Crowd Science

Module 5, lesson 1 · 40 minutes

Anatomy of a mass-participation race

Waves, corrals, start lines, pinch points and finish funnels: the parts of a big race, and the hidden variable that decides how crowded each of them gets.

You’ll be able to

  • name the parts of a race that shape crowding: waves, corrals, the start line, the course’s width profile, pinch points, aid stations and the finish funnel;
  • explain why the spread of runners’ paces is the hidden variable;
  • work out runners per minute and space per runner at any point from start times, paces and road width.

Introduction

In April 2026, 59,830 people finished the London Marathon, a Guinness World Record for the largest marathon, beating the 59,226 who had finished New York the previous November. Seven years earlier, London had 42,549 finishers. That is about 40% more runners, and none of the roads got 40% wider.

A marathon is an unusual crowd. You know almost exactly who is coming, roughly when each of them will start and, from the finish time they predicted when they entered, roughly how fast each will go. That makes it the most plannable crowd there is. This lesson takes a race apart so that, by lesson 3, you can plan one.

The biggest races keep getting bigger

The six long-established World Marathon Majors became seven when Sydney joined; its first race as a Major was on 31 August 2025. Table 1 shows how large the biggest of them now are. Several numbers come with a caveat, which is normal for this kind of figure: race reports, record bodies and magazines count starters and finishers differently and sometimes simply disagree.

Finishers at the largest marathonsNumbers as reported; where sources disagree, the note says so.
RaceFinishersNote
London 201942,54942,906 starters
London 202343,965One secondary source
London 2024about 53,800contested Reports give 53,802, 53,881, 53,745 and 53,846; the World Marathon Majors says “over 51,000”
London 202556,640Guinness World Records title
London 202659,830Extended the record
New York 202455,646contested London Marathon Events’ figure; the World Marathon Majors gives 56,646
New York 202559,226The record London beat in 2026
Berlin 202454,280One secondary source

Fifty or sixty thousand people is the population of a market town, all moving the same way along streets that were built for traffic.

The parts of a race

Figure 1 lays out the parts of a big race that matter for crowding. Start at the left.

The anatomy of a mass start. Runners wait in corrals by wave, cross the start line at a limited rate, then meet a road whose width keeps changing. Schematic, not to scale.
  • Waves and corrals. A field this size cannot start at once. It is split into waves: groups released across the start line one after another, each starting a set time after the previous one. Before the start, runners wait in corrals: fenced pens where the runners of one wave, or one pace group within a wave, gather before their start. London bases its waves on runners’ predicted finish times. A runner may move to a later wave but not to an earlier one.
  • The start line. However wide the road, only so many runners a minute can cross the line. This start-line throughput is the number of runners per minute who cross the start line while a wave is being released. It is the single most important number in this module.
  • The width profile. A course is a sequence of roads, bridges and junctions, each with its own usable width. Planners think of it as a width profile: width against distance.
  • Pinch points. A pinch point is a short stretch of a route that is much narrower than the road either side of it, such as a bridge, a gate or a narrow street. Boston’s course begins in Hopkinton, where Main Street “squeezes to just 39 feet wide”, which is about 11.9 m.
  • Aid stations. Runners slow down, swerve or stop to drink, so the same flow of runners occupies more road.
  • The finish funnel. The road narrows into chutes where runners stop running, collect medals and bags, and need medical attention. Everyone arrives on foot, but they leave much more slowly than they came.

The hidden variable: the spread of paces

Runners do not move as a block. Each has their own pace: time per kilometre, in min/km; a runner’s predicted finish time divided by 42.195 km. If a runner crosses the start line at time s and holds pace p, they reach distance x at time

t(x) = s + p · x

s
time they cross the start line, min
p
pace, min/km
x
distance, km

Two runners who cross the line together at 5 and 6 min/km are 10 minutes apart at 10 km and 42 minutes apart at the finish. The gap grows in proportion to the distance run. So a field with a wide spread of paces stretches out along the course and gets thinner as it goes. Figure 2 shows it.

A pace spread fans the field out. 10,000 runners cross the line over 10 minutes; by 10 km they arrive over 30 minutes, by 40 km over 90. Time runs downwards, as in the wave planner in lesson 3.

Worked example: runners per minute at a point

10,000 runners cross the start line evenly over 10 minutes, 1,000 a minute. Their paces are spread evenly between 5 and 7 min/km.

  1. At 10 km the first arrives at 0 + 5 × 10 = 50 minutes and the last at 10 + 7 × 10 = 80 minutes. 10,000 runners over 30 minutes is about 330 a minute.
  2. At 40 km: first at 0 + 5 × 40 = 200 minutes, last at 10 + 7 × 40 = 290. 10,000 over 90 minutes is about 110 a minute.

The start line saw 1,000 a minute. The 10 km point sees a third of that and the 40 km point a ninth. The field is at its most compact just after the start. That is why the start, and the first pinch point after it, is where crowd planning for a race begins.

The exception is a field that is started in the wrong order. If slower runners are sent off in front of faster ones, the fast runners close the gap and the field bunches mid-course. You will see exactly that in the wave planner.

From runners per minute to space per runner

A flow of runners becomes a density once you know how fast they are going and how wide the road is. This is the same flow equation as Module 1, lesson 2, with runners instead of walkers:

ρ = q / (v · w) space per runner = 1 / ρ

q
runners passing per minute
v
their speed, m/min (1,000 ÷ pace)
w
road width, m
ρ
density, runners/m²

Worked example. At 10 km in the example above, about 330 runners a minute pass at around 6 min/km, which is 1,000 ÷ 6 ≈ 167 m a minute. Each metre of road holds 330 ÷ 167 ≈ 2 runners. On a road 10 m wide, that is 0.2 runners/m², or 5 m² each.

Now compare the start. 1,000 runners a minute at the same speed means 6 runners on every metre of road. On a 12 m road that is 0.5 runners/m², 2 m² each, and on a 5 m pinch it is 1.2 runners/m².

What counts as enough room for runners? The design target reported for New York is “three square meters for each runner”, about 0.33 runners/m². That is far more space than walkers need, which makes sense: a runner needs clear road in front of every stride that a walker does not.

How many runners a minute arrive (set by the start and the spread of paces), how fast they are moving, and how wide the road is. Slower runners take up more road for the same flow, which is why aid stations and the back of the field are denser than you might expect.

Two runners cross the start line together, one at 5 min/km and one at 6 min/km. How far apart in time are they at 20 km? And at an aid station where runners slow from 167 to 100 metres a minute, what happens to the density if the number passing per minute does not change?

At 20 km the gap is (6 − 5) × 20 = 20 minutes. At the aid station, density is flow divided by speed and width, so slowing from 167 to 100 m a minute at the same flow raises the density by 167 ÷ 100, about two-thirds. So it pays to put aid stations where the road is wide.

  • “The finish is the most crowded part of a race.” Runners reach the finish spread over hours. The field is most compact just after the start, before the spread of paces has had any distance to work on. The finish is busy for a different reason: runners stop there.
  • “A bigger field means proportionally more crowding everywhere.” Not exactly. Adding runners lengthens how long a point stays busy at least as much as it raises the peak. Lesson 3 shows when each happens.
  • “Waves are just about fair timing.” They are the main tool for controlling how many runners enter the course per minute, and so how dense the first kilometres are.