Parkrun spread
A Socratic walk-through of Parkrun spread — reasoned out one step at a time, not lectured.
The question we started with
THE QUESTION #Why does a free weekly run spread faster through a region the more towns already host one?
A free, timed, weekly five-kilometre run needs almost nothing: a park, a stopwatch, a few volunteers with barcodes. Nothing about that recipe changes from year to year. So why did the first one sit alone for a while — one event, Bushy Park, October 2004, thirteen runners — and why do regions now seem to fill in a rush, three or four new towns in a season?
If the idea is equally available to everyone, the obvious expectation is a steady trickle: some fixed number of new events per year, wherever an enthusiast happens to appear. That is not the shape it takes. Something about already having events nearby seems to make the next one more likely. What could that something be?
Reasoning it through
REASONING #Start with what it actually takes to launch one. Not the idea — the idea is free and everybody has heard it. It takes a person willing to be there at 8am every Saturday for years, a small team around them, a landowner persuaded, a risk assessment, equipment, and the confidence that the thing will work. Ask yourself: where does such a person come from?
Almost never from a standing start. They come from an existing event — they ran there, then volunteered there, then watched a run director do the job forty times and thought I could do that in my town. So the supply of people capable of founding event number N+1 is drawn from the population already attending events 1 through N.
Hold that thought and notice what it implies. If each existing event produces, on average, some small number of would-be founders per year, then the number of new events per year is roughly proportional to the number of events that already exist. Ten events seed more than one event does — not because the idea got better, but because there are ten times as many places for a founder to be manufactured.
Now, what kind of growth is "the rate of increase is proportional to the current amount"? That is the definition of exponential growth. Its signature is not speed; it is that the increment grows. One event begets a trickle; a hundred events beget a flood, from exactly the same per-event rate. The region does not become more enthusiastic. It becomes more populated with seeds.
Does distance matter? Yes, and this is where the regional pattern comes from. A founder needs to have been a regular somewhere, and regular attendance falls off sharply with travel time. So the seeding is local: an event mostly recruits founders from towns within its own catchment. Growth that is proportional and local looks like ink spreading — a filled area with a ragged edge, new events appearing next to old ones, rather than scattered at random across the map.
There is a second, quieter multiplier. Founding is not just about willingness; it is about the cost of the attempt. A new team in a region with ten neighbouring events can borrow a timer, copy a course-measurement, ask which landowner objections came up last time, and recruit volunteers who already know the routine. Each existing event lowers the cost of the next one. So the per-event seeding rate is not even constant — it drifts upward as the local network thickens.
Then ask the question that keeps this honest: does it run forever? No. Every proportional-growth story has a ceiling, and here the ceiling is physical. There are only so many parks of the right size with a willing landowner, and once a town's neighbours all have an event, a new one competes for the same runners rather than finding new ones. Growth proportional to N, divided by a shrinking supply of unfilled sites, bends the curve over into an S. Britain, where the density is highest, reached that bend well before the newer countries did.
I should flag a limit on what I can claim: that founders come predominantly from existing participants is well attested by how the organisation trains and approves new teams, but I cannot give you a reliable figure for what fraction, nor a measured doubling time per region. The shape of the argument is solid; the constants are not something I would quote.
The analogy
THE ANALOGY #It behaves like a fire in dry grass rather than like a row of candles being lit one by one. A candle-lighter works at a fixed pace no matter how many candles are already burning. A fire's spread rate depends on how much of the field is already alight, and on how close the unburnt grass is to a burning edge — so it creeps for a long while and then crosses the field in an afternoon.
fire consumes what it spreads to and leaves it dead, whereas an established event keeps producing founders for years — the burnt ground here is what does the burning.
Clarifying the model
THE MODEL #Two misreadings are worth heading off.
The first is that this is popularity. It is tempting to say events multiply because the idea became fashionable, and fashion certainly helps recruitment. But the mechanism above needs no change in enthusiasm at all: hold the per-person keenness perfectly constant and you still get acceleration, purely because the pool of people positioned to act has grown. Fashion changes the constant; proportionality changes the shape.
The second is that acceleration means the region is being saturated faster in some absolute sense. Exponential growth from a small base is agonisingly slow in its early years — the first few events took a long time and looked like a hobby. Nothing dramatic happened at the moment the pace picked up; the same rule was running all along. That is the genuinely counter-intuitive part, and it is why early-stage growth of this kind is so easy to dismiss as insignificant.
A picture of it
THE PICTURE #How to readthe back-edge from the new event to the top is the whole story — each launch enlarges the pool that produces the next launch, so the loop compounds until the decision node starts answering "no" and the curve flattens.
What became clearer
WHAT CLEARED #The spread is not driven by the idea getting better or the public getting keener. It is driven by where founders are made: inside existing events. That single fact converts a constant per-event rate into growth proportional to the current number, which is exponential by definition — and it also predicts the plateau, because the parks and the runners are finite.
Where to go next
ONWARD #- What sets the local catchment radius, and how would you measure it from event attendance data?
- Why do some regions stall well below their apparent park capacity?
- Does the same seeded-founder mechanism explain the spread of other volunteer-run formats, or is
Key terms
TERMS #| Term | What it means |
|---|---|
| Exponential growth | growth in which the rate of increase is proportional to the current |
| Logistic curve | the S-shape that results when proportional growth meets a finite ceiling. |
| Catchment | the area from which an event actually draws its regular participants, bounded in |
| Event director | the volunteer role responsible for running a given event, and in practice |
Every term the collection defines is gathered in the glossary.