Every flash is a death.

Do you want to know how many people die in a second worldwide? Let's ask the machine.

The problem is that that is not true, or not completely true. For the last couple of years we have observed between 60 and 63 million deaths a year, worldwide. An average year has 31,557,600 seconds, and dividing one by the other gives about two deaths a second. But that is a yearly average, and nothing about a death is average.

In reality there's about a 14% chance that during any given second nobody dies, if deaths are randomly distributed across the year at the observed annual average. Under the same model, there is about a 27% chance that exactly two people die in any given second, and roughly the same chance that exactly one person dies in that second.

So, how many people die in a given second? Our new (better) answer is: if people die randomly throughout the year, between 0 and 4 in about 95% of one-second intervals.

We made a bold assumption when timing the events: that they happened randomly. As we will see, this is far from the truth and we'll try improving our timing model. Nevertheless, we'll be equally naive for our first spatial distribution model: deaths will happen at random times and at random places.

I think most people wouldn't get triggered by our timing model, but our spatial model is painful to watch. Most randomly placed dots (~71%) fall in the ocean, as this is the proportion of Earth's surface covered in water. The dots falling on land fall overwhelmingly in areas without any permanent human settlements (deserts, forests, …). I classify those points against the GPWv4 population-density grid used by the model.

We can agree that if our goal is an accurate mortality model it should be way better than that. Maybe instead of using the global mortality numbers we could use country-level data. The good news is that the World Bank publishes estimates of crude death rate (how many people die in a year for every 1,000 inhabitants). The bad news is that many countries don't provide that data, and virtually all the ones that do overcount or undercount some deaths.

Even if imperfect, mortality rates by country will be a huge upgrade from placing points without taking account of where people live.

A country is not an average

Not having deaths pop up in the middle of the ocean is neat. And seeing the dots pop up in the countries they should be in is also a great improvement. But if you look carefully, you'll notice that the dots always appear exactly in the center of a given country. Sometimes that's in an uninhabited or even uninhabitable part of the country. According to the current simulation, all deaths in Russia happen at Lake Vivi, roughly 400 kilometers from the closest hospital: a regional study places the lake 366 kilometers from Tura and identifies the town's central district hospital. But we know that people tend to die where people tend to be, so let's apply a density map to our calculation. This way, the dots will have a greater chance of appearing where there are more people and little chance of appearing in unpopulated areas.

Small problem though: the density map is a grid of ~55 km wide cells (0.5°). It's pixelated, so to speak. But country borders aren't pixelated (colonialism got close but not quite), they often follow rivers, mountains or the sea.

The way we get around this is by converting every source, every complexity layer to a grid. And we assign each pixel to whichever country has the most population in that specific cell.

This map is cheating a little bit: it uses a logarithmic scale by default. Otherwise you wouldn't see much. The fact is that Earth, even the land, is mostly empty. Toggle between log and linear scale to see how empty it is.

On a linear scale you barely see anything other than a dozen megacities and some shading around the Indo-Gangetic Plain (the region south of the Himalayas that's home to about one-seventh of the world's population).

Now our dots appear mostly in cities and in very populous areas.

CDR by region

A single national rate hides enormous internal spread. In Japan, rural Akita dies at nearly twice the rate of Tokyo; in the US, West Virginia runs well above Utah; in Europe, north-west Bulgaria and eastern Germany far exceed Ireland or the Nordic capitals. Most of the gap is age structure (older regions bury more of their people each year), layered over real differences in health, poverty, and access to care. Japan's official 2023 table puts the crude rates at 19.3 per 1,000 in Akita and 10.2 in Tokyo; after age standardisation, they narrow to 14.4 and 12.3.

An illustrative example of how much the age structure of a place matters to its CDR is that of Mexico and Lithuania. In 2000, both countries had a life expectancy of around 72 years, but Mexico's crude death rate was about 4 per 1,000, while Lithuania's was about 11 per 1,000. Same life expectancy, almost 3× crude death rate difference.

Sources: World Bank series for life expectancy at birth and crude death rate.

Borders are the wrong unit

Source: Eurostat's 2023 regional crude death rates.

Death rate by time of year

From a timing perspective, we're still at the same place that we were at the beginning. Dots still appear at random moments. This definitely looks better than having regular intervals like a metronome, but it's not closer to reality. Randomness feels more organic, but we're striving for something more than feeling.

Do we have something better than random? Yes, at least for some countries that provide monthly or even weekly CDR numbers. Mortality rates in a given month in a given country vary from year to year, but not by much. The coronavirus pandemic is the obvious exception: mortality during 2020–2022 did vary sharply, which is why those years are excluded from the fitted curves below. Actually, it is quite easy to draw a curve showing when in the year more or fewer people die. And the data is not only consistent from year to year but also between countries.

A cluster of similar curves

Add or remove any country with a directly measured curve to compare.

From observations to a continuous multiplier

Weekly, monthly, quarterly: that's how often a country reports, and it decides how much of the shape survives. The smoothing is a separate step. Pick a country below that reports weekly to see what each cadence keeps, compare it with the three-month circular average the globe used to run on, and switch the harmonic curve between orders 1 and 4. The globe now uses order 4.

Loading the smoothing comparison…

A factor above 1 means deaths are firing faster than the year's average, below 1 slower. The curve the globe uses is an order-4 Fourier regression pooled over every complete non-COVID year. Weekly observations stay weekly, counts become a daily intensity, and the fitted curve gives a value for any day of the year, including the ones nobody reported.

Most temperate countries look alike: winter kills noticeably more than summer. Nearer the equator the curve is flatter, or follows the rainy and dry seasons instead of winter and summer. That's why the harmonic model doesn't assume a winter peak anywhere; it fits whatever shape the data has.

When the chart lines southern-hemisphere countries up against northern ones, it shifts them by half a year so the shapes can be compared. The globe doesn't: there, July in Chile is still July.

These choices in my wording reveal an assumption that, even if quite obvious, could be flawed: that changes in rates over a year are mostly based on climatic seasons. In theory they could reflect something different: think social mechanisms like Ramadan or data artifacts like late reporting of deaths, default dates of death, and so on.

Trying to understand what causes seasonality is very interesting, but it isn't critical for the countries from which we have observed seasonal data. What do we do with the other ~100 countries that only provide yearly CDR?

When I'm missing the data I need I always ask the question: are there any proxies for the data I'm looking for, that are easier to get? Are they causes of the phenomenon we study, consequences of it, or do they share a common cause with our subject? In this case I can think of a couple, each with its own strengths and weaknesses.

Before committing to one, it's worth seeing what actually tracks the strength of a country's seasonal swing among the countries that already report a curve. Many are roughly unimodal, while some tropical climates can have broader or multiple rainy-season features. Amplitude is still a useful first summary of how strongly the curve moves away from its annual mean, without claiming that every shape has one winter peak.

In the charts that follow, every dot is a country with observed seasonal data. The y-axis shows amplitude: the higher a dot is, the stronger the seasonal swing. The x-axis places countries on each of the proposed proxies.

The bottom axis shows absolute latitude, how far a country is from the equator. Points at the left are tropical, points near the right edge are near the poles.

We see an expected pattern: amplitude is lowest between the tropics, as countries there don't experience astronomical seasons. And an unexpected one (at least for me): above 35° seasonality decreases, instead of climbing with colder and longer winters. A possible explanation is that above a certain threshold people understand that they should adapt to winter and implement social, behavioural and housing adaptations. That Spain, with a more temperate climate, shows higher winter mortality than Sweden would point in this direction.

Here we put all countries and regions in their respective climatic bucket. If this is to be a good proxy we should see that the dots in each climate are packed together.

Well, this doesn't change the picture much. We confirm that there's a correlation, that seasonality is lower between the tropics, and that climate, like latitude, best predicts seasonality where seasonality is low.

How many older people live in a country seems like a very poor proxy. I just see a cloud of dots here. Richer countries also tend to have older populations, which may be part of what we're seeing. The GDP shading supports that association: countries with fewer older people tend to be poorer than countries with more older people. It does not tell us whether wealth offsets seasonal mortality.

More of the same. There's no clear relationship in this sample between how rich a country is and how strongly its mortality is affected by the seasons. One possibility is that stronger health systems and better adaptations offset some of the seasonal risk in richer countries, but this chart cannot tell us whether that's the reason.

How about neighbouring countries? That's better. There's a strong correlation here. Of everything I tried on the countries with measured curves, borrowing from bordering neighbours wins: lowest median error, highest correlation, and the only method that beats both the mean-curve floor and latitude. Latitude and climate class come close behind, with climate slightly ahead of latitude for the typical country.

So how did your ranking do?

The ranking asked which proxy tracks the size of a country's swing. The leave-one-out test asks something else: how well does each method rebuild the whole curve when I hide it? If you ranked the five before the charts, here's where your guess landed.

The seasonality tables have not loaded, so there is nothing to score the ranking against yet.

Bordering regions, not just bordering countries

Neighbouring regions inside one country track each other even more tightly than neighbouring countries do, which is why the nearest-region reconstruction beats every other region-level proxy. Two Russian regions, Ingushetia and Chukotka, had raw weekly data I couldn't use (weeks with zero deaths, or spikes far too big to be real), so instead of showing them as they are or dropping them I filled them with the average of their nearest good neighbours.

Where the extra deaths fall, month by month

Each square is a half-degree cell of the same grid the globe samples, coloured by the deaths this month's season adds to, or takes from, an ordinary month there. Drag through the year and the hemispheres trade places: Europe's January surplus is southern Africa's January deficit, and by July they've swapped.

The texture you see inside a country is population. Only ten countries have measured regional curves, and in this frame that comes down to South Africa, western Russia, and climate-modelled India and China; Europe has none at all. Everywhere else every cell of a country shares one curve, and the outlines tell you which unit that curve belongs to: solid where somebody counted deaths in it, dashed where I reconstructed it from a neighbour, a climate class or a latitude. Inside one of those borders, what changes from cell to cell is how many people live there. When they die is the same everywhere.

A war is not a Poisson process

Everything so far is slow mortality: the long-term trends that account for most deaths worldwide. But some deaths don't follow a trend, and the biggest group of those is war. ACLED publishes weekly aggregates of reported conflict fatalities, pinned to country and Admin-1 centroids. ACLED sums each week's events at the middle of a province; it doesn't say where each one happened.

Every other layer so far has been a factor we multiply the crude death rate by: density, season. This one is a count. We get 12 complete reported weeks, ending at the oldest publication date the six ACLED regions share. So how many people are dying in wars in a given week right now?

I take a weighted average that trusts recent weeks more than old ones and squashes the extremes before averaging. The name for that is a robust exponentially weighted moving average, Robust EWMA. One wild week can't swing the estimate much. The flip side: when a war suddenly gets worse, the estimate lags behind it.

Here's how it works on seven invented weeks (the real estimate uses 12; seven keeps the arithmetic short).

First the 10th and 90th percentiles.

Anything outside them gets pulled in:

Then the weights. They come from a half-life: how many weeks until a week counts half as much as it did. I haven't fitted this (that would take a proper validation exercise); the globe uses four weeks.

With a four-week half-life the weights are:

Weighted average of the capped values: 28.4. The plain average of the raw numbers is 33, dragged up by that one week of 90.

Both knobs (how fast a week fades, how hard the extremes get pulled in) are my choices; the data didn't pick them. The globe always runs the default, four weeks and P10–P90, then splits the result across Admin-1 regions by each one's share of the 12-week fatalities, and annualises it. The sliders below let you see what other settings would give. Dragging them doesn't touch the globe.

The map shows the same 12 weeks of fatalities at ACLED's Admin-1 centroids. On the globe each centroid snaps to the nearest populated grid cell in the same country, so a dot can't land in an empty desert just because that's where the province's middle is.

Sex, age, then cause

Age and sex come from the UN World Population Prospects table of deaths by age and sex, 2023 figures. Cause comes from the WHO Global Health Estimates, the GHE 2021 edition published in 2024. I use its 2019 estimates, the last year before the pandemic, because I don't want COVID-19 drawn as the way people ordinarily die. For each country, sex and age band I keep the eight most common recognisable causes and fold the rest into "other causes".

I don't draw age, sex and cause independently. First sex and age, then the cause from the distribution for that group. Otherwise we'd get combinations the source data almost never shows.

Both tables (age and sex, cause) ship as JSON in the repository, so the feed makes no API call at runtime and reads the same offline. The cause table used to come from the IHME Global Burden of Disease, which I had to export by hand from a results tool that hides every download behind a sign-in and caps it at a hundred thousand rows. The WHO table is one request and no account. That's most of why it's the one here.

Getting cause below the country level means going back to IHME, and back to that cap. The subnational export is 723 places × 22 age groups × two sexes × 22 cause groups: seven hundred thousand rows, or eight downloads, against an allowance that's spent per release and never refills. So I ordered the eight by how many deaths each carries, instead of the order the tool lists them in. The allowance ran out after the first one.

That one download holds cardiovascular disease, the cancers and chronic respiratory disease, 55% of all deaths, at regional resolution. In the tool's own order the same download would have held about a tenth of that. It's in the feed now. How far does it reach? Two fractions are at work. The regions cover 44.6% of the deaths drawn; the three groups are 55.0% of the causes. The region only decides where both hold, so 24.5% of all cause draws now move with the place instead of the country. The rest keep the national mix.

What the feed knows, by share of the deaths it draws:

The reweighting is a ratio. Twenty-two clinical groups can't carry eighty-seven named causes, so I never ask GBD to name anything. For each region, age band and sex it gives one number per group: that group's share of deaths there, divided by its share nationally. The WHO labels inside the group get multiplied by it. Everything outside the three groups moves together on the remainder, so the three can't quietly inflate.

Three things are still missing, and none of them is small. Nineteen of the twenty-two groups have no regional data at all: seven downloads I'm still owed by an allowance that hasn't refilled. 55% of deaths happen outside the 474 regions (all of China, which has no subnational units here) and draw a national cause mix. And seventeen of the regions are cities too small for a half-degree cell to award them. Delhi, Ōsaka, Greater London, Mexico City, Jakarta, Manila and eleven more win no cell of their own, so their deaths are drawn with the surrounding region's mix. That's 2.6% of the deaths inside the regions. Blame the grid; the data is fine.

Then the month tilts it

The time of year also changes the age and cause we draw. I estimate those changes from the records I have, then lend the patterns to countries that have none. That lending is one of the shakier parts of the model.

Age and cause use different records. Age curves are measured from Eurostat weekly records for 24 European countries. Cause curves come from monthly death records in Brazil's DATASUS mortality system and Mexico's Secretaría de Salud, the two country sources here whose microdata carries a date and a cause together. Both are fitted as continuous order-4 harmonic curves. The twelve monthly values in the chart are snapshots of those curves; what the model keeps is the curve itself.

Countries without those records borrow through the same donor cascade as timing: regional averages, neighbouring countries, climate, latitude. All nine age bands have measured curves in the 24 source countries. Cause is patchier: 55 of the 87 labels borrow the curve of their ICD-10 chapter, and the other 32 I leave flat, multiplied by one. The largest of those is "other causes" itself, the bag the strongest-eight truncation sweeps everything else into, typically a third of the weight in the adult bands and up to a half. I left it flat on purpose. It's a pile of unrelated deaths with no chapter of its own, and giving it the average death's curve would claim a shape I never measured.

At sampling time these multipliers change the conditional age and cause weights, which are then normalised together. Each curve averages one over the year, but that alone doesn't guarantee every category keeps its exact annual share once the weights are combined.