of road segments (making ~100 m each), the average score (log-normalized), and the ratios to the baseline for high and low-risk thresholds.
➡️ The x-axis shows the range (min-max) of scores obtained across the French road network, composed of 23 million segments. Since the probabilities are small, the scores are logarithmically scaled.

⬆️ The y-axis represents the cumulative distribution (CDF), ranging from 0% to 100%. The CDF follows a sigmoid (normal) shape.

☰ Horizontal lines indicate the thresholds. The area under the curve is shaded green for the lower decile (low risk) and red for the upper decile (high risk).

━ The thick curve represents the theoretical distribution of the risk score, while the background curve shows the actual empirical distribution across the French network.
📌 Note that the empirical distribution is divided into 1,000 steps, with each step representing therefore 0.1% of the values.
#results

💡 | Key results

1️⃣ An average risk per 100-meter segment across the network of 0.015% (incidence rate or baseline).

2️⃣ A risk of 0.058% for high-risk segments (top 10%), which is 3.9x higher than the baseline.

3️⃣ A risk of 0.0038% for safe segments (bottom 10%), which is 0.26 times the baseline or 4x lower.
📌 Note that the number of events per year (3,402) divided by the number of road segments (23,000,000) leads to the average incidence rate of 0.015%.
#get-started

The reasons to select SAMRoute

— Why SAMRoute could be an innovative solution to improve the safety of your organization's transport infrastructure?

Because:
  • SAMRoute evaluates 100% of the road network, including often overlooked segments.
  • You are not limited by administrative boundaries.
  • You stay ahead of new regulations, such as the EC 2019/1936 directive, which mandates proactive road assessment for major roads by 2024.
  • By identifying high-risk segments early, you have the chance to avoid human and material costs resulting from accidents.
  • The risk score from SAMRoute is linear and explainable, unlike AI models that are non-linear and opaque.
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