Conventional infrastructure indices measure stock: kilometres, gigawatts, berths. Because this register scores every asset on the same absolute rubric and knows where each one sits, it supports a different class of question - about concentration, substitutability, control, decay and evidence. The pairing is deliberate. Concentration without redundancy reads as efficiency; scale without adequacy flatters large states; and an index with no measure of its own evidential quality is asking to be trusted rather than audited.
Computable now from the register as it standsNeeds one more layer needs ownership, dependency or location data the register lacksNeeds external data needs population, hazard or economic data
Computing across 196 unequal nations
The register was not built evenly, and the nations in it are not alike. An index that ignores either will rank the method before it ranks the country. Six facts about the register, measured rather than assumed, set the rules every index below follows.
Notation
R the nation's top 100 (countryRank ≤ 100) · R20 its top 20 · s strategic score, 0–25 · s̃ score after pass calibration
w(s) = 2s/3 every three points doubles the weight, so a 25 counts sixteen times a 13
SX = Σ s over set X · WX = Σ w(s̃) over X · g capability group (10) · c capability (62) · ng assets in g
P population · Y GDP at PPP · A land area · tier T1–T5, the economic-scale bands in scripts/tiers.py
DTF(x) = (x − xP5) / (xP95 − xP5), clipped to 0–1: distance to frontier with the 5th and 95th percentile nations as goalposts
Nine rules
- One frame. Every index is computed over the nation's top 100 unless it says otherwise. Every nation that could fill 100 did, and the twelve that could not stopped at a real ceiling, so the frame equalises search depth. The full register is used only where depth inside a group is the point, and then with the depth stated.
- Calibrate the seam before comparing. Simple: publish the first-pass twenty and the other 176 as separate cohorts and never rank across them. Full: map each pass onto the reviewed first-pass scale with its per-band offset. The sample for that now exists: 293 assets blind-rescored across score bands, tiers and all three passes (data/evidence/ginc_calibration_rescore.csv). It found offsets of well under a point in most bands, far smaller than the 25-asset test suggested, so the correction is small and search depth is the larger problem. A flat shift is still wrong, because the offset changes sign across bands.
- Size: never raw alone, never per capita alone. Extensive indices grow with the country (Endowment, counts, Catchment); intensive ones are shares or ratios (Chokepoint, Spread, Attrition). An extensive index is published three ways: raw, per capita, and against the value expected for a nation of that size and income, X / X̂ with ln X̂ = a + β ln P + γ ln(Y/P) fitted across nations. The elasticity decides the reading: β = 1 makes per capita right and β = 0 makes the raw value right. The register's own β runs from 0.07 for the top-100 total to 0.58 for the count at 22+, so neither is. Intensive indices are not size-free either, because a small register concentrates by arithmetic, so they are read against their floor (rule 4) and within tier.
- Respect small numbers. A share over one asset is 1, and a Herfindahl index over n assets cannot fall below 1/n, so use H* = (H − 1/n) / (1 − 1/n). A ratio that needs two assets is “not applicable” with one, never zero. Noisy national values shrink toward their tier: x̂ = (n·x + k·x̄tier) / (n + k), with k the count at which a nation's own evidence starts to dominate.
- Weight the top. Importance is not linear in the score: a 25 is a national chokepoint and a 13 is not half of one. Simple versions sum raw scores; full versions use w(s), with the doubling interval tested from two to five points.
- Carry the uncertainty. Independent scorers differ on single assets with a standard deviation of 5.1 points; national aggregates are much steadier. Full versions redraw every score from its confidence (a working assumption of ±2 for high, ±3.5 for medium, ±5 for low, to be refitted from the calibration sample), recompute a thousand times, and publish the median, a 90 per cent interval and a rank band. Two nations whose bands overlap are not ranked apart.
- Mask what cannot apply. A landlocked nation is not short of seaports and a city-state has no regional spread. Masks come from authoritative lists (the UN lists of landlocked developing countries and small island developing states, plus Europe's landlocked states), never from absence in the register, because absence is what is being measured.
- Aggregate with care. Where an index combines measures: winsorise at the 2.5th and 97.5th percentiles, rescale with DTF rather than minimum and maximum (which are Tuvalu and China on most measures), and combine with a geometric mean so that strength in one cannot fully buy off weakness in another. Test every choice for rank stability, following the OECD–JRC Handbook on Constructing Composite Indicators (2008).
- Shared assets. A cross-border or supranational asset counts in full in each nation's own index. The full versions allocate it by ownership share where that share is known. No national values are added into a regional or global total without de-duplicating first.
External data
Demand-matched denominators
Population is the right denominator for water and health and the wrong one for ports. Where an index measures fit to need, each capability group is normalised by what drives demand for it.
Energy → electricity consumption · Transport → trade volume and population · Communications & Digital → internet users
Financial → GDP · Water, Sanitation & Waste → population · Social → population · Agriculture & Food → population and farmland
Resource → resource rents · Advanced Manufacturing → manufacturing value added · Space, Aerospace & Defence → military expenditure
Each index below keeps its question, carries a simple version that can be computed and read by hand, and a full version that applies these rules. Where the review found the original method would not hold, the method line has been rewritten and the reason is given.
How much strategically weighted infrastructure a nation holds, and how deep its very top is. Two nations can carry the same total and be entirely different states: one with forty assets near the ceiling, another with three and a long tail.
How much strategic infrastructure does this nation hold?
- Measures
- Total strategic score across the national register, expressed against the frontier nation rather than as a raw sum.
- Method
- Weighted total of calibrated scores over the national top 100, as distance to the frontier, published beside its per-capita and size-adjusted readings.
How to compute
- Inputs
- strategicScore, countryRank, layer, verificationStatus (drop records judged not discrete assets). Population and GDP for the size-adjusted reading.
- Comparing
- Extensive. The raw top-100 sum barely moves with size (2.8-fold across a 154,000-fold population range), so it reads average quality rather than stock; over the whole register it reads search depth. The convex weight restores the stock reading, because heavy assets dominate it. First-pass nations lead by construction until the seam is calibrated.
- Simple
E = Σi∈R si → E / EP95
beside: count of i ∈ R with si ≥ 20
cohorts reported separately
- Full
E* = WR = Σi∈R 2s̃i/3
index = DTF(ln E*)
size-adjusted = E* / Ê*, ln Ê* = a + β ln P + γ ln(Y/P)
per capita E*/P shown, not ranked; 90% interval
- Changed
- The original summed every scored asset, which ranks register depth: the twenty first-pass nations hold 5.7 times the records of the rest.
How deep is the very top of the estate?
- Measures
- The strategic score of the nation's tenth-ranked asset - the height of the plateau rather than of the peak.
- Method
- Median calibrated score across national ranks 6 to 15, beside the size-adjusted count of assets at 22 and above.
How to compute
- Inputs
- strategicScore, countryRank, layer. Population and GDP for the count.
- Comparing
- Intensive, and the index most exposed to the seam: the second pass is 2.7 points stricter exactly where Apex looks. Rank 10 exists in every nation, since the smallest register holds 75. The count at 22+ is extensive and must be size-adjusted.
- Simple
A = median(s at ranks 6–15)
C22 = count of i ∈ R with si ≥ 22
- Full
A* = median(s̃ at ranks 6–15), with interval
C*22 = Σi∈R 1[s̃i ≥ 22]
log E[C*22] = a + β ln P + γ ln(Y/P) (Poisson)
ratio = C*22 / Ê[C*22], read like a standardised mortality ratio: 1 is as expected
- Changed
- A single rank inherits one asset's scoring error, a standard deviation of about five points; a ten-rank median does not.
02Concentration
Where the weight sits
Concentration cuts two ways and the index should not pretend otherwise. A single dominant gateway is efficient and it is also the thing an adversary, a storm or an accident only has to hit once.
How much of the nation rests on its single largest node?
- Measures
- For each national flow - electricity, container trade, crude export, data, payments, water - the share of that flow's total strategic score carried by its highest-scoring asset.
- Method
- Per capability group, the leading asset's share of the group's weight, corrected for the number of assets, weighted by the group's share of national weight.
How to compute
- Inputs
- v11CapabilityGroup, v11Capability, strategicScore, status. Full version: published capacity where it exists (generation MW from Global Energy Monitor, port throughput in TEU, refinery capacity).
- Comparing
- Intensive but biased by n: with one asset the share is 1. Because 34 to 41 per cent of a nation's capabilities hold a single top-100 asset, a per-capability version mostly reports n = 1. Groups are dense enough to measure.
- Simple
per group g with ng ≥ 2: dg = max s / Sg
CP = Σg (Sg/SR) · dg
beside: number of groups holding one asset
- Full
d*g = (dg − 1/ng) / (1 − 1/ng) on w(s̃), operational assets
shrink d*g toward tier mean for small ng
where capacity is published, capacity share replaces weight share
CP* = Σg (Wg/WR) · d*g
- Changed
- A score share is a proxy: it names the asset that matters most, not the fraction of electricity it carries. Per sub-sector it was also mostly measuring single-asset sub-sectors.
Clustering
Needs one more layerHow geographically concentrated is it?
- Measures
- Whether a nation's strategic weight sits in one metropolitan region or is spread across its territory.
- Method
- Excess concentration of strategic weight over population across first-level regions, with the largest region's share beside it.
How to compute
- Inputs
- region, cityLocation, latitude, longitude, coordinatePrecision. First-level region boundaries and population by region.
- Comparing
- Coordinates exist only for the first-pass twenty, and region is free text: 5 per cent of top-100 records say only “National” and 10 per cent name a span. A raw Herfindahl index punishes small states, since a city-state is one region and scores 1, and ignores people: infrastructure as concentrated as the population is not clustered. Mask nations with one first-level region.
- Simple
geocode region → first-level region r; drop national and multi-region records
H = Σr (Sr/S)²
beside: largest region share, share dropped
- Full
KL = Σr pr ln(pr / qr)
pr = Wr/WR (weight), qr = population share
0 means weight follows people; span records split across their endpoints
unlocated records placed at region centroid with that uncertainty
- Changed
- Marked computable now, but the fields it needs exist for twenty nations. It needs a geocoding layer for the other 176.
03Redundancy
The ability to absorb a loss
Substitutability is scored at asset level already. These two lift it to the national level and ask a different question: if the best one goes, what is actually behind it?
Second Best
Computable nowIf the leading asset fails, how good is the next one?
- Measures
- Across every sub-sector, the ratio of the second-ranked asset's score to the first. A nation whose runners-up are nearly as capable as its leaders can absorb a loss.
- Method
- Per capability group, the runner-up's score over the leader's, weighted by group weight; groups with no runner-up reported separately.
How to compute
- Inputs
- v11CapabilityGroup, v11Capability, strategicScore, status, assetType. Full version: coordinates and published capacity.
- Comparing
- Undefined where a group holds one asset, and depth-biased across the whole register: the first pass swept twenty assets per sub-sector, so a runner-up always exists there. Inside the top 100 the median nation holds two or more assets in all ten groups.
- Simple
per group g with ng ≥ 2 in R: rg = s(2) / s(1)
SB = Σg Sg rg / Σg Sg over those groups
groups with ng = 1 listed, not scored as zero
- Full
per capability c, same asset type, runner-up counts only if > d km from the leader
rc = min(1, cap(2)/cap(1)) where capacity is known, else w(s̃(2))/w(s̃(1))
neighbouring nation's substitute counted at a discount
SB* = Σc Wc rc / Σc Wc, shrunk for small n, with interval
- Changed
- Run per sub-sector over a top 100, most sub-sectors have no runner-up. A second terminal in the same port is not a backup, so the full version needs separation.
Substitution
Computable nowHow replaceable is the estate as a whole?
- Measures
- National exposure to irreplaceability, weighting each asset's substitutability by how critical its flows are.
- Method
- Flow-criticality-weighted mean of lowSubstitutability, inverted so a high index means a replaceable estate.
How to compute
- Inputs
- flowCriticality, lowSubstitutability, strategicScore, layer.
- Comparing
- Intensive, built from asset dimensions that carry their own seam: four of the five run about 0.5 lower in the second pass, geographic reach does not. Small states are genuinely less substitutable, so read it raw and within tier. 239 first-pass records have dimensions that do not sum to their score, because review lowered the total only.
- Simple
Sub = 1 − Σi∈R Fi Li / (5 · Σi∈R Fi)
- Full
calibrate each dimension by pass: F̃, L̃
Sub* = 1 − Σ w(s̃i) F̃i L̃i / (5 · Σ w(s̃i) F̃i)
operational assets; tier z-score beside the raw value; interval
04Sovereignty
Who actually controls it
Infrastructure inside a border is not the same as infrastructure under national control. This pair separates the two, and the gap between them is often the most strategically interesting number a country has.
Control
Needs one more layerHow much of the estate does the nation control?
- Measures
- Share of national strategic score held by domestic public bodies, state enterprises or domestic private owners.
- Method
- Strategic score weighted by publicPrivateStatus and owner nationality.
How to compute
- Inputs
- owner, operator, publicPrivateStatus, which exist for the first-pass twenty only (37 per cent of records). New layer: owner and operator nationality, equity shares, ultimate parent (GLEIF relationship data, company filings), concession holder.
- Comparing
- Intensive. The trap is the ownership chain: a domestic company can be foreign-owned, a state port can be run by a foreign concessionaire, and a supranational central bank is pooled rather than foreign.
- Simple
Ctl = Σi∈R si · 1[majority owner domestic] / SR
state and domestic private reported separately
- Full
Ctl* = Σ w(s̃i) [α Σk eik dk + (1 − α) oi] / WR
eik equity share of owner k; dk = 1 if k's ultimate parent is domestic, the nation's share for a supranational
oi = 1 if the operator is domestic; α = 0.5 until tested
External Reliance
Needs one more layerHow much depends on someone else?
- Measures
- Share of strategic score in assets whose operation depends on a foreign operator, foreign technology, a cross-border route or a single foreign supplier.
- Method
- Strategic score across assets with a foreign operator, a cross-border dependency edge or a flagged technology dependency.
How to compute
- Inputs
- operator, assetType (interconnectors, cables, cross-border pipelines). New dependency layer: foreign operator, foreign technology vendor, cross-border supply route, sole foreign supplier. External: import dependence by fuel (IEA), supplier shares (UN Comtrade).
- Comparing
- Intensive, but small and landlocked states depend on others by geography, which is real rather than a failure, so read it within tier and with the landlocked mask. How many suppliers a nation depends on matters as much as how much.
- Simple
ER = Σi∈R si · 1[foreign operator or cross-border asset] / SR
- Full
per asset, dependency edges j with share dij and substitutability uj:
ρi = 1 − Πj (1 − dij(1 − uj))
ER* = Σ w(s̃i) ρi / WR
beside: Herfindahl index over foreign source nations
05Composition
The shape of the estate
Every nation has an infrastructure signature. The useful question is not what it contains but how far it departs from what a country of that size, geography and income normally looks like.
Is the estate balanced or specialised?
- Measures
- How evenly strategic weight is distributed across the ten capability groups.
- Method
- Inverse Herfindahl-Hirschman index of strategic score by capability group.
How to compute
- Inputs
- v11CapabilityGroup, strategicScore.
- Comparing
- Intensive, read as an effective number of groups from 1 to 10. The first pass's equal quota flattens the twenty nations' group shares and inflates their Spread; a small register looks specialised by arithmetic. The top-100 frame removes most of the depth effect, and the full version removes the rest by comparing with chance.
- Simple
Spread = 1 / Σg (Sg/SR)²
- Full
observed = 1 / Σg (Wg/WR)²
expected = mean over 1,000 draws of the nation's n assets from the global top-100 pool
Spread* = observed / expected: above 1 is more balanced than chance; interval
Signature Distance
Computable nowWhat makes this nation unusual?
- Measures
- How far a nation's capability-group profile sits from the median profile of its peer group, and in which direction.
- Method
- Distance between the nation's group profile and its peers' after a log-ratio transform, with the two groups most over- and under-weighted.
How to compute
- Inputs
- The Signature page's vector: score-weighted capability-group shares over each nation's top 200. Peers: size tier for the simple version; population, GDP per head, land area, landlocked and small-island status and resource rents for the full.
- Comparing
- Shares sum to one, so ordinary distance misreads them, a zero share breaks a log-ratio, and “unusual” depends on the peer. It reuses the Signature page's vector so the two pages agree; the archetypes there describe clusters, this measures how far each nation sits from its expected shape.
- Simple
D = √Σg (xg − mg)²
x = group shares, m = median shares of the nation's tier
beside: the two largest xg − mg each way
- Full
replace zero shares, then z = clr(x)
expected ẑ from regression on ln P, ln(Y/P), ln A, landlocked, island, resource rents
D* = √((z − ẑ)ᵀ Σ−1 (z − ẑ)), Mahalanobis on the residual covariance
per-group contributions; bootstrap interval
- Changed
- Its peer group can come from the size tiers already in the repository, so the simple version needs no new layer.
06Adequacy
Fit to requirement
Absolute scale rewards large countries for being large. These two normalise against what a nation actually needs, which is where small states start beating big ones.
Sufficiency
Needs external dataIs there enough of it for this country?
- Measures
- Strategic endowment measured against population, output, land area and trade volume rather than in the absolute.
- Method
- Endowment against the estate expected for a nation of that population, output and demand, using the scale elasticity estimated from the register, never raw per capita.
How to compute
- Inputs
- Endowment (E*), population, GDP at PPP, land area, and each group's demand driver.
- Comparing
- This is where per capita is tested and fails. The top-100 total scales with population0.07, so E/P is almost exactly 1/P and ranks Tuvalu first and India last. A national estate has indivisible parts: every state has a central bank, an international gateway and a grid operator. Need grows with size, but far less than in proportion.
- Simple
Suff = E*n / median(E* of the nation's tier)
beside, labelled as such: E*/P per capita
- Full
for each group g: ln Wg = ag + βg ln Dg + γg ln(Y/P) + εg
(robust regression across nations; Dg the group's demand driver)
ratiog = exp(εg): 1 is the estate expected
Suff* = Πg ratiogωg, ωg the expected group share; interval from scores and fit
- Changed
- The original combined per-capita, per-GDP and per-freight ratios directly. On this register a per-capita ratio is a population ranking turned upside down.
Deficit
Needs external dataWhere are the holes?
- Measures
- The gap, sub-sector by sub-sector, between the infrastructure a nation of this size and structure would be expected to hold and what it actually holds.
- Method
- Expected sub-sector score modelled on population, GDP, urbanisation, geography and trade, minus observed.
How to compute
- Inputs
- W per group over the top 100, W per capability over the whole register; the Sufficiency covariates plus urbanisation and the landlocked and small-island masks.
- Comparing
- A gap needs an expectation, and the expectation must come from calibrated scores on an equal frame, never from absence. A landlocked nation is excluded from seaport expectations rather than shown a deficit.
- Simple
per group g: expectedg = median Wg of the tier
deficitg = max(0, expectedg − Wg) / expectedg
masked groups excluded
- Full
per capability c, two-part model:
presence πc = logit−1(Xδc); amount μc = exp(Xβc) given presence (Gamma)
expectedc = πcμc; zc = (expectedc − observedc) / sdc
partial pooling across capabilities; national deficit = Σ max(0, zc) weighted by expected share
07Renewal
Forward motion and decay
A static register flatters nations with historically well-built systems and hides nations that are building hard. Renewal separates the estate being built from the estate falling over.
How much is being built?
- Measures
- Share of national strategic weight sitting in assets under construction or committed, and how far that pipeline would move the national ranking on completion.
- Method
- Calibrated weight of assets under construction, with planned assets discounted, read as the change in Endowment on completion.
How to compute
- Inputs
- status normalised (under_construction and its variants, planned, under_development), strategicScore, evidenceConfidence. Full version: expected completion year and capital cost, neither held yet.
- Comparing
- An intensive share, but noisy in small registers, where one project in a top 75 moves it a long way. The top 100 holds 370 assets under construction and 224 planned, and “planned” runs from financed to announced. Movement in a nation's own ranking cannot be compared across nations; a change in Endowment can.
- Simple
Pipe = (Sunder construction + 0.5 · Splanned) / Soperational over R
- Full
R′ = the top 100 re-ranked with unbuilt assets at completion probability p
(0.9 under construction, 0.4 planned, each scaled by confidence)
Pipe* = E*(R′) / E*(R) − 1, simulated over completion and scores
shrunk toward tier; per unit GDP where capital cost is known
- Changed
- The ranking-movement half of the original is not comparable across nations; the change in Endowment replaces it.
How much is failing?
- Measures
- Share of strategic weight in assets that are damaged, idle or decommissioned - the decay side of the same ledger.
- Method
- Severity-weighted share of national weight in damaged, idle, inactive and decommissioned assets.
How to compute
- Inputs
- status normalised (damaged_or_idle, damaged, inactive, decommissioned, partially_operational), strategicScore. Full version: status date, severity, and conflict events to corroborate.
- Comparing
- Intensive, and dominated by states at war, which is correct. The register was built to find working assets, so retired ones are mostly absent (135 decommissioned in all 51,588): this measures damage and idling, not retirement. Status carries no date, so a repaired asset still reads damaged. Status vocabulary must be normalised first: 136 top-100 assets say “inactive”.
- Simple
Attr = (Sdamaged or idle + Sinactive + Sdecommissioned) / SR
- Full
Attr* = Σ w(s̃i) vi / WR
severity v: destroyed 1, damaged 0.6, idle 0.4, partly operating 0.25, to be set against a reviewed sample
v decays with status age unless reconfirmed; shrunk toward tier; interval
- Changed
- The original counted only damaged_or_idle and decommissioned, missing 136 top-100 assets recorded as inactive.
08Exposure
The threat surface
Strategic importance and physical exposure are independent. A nation can hold a resilient estate in a dangerous place, or a fragile one somewhere safe, and only crossing the two tells you which.
Hazard
Needs external dataHow much sits in harm's way?
- Measures
- Share of strategic weight within defined distance of coast, flood plain, seismic zone or cyclone track.
- Method
- Share of located strategic weight exposed to seismic, flood, cyclone and coastal hazard, by hazard intensity rather than distance.
How to compute
- Inputs
- latitude, longitude, coordinatePrecision (site precision for 10,023 records, first-pass twenty only), assetType. Geocoding layer for 176 nations; hazard layers; damage curves by asset type.
- Comparing
- An intensive share. A small island is entirely coastal, so a distance rule reads 100 per cent and says nothing; hazard intensity separates a sheltered island from an exposed one. Networks and routes are not points. The share of weight that could be located at all is published beside the index.
- Simple
Haz = Σlocated si · 1[in any hazard zone] / Σlocated si
illustrative zones: 1-in-100-year flood; 475-year ground shaking ≥ 0.2 g; land < 10 m and < 5 km from the sea
beside: share of R located
- Full
Ei = 1 − Πh (1 − Σk pihk · vtype,h,k)
p annual probability of intensity band k of hazard h; v damage fraction for the asset type
routes sampled along their length; unlocated assets at region level with that uncertainty
Haz* = Σ w(s̃i) Ei / WR
Contest
Needs external dataHow much sits where it could be reached?
- Measures
- Share of strategic weight near a contested border, a maritime chokepoint or a foreign military installation.
- Method
- Exposure of the estate to recorded conflict and maritime chokepoints, relative to the exposure of the nation's own territory.
How to compute
- Inputs
- Coordinates (as Hazard). External: international boundaries, UCDP georeferenced conflict events, a maritime chokepoint list, the routing of each gateway port's trade.
- Comparing
- A fixed distance from a border means nothing across nations of different size, since all of Luxembourg is within 50 km of one. What is contested is recorded conflict, not the border line. The full version compares the estate with the country it sits in: an estate no closer to conflict than its territory is not exposed by siting.
- Simple
Cont = Σlocated si · 1[< 50 km of a state-based conflict event in ten years, or of a listed maritime chokepoint] / Σlocated si
- Full
e(x) = Σj κj f(dxj), κ conflict intensity decayed by recency, f distance decay
Cont* = [Σ w(s̃i) e(xi) / WR] / [mean e over the nation's land area]
above 1: the estate sits closer to contest than the country does
gateway ports add route dependence on each chokepoint
- Changed
- Proximity to a border line cannot be compared between Luxembourg and Russia; exposure relative to the nation's own territory can.
09Reach
Who it actually serves
An asset register says what exists. It does not say who it reaches. This pair connects the estate to the population and the output that depend on it.
Catchment
Needs external dataHow many people does the estate reach?
- Measures
- Population and economic output within defined travel time of the nation's leading transport, energy, water and health assets.
- Method
- Share of the national population within travel time of the leading transport, energy, water and health assets, capacity-weighted in the full version.
How to compute
- Inputs
- Coordinates of top-100 assets in transport, energy, water and health. External: gridded population, gridded GDP, travel-time friction surface.
- Comparing
- Extensive if counted in people, because large nations reach more, so it is expressed as a share of the nation's own population. Grid services reach people through networks rather than travel time: use travel time for transport and health, and service territory for power and water.
- Simple
Catch = mean over the four groups of the population share within 60 minutes of any located top-100 asset in that group
- Full
two-step floating catchment: Ri = w(s̃i) / Σk popk f(tki); accessk = Σi Ri f(tki)
Catch* = population share with access above the global median
beside: Gini of access; GDP-weighted variant
Corridor Load
Needs one more layerHow much rides on how few routes?
- Measures
- Share of national strategic weight sitting on the small number of corridors that connect the largest catchments.
- Method
- Strategic score of assets on identified national corridors, as a share of the total.
How to compute
- Inputs
- Assets on named routes, from name and location. New corridor layer; urban centres (GHS Urban Centre Database); road and rail network (OpenStreetMap).
- Comparing
- A nation with two cities needs one corridor, so a high share is not fragility on its own: load is read against the number of large centres it must connect. Not applicable to a nation with a single centre.
- Simple
tag assets on routes linking the three largest urban centres and the main gateway
CL = Σi∈R si · 1[on corridor] / SR
- Full
multimodal network, register assets as nodes
flows Fab = PaPb / dabγ between centres, assigned to shortest paths
CL* = weight of the smallest asset set whose loss cuts half of all flow, as a share of WR
read against the expected cut for a network of that many centres and that area
10Evidence
What can actually be known
The last pair measures the register rather than the nation, and it is the one most indices leave out. An index that cannot say how much of itself rests on thin evidence is asking to be believed rather than checked.
Transparency
Computable nowHow much of this is documented?
- Measures
- Share of national strategic weight carried by assets with a public reference and high evidence confidence.
- Method
- Share of national top-20 weight carried by assets with a public reference, the frame searched to the same standard in every nation.
How to compute
- Inputs
- wikipediaUrl, sourceUrl, designation, verified, evidenceConfidence (every record). confidenceValue exists for the first-pass twenty only.
- Comparing
- Two traps. The original threshold, confidence of 0.90, uses a field 176 nations do not have. And the index measures the register as much as the state: reviewed top-100 records are 56 per cent referenced and unreviewed ones 1 per cent, while unreviewed records claim high confidence more often. The top 20 is the one frame in which every unlinked asset in every nation went through the same reference search. English Wikipedia under-documents non-anglophone states, so full references are counted in any language.
- Simple
Tr = Σi∈R20 si · 1[public reference] / SR20
- Full
evidence ei = reference tier × calibrated confidence
tiers: official designation 1.0 · regulator or operator 0.8 · encyclopaedia, any language 0.6 · none 0
Tr* = Σ w(s̃i) ei / WR, once reference search covers the top 100 evenly
state openness reported separately, from the designation research
- Changed
- As written it was computable for twenty nations, and it would have ranked review effort rather than openness.
Opacity Gap
Computable nowHow much of the claim rests on thin evidence?
- Measures
- The distance between how important a nation's estate is assessed to be and how well it can be evidenced - high where a state is both strategically heavy and closed.
- Method
- Percentile rank of Endowment minus percentile rank of Transparency, after confidence claims are calibrated against review.
How to compute
- Inputs
- strategicScore, evidenceConfidence, verified, layer, and the review's before-and-after confidence table for calibration.
- Comparing
- As written it subtracted a 0–1 confidence from a 0–25 score, which is not a quantity. Raw claims are also inflated where unchecked: in the reviewed set, 86 per cent claimed high confidence before review and 37 per cent held it. On raw claims the gap looks smallest exactly where evidence is least checked. Percentiles compare without units.
- Simple
OG = pct(Endowment) − pct(Transparency), across nations
−1 to 1; high is heavy and poorly evidenced
- Full
calibrated confidence ĉi = E[post-review level | claimed level, pass]
OG* = pct(E*) − pct(Σ w(s̃i) ĉi ei / WR)
beside: share of weight below medium after calibration; interval
- Changed
- The original difference had no common unit, and it rested on the one field the unreviewed register overstates.
Reading them together
Taken individually these are descriptive. Taken in pairs they are diagnostic. High Chokepoint with low Second Best is a nation one failure away from a national problem. High Endowment with low Sufficiency is a large country that has not built to its own size. High Pipeline with high Attrition is a state replacing its estate rather than expanding it, which reads as growth in any stock-based index. And a high Opacity Gap should change how every other number on that nation is read.
These are specifications, not results: no index here has been computed. Before any is published as a number about a country, three things are needed: the seam calibration sample, the external denominators, and a sensitivity test of every choice made above against the ranking it produces.
