Contents

Across 85,556 geocoded incidents over 12 weeks in a 14 × 14 km study area, the headline result is not that night is busier. It is not: the night window carries 3,640 incidents per hour against 3,534 in the day, a difference of 3%. Night is different in shape, not in volume. Incidents after 22:00 are more severe (mean severity weight 2.39 against 2.25; t = 14.5, p < 0.0001) and far more tightly clustered — the top 5% of the area holds 39.2% of night incidents against 30.2% of daytime ones, with a Gini coefficient of 0.56 on the night surface against 0.43 on the day surface.

That difference is what makes routing worth doing. A risk that is spread evenly cannot be driven around. A risk that concentrates into 9.8 km² can.

The five findings

The brief came from a distribution operator running night deliveries across the metropolitan area. Vehicles leave a single depot between 22:00 and 02:00 and serve fixed destinations. The operator had anecdote — drivers avoiding certain streets, two incidents in a quarter — and wanted evidence.

Definitions adopted for this programme

Police dispatch logs are published as open data by a growing number of forces, typically as a daily or weekly CSV of calls for service. They are not a crime dataset: a dispatch record is a call, and a proportion of calls turn out to be non-crime, duplicated, or later unfounded. The cleaning sequence below exists to convert one into something usable for the other.

Cleaning sequence and yield

118,400 dispatch records were published across the window; 85,556 survived to analysis, a yield of 72.3%. The largest single loss is the call-type filter, which is expected — most calls for service are not crime.

Day and night are the same size — per hour

The night window is seven of twenty-four hours, or 29.2% of the clock, and it carries 29.8% of incidents. The ratio is 1.02. Night is, in raw volume, an unremarkable part of the day. Every claim in this report about night risk rests on concentration and severity, never on volume, and the distinction is made explicitly wherever it matters.

Severity weights are ordinal and set before analysis: robbery 5, assault 4, vehicle theft 3, theft from vehicle 2, vandalism 1.5, public disorder 1. They are a stated judgement, not a measurement, and every weighted figure in this report can be recomputed on a different scale from the delivered table.

The night shift in the mix is the finding on this page. Assault runs at 38.6% night share and vehicle theft at 33.9%, against 22.0% for theft from vehicle — the highest-volume category in the corpus and the one most tied to daytime parking. The night window does not add incidents; it swaps opportunistic property crime for confrontational and vehicle-directed crime, which is precisely the exposure a delivery driver carries.

The volume curve peaks in the evening and decays through the small hours, which is unremarkable. The severity curve does not follow it: mean severity per incident stays elevated across the whole night window while volume falls away. An operator dispatching at 01:00 faces fewer incidents than one dispatching at 19:00, but a worse mix.

Counting incidents per zone answers a different question from the one asked. Zone counts depend on where the zone boundaries happen to fall, and a hotspot sitting on a boundary disappears into two unremarkable halves. Kernel density estimation removes the boundary entirely: every incident contributes a small, smooth bump of probability mass to the surface around it, and the surface is the sum of those bumps.

The bandwidth is the only subjective choice in the method, and it is a real one. Too small and every cluster of three incidents becomes a peak; too large and the whole city becomes a single warm blob centred on downtown. Scott's rule is used because it is data-driven rather than hand-picked, and §07 tests what happens when it is overridden in both directions.

Side by side and hour-normalised, the two surfaces tell the story the summary table only implied. The daytime surface is broad: the central core dominates but every commercial sub-centre carries visible warmth. The night surface is peakier — the same core reaches a higher per-hour rate while most of the map goes cold. Peak night density reaches 1139 incidents per km² against a surface mean of 128, a ratio of 8.9 to 1.

A heat map can be made to show almost anything by moving the bandwidth, which is why a density map published without a sensitivity test should not be acted on. The night surface was refitted at 60%, 80%, 100% and 140% of the Scott bandwidth and the hotspot extraction repeated at each.

Peak height moves a great deal — from 820 to 1,809 across the range, which is exactly what smoothing does and why peak values should never be quoted on their own. What barely moves is the thing the routing decision depends on: the share of night incidents captured inside the top 5% of the area varies only between 33.1% and 41.2%.

Thresholding the night surface at its 95th percentile yields 9.8 km² of hotspot — 5.0% of the study area — containing 39.2% of all night incidents. That is a concentration factor of 7.8: a randomly chosen square kilometre inside the contour carries 7.8 times the night incident load of the area average.

The contour resolves into 4 separate clusters above the 0.12 km² minimum extent. One dominates: H1 spans 6.77 km² and holds 6,724 night incidents on its own, 67% of everything inside the contour. The remaining three are compact, between 0.85 and 1.21 km².

For a fleet, the shape matters as much as the size. A single large cluster astride the depot-to-destination axis is a routing problem with a clean solution. Four scattered small ones would not be.

H1 sits directly between the depot in the north-west and three of the four night destinations in the south and east. That geometric accident — and it is an accident, not a property of the crime pattern — is why this fleet has an exposure problem at all, and why §13 can solve so much of it with such a short detour.

The density surface is the right object for a router and the wrong one for a dispatch briefing. For reporting, the study area is divided into 49 zones of 2 × 2 km and each is scored on severity-weighted incident load per square kilometre, rescaled across the set to a 0–100 index.

Z-25 scores 100 against 66 for the next zone — it carries 1.5 times the weighted load per square kilometre of its nearest rival and contains hotspot H1. Note that the highest night share in the top ten is not the highest-volume zone: Z-24 runs at 38.4% night, which makes it a smaller problem overall but a disproportionately night-weighted one for this operator.

A hotspot that has been in the same place for a decade is a known quantity; drivers and dispatchers have already adapted to it. A hotspot that appeared six weeks ago has not been adapted to by anyone. Splitting the night corpus at the midpoint and differencing the two density surfaces isolates exactly that.

Three zones grew significantly. Z-41 rose from 515 to 884 night incidents, a rate ratio of 1.72 (p < 0.0001); Z-16 from 439 to 740 (1.69, p < 0.0001); and Z-09 from 325 to 562 (1.73, p < 0.0001). Below those three, growth falls away and the p-values stop clearing 0.05 — Z-15 at +22.3% (p = 0.1127) is the first zone that should be read as noise.

Tested against the significance threshold, the emerging set is small and clean. That is the useful outcome: three places to watch, not a map of amber warnings that an operations team will learn to ignore within a fortnight.

Is the clustering real, or would random points look like this?

NEAREST-NEIGHBOUR INDEX

NNI = d̄_obs
d̄_exp   where   d̄_exp = 1
2√(n/A)

Mean observed distance to the nearest other incident, against the value expected under complete spatial randomness for the same intensity. NNI below 1 indicates clustering, above 1 dispersion.

d̄_obs = 80 m  ·  d̄_exp = 90 m  ·  NNI = 0.885 (z = -17.03, p < 0.0001, on a random subsample of n = 6,000)

An NNI of 0.885 is a modest departure from randomness in absolute terms — incidents are roughly 11% closer to each other than chance would predict. At this sample size it is nonetheless overwhelming evidence against randomness, and it sets an important expectation: this is a city with some concentration everywhere, not a handful of crime islands in an empty sea. The routing gain comes from the top of the surface, not from its general shape.

Is the total moving?

No. The fitted weekly slope on night volume is -3.93 incidents per week (SE 3.36; 95% CI -10.52 to +2.65; R² = 0.12; p = 0.2690). The interval comfortably contains zero and the R² is negligible. Over the window the city recorded no meaningful change in how much night crime occurred.

The composition test completes the picture: the association between category and time window is significant at χ²(5) = 1,201, p < 0.0001, with Cramér's V = 0.12. A small effect size, as expected — night changes the mix noticeably but does not transform it.

A heat map is where most geospatial crime work stops, and it is the least useful place to stop. A map tells a dispatcher that an area is dangerous; it does not tell a vehicle which way to go. Converting the surface into an edge-cost field turns the analysis into something a router can optimise against.

The 100 m lattice becomes a graph: every cell is a node, connected to its eight neighbours. Each edge carries a cost that blends the physical length of the move with the risk of the ground it crosses.

Choosing λ

λ is a policy parameter, not a statistic. It encodes how much additional driving the operator is willing to buy a unit of avoided exposure with, and it should be set by the operator rather than by the analyst. Setting it to 9 was a deliberate choice: it is high enough to route firmly around the peak and low enough that the router will still cross moderate risk rather than taking absurd perimeter detours. §17 recommends the operator tune it themselves against the exposure-versus-distance curve.

Four destinations were solved from a single depot in the north-west of the study area. The dashed baselines are what a conventional navigation system returns, and the pattern in them is immediate: three of the four run on a straight north-west to south-east diagonal that passes directly through hotspot H1.

That is not a coincidence of this dataset. Depots sit on cheap peripheral land, destinations cluster around commercial and industrial centres, and the straight line between them tends to cross the dense inner area where night incidents concentrate. The geometry that makes a route short is the same geometry that makes it risky.

Re-solved at λ = 9, the routes swing wide, following the low-density corridors around the northern and eastern edges of the core before dropping into their destinations. Total exposure across the four falls from 9.93 to 4.13 risk-kilometres, a reduction of 58.4%.

The gains are highly uneven, and the unevenness is the practical finding. R1 and R3 — the two routes that ran straight through H1 — lose 68% and 72% of their exposure for 17% and 12% more distance. By contrast R4, which already ran through low-density ground, gains only 18% — and correctly so. A router that produced a large detour for R4 would be optimising noise.

The profile shows something a summary figure hides. On the baseline route, exposure accumulates almost entirely in a single stretch: a near-vertical rise as the vehicle crosses H1, with flat sections either side. The risk-aware route has no such step — it accumulates slowly and evenly across a longer drive.

For R1 the cut is 72% of exposure for 1.70 km and 3.6 minutes. Almost all of that saving is bought in one decision, several kilometres from the destination.

That concentration has an operational consequence worth more than the routing change itself: it means the exposure is avoidable by a single turn, not by a continuous sequence of micro-decisions. A driver briefing that names one corridor to avoid captures most of the benefit even without any change to the navigation system.

Fleet-level arithmetic

Quantity	Value	Basis
Mean exposure reduction	−47.3%	Unweighted mean across the four routes
Mean distance penalty	+11.3%	Unweighted mean across the four routes
Extra time per trip	+2.7 min	At a 28 km/h night average speed
Trips per night	42	Operator-supplied
Operating nights per year	312	Operator-supplied
Additional distance per year	16,312 km	Mean penalty × trips × nights

16,312 additional kilometres a year is the entire cost side of this recommendation, and it is a number the operator can price precisely from their own fuel, wear and driver-hour rates. The benefit side cannot be priced the same way, because the value of an incident that does not happen is not observable. What the study can say is that the fleet's night-time exposure falls by 47% for that spend.

ON NOT OVERCLAIMING

Exposure is a proxy. A 47% reduction in risk-kilometres is not a 47% reduction in incidents involving this fleet, and this report does not claim it is. The relationship between area incident density and the victimisation rate of a specific passing vehicle is unmeasured here and would need the operator's own incident history to estimate.

A density surface is not an operating procedure. The rules below are the translation, written so they can go into a dispatch handbook without reference to any of the mathematics behind them.

The analysis resolves into one mechanism, and like most useful ones it is simpler than the machinery used to find it. Night-time crime is not more frequent than daytime crime; it is more concentrated and more severe. Concentration is what makes it avoidable, and avoidability is what makes it a logistics problem rather than a security problem.

Answering the three commissioned questions

The core recommendation

Adopt risk-weighted routing for the night window on the two routes that cross hotspot H1, adopt the stationary-time rule fleet-wide, and refit the surface quarterly. Nothing here requires new vehicles, new staff or new systems beyond a cost layer in the existing routing software.

MODELLED EFFECT AT FLEET LEVEL

E′ = E · (1 − c),   D′ = D · (1 + a)

c = 0.473 mean exposure cut  ·  a = 0.113 mean distance penalty  ·  across 42 trips per night and 312 operating nights.

Night exposure index 100 → 53  ·  additional distance 16,312 km/year  ·  additional driver time 583 hours/year.

Two cautions. The exposure figure is a proxy for risk, not a count of prevented incidents (§14). And the modelled penalty assumes the risk-aware geometry is drivable — the lattice router does not know about one-way systems, weight limits or bridge clearances, so every proposed route needs a drivability check before it goes live.

Ninety-day action plan

Formula glossary

Variable dictionary — delivered incident table

Delivered with this report

Continuation options