UPDATE: This article is based on the assumption that people were leaving the area of the march as it progressed. A reply from Alan Wilson on April 6th asserts that this was not the case and so I retract the claims made in this article until evidence of outbound flow becomes available.

Today (March 25th), wired put out an article claiming that Crowd Estimation Experts put the People’s Vote March numbers at:

between 312,000 and 400,000 people

Manchester Metropolitan University’s Keith Still

That figure is easily proven incorrect with some simple maths.

All Professor Still did was map out the rough area of the march, and multiply it by between 2 and 2.5 based on the assumption that 1 square metre comfortably holds around 2 – 2.5 people.

He worked out how many people the area could hold; the capacity. The trouble is that the people on the march weren’t held there. So the area was constantly getting topped up with new people as others fell away.

Still’s analysis fails to account for the ebb and flow of people during the day. It would work great for football stadiums, theatres, or inauguration crowds, but completely fails when movement is involved. Like on a march. (Or more specifically, when the area isn’t contained and people can come and go over time).

We can confirm Still’s method via the article text; “The total area of the space where people were standing was around 156,250 square metres”. Multiply that by two and you get 312,500 – Still’s lower estimate. Multiply by 2.5 and it’s 390,625, within rounding distance of his 400k upper estimate.

There are two ways the estimates could yet be correct.

1) If everyone filled the area and then stood still.

2) If the actual area of the march was a lot smaller than 156k, and Still artificially expanded the area in his calculations to account for the flow of people. This would be a valid approach – imagine a metre of pipe with water flowing through it at 1 metre per second. To work out how much water went through in ten seconds, you could forget about flow and work it out as if it was just a full pipe 10 times the length. Maybe Still applied a similar principle to the area of the march.

Number 1 didn’t happen, plainly.

To rule out number 2 I roughly mapped the area of the march against Google maps using a nifty free tool. The area I got was 118k (I missed out a chunk of Park Lane in my haste). That’s close enough to Still’s 156k that I think we can safely say the area in his calculation is the actual area of the march, not an artificially inflated area to account for flow.

The only possible conclusion is that Still simply didn’t account for people arriving as the march went on. He’s applied a method for counting static crowds to a dynamic one.

At just after 2PM the People’s Vote twitter account stated “Park Lane is still full of marchers as the front of the march reaches Parliament Square”. At that point, the 300-400k figure would have been approximately correct – the area has ‘filled up’. But then more people joined. And more throughout the day. From all angles.

The march set off at 1, and took about an hour to reach Parliament Square.

At that rate it’s 300-400 thousand people *per** hour*.

Former Guardian Home Affairs editor Alan Travis stated on twitter that the back of the march left Park Lane at 3PM, however others have stated that there were still people joining at 4PM and possibly later. Even taking the 3PM figure that means we’re essentially looking at two crowds. The crowd that left between 1 and 2, and the second crowd that left between 2 and 3. That’s the crowd Prof. Still missed. If people were still joining after 3 as well, that’s a third crowd, but let’s leave it there.

In conclusion, Professor Still only measured a snapshot of the march area at a single point in time, neglecting to notice that the march went on for several hours. The first crowd we can estimate to be 300-400k people using population density just as Prof. Still did, because they filled the area. Then there’s the people who joined between 2PM and 3PM. If that’s the same volume as the first crowd then total attendance is 600-800k people. Erring on the side of caution and halving the number for the second crowd it’s still 450-600k people in total. Still short of a million, but twice the estimate in Wired – and that’s discounting anyone outside the marked area, and anyone who joined after 3PM.

Update: This article originally assumed the march went on until 4PM. I have revised my estimates downwards in the interest of being as conservative as possible.