This is re-posting from Lauren Rose on Facebook. She took the reasonable approach of using geometry and sampling to estimate the crowd size of the rally to restore sanity. Her first estimate was (gasp!) 420,000. However, that was before she could find a good areal photograph. After recalculating with better photos, her revised estimate is 284,250. (But I think the accuracy could be +/- 25,000 without more photos, and I’d like to actually use Amazon Mechanical Turk to physically count all the heads and replicate three times over for a very accurate “calibration” estimate that can be used for all future rally tallies.)

Lauren Rose explains:

The Rally was supposed to take up the area between 3rd St. and 7th St, and very dense crowd actually stretched very beyond 7th to just after 9th with less dense crowd  working back to the 12th Street Tunnel to near 14th. The buildings located along the mall also had dense crowds around, and in front of them.

The total occupied area is 2.15 million square feet from just after 3rd to just after 7th. It’s in this area that the densest crowd is found as shown by photographs. Physically, 300 average-sized people can squeeze into an area of 1,000 square feet. The crowd density is needed to find the total crowd, and in this case we have a very consistent crowd density from the stage back to 9th street of about 120 people per 1,000 square feet. This provides a crowd of 258,000 in this dense region.

The less dense to sparse region is 1.05 million square feet from just after the dense crowds at 9th to just beyond the 12th street tunnel. The crowd density in this region varies considerably, and therefore I have averaged the density of the densest areas to the sparsest ones and calculated a crowd density of 25 people per 1,000 square feet. This provides a crowd of 26,250 in this area.

So, then just add the two regions together and the Rally to Restore Sanity had a crowd of 284,250.

Here’s the final calculation: Total estimated area: 2,150,000 square feet / 1,000 X 120 people per 1,000 sq. feet = 258,000 + 1,015,000 / 1,000 X 25 people per 1,000 sq.feet = 26,250. (258,000 + 26,250 = 284,250).

I feel as though even this figure is conservative. Perhaps not by much, but just a bit.

[Marc’s note: I think she forgot to count the crowds between 7th and 9th street in her second estimate if I interpret it correctly. Since I was standing on the other side of 7th street, I can attest that there was heavy density, but also some fenced off patches of grass in the middle of the mall that remained unoccupied until 2pm. I don’t know if we have enough time-stamped images to get a map of these areas well yet. She also used 25 people per 100 square feet in the more sparsely populated area – which is quite low, so the 284,000 is very conservative in my opinion.]

Crowd counting is difficult without a lot of photos. Lauren wrote in her first draft:

You are likely to hear 150,000 to maybe 250,000. For those figures to be accurate you have to assume that there were only 50 to 80 people per 1,000 square feet. For some perspective on this, a typical school classroom is 600 sq. ft. and holds 18 to 30 students very comfortably. You could easily crowd those 30 students a little looser than the people in this crowd and not take up more than 1/3 of the room.

She then adds:

I am sorry for being wrong about my previous estimate of 420,000. I hadn’t yet seen any aerial views of the rally, and did my best to account for that. I didn’t do a very good job apparently, but I am extremely confident in this revised number.

Now, let’s not leave out the Satellite Rallies, cable viewers, and online streamers. The following are conservative estimates:

Satellite Rallies [Global]: 35,000 – 60,000

Cable Viewers [Comedy Central & CSPAN runs 1 & 2]: 600,000 – 700,000

Online Streamers: 175,000 – 225,000

Total # of Viewers in all media:  1,094,250 – 1,269,250

Lauren Rose provides an RSS subscription link to more of her notes.

End quote of Lauren’s note.

Personally, I found both her first estimate of 420,000 and her second of 284,250 to be equally beyond any point of my personal reference. I was there, and saw the arial photos, and was physically trapped in my spot for 3 hours, and read her detailed counting explanation, yet none of this tells me whether 275,000 or 420,000 is closer to the truth. Both are simply beyond my experience, which is the point of why I find this topic so fascinating.

Media pundits like to prognosticate about crowd sizes with truthiness instead of calculations. The ideal calculation would be to do a full head count with a set of detailed areal photographs and Amazon Mechanical Turk. The idea is that a lot of cheap labor plus a lot of zoomed-in photos of the crowd can provide a means to count everybody that was there at one instant in time. Having done this once for a physical space that is frequently the site of large rallies with disputed attendance levels, we can then use this estimate to better guestimate future crowd sizes. Sampling a portion of the total with a head count is inaccurate because the density is always uneven at the edges. The value of having at least ONE TRUE TALLY extends beyond this rally to a more general reference point. Humans often make mental errors in predictions that are  beyond any one person’s experience. Crowds ranging in the hundreds of thousands approach a “number numbness” where we simply get it wrong.

The estimation errors that pundits in the media make with crowd sizes are emblematic of the same errors that international development experts make when predicting AID priorities in Africa. After I started quantifying these estimation errors, as explained in this Huffington Post article, the organization I work for was able to demonstrate that some types of predictions are more difficult to do well than most would people believe.

But to reiterate one of comments on this post: what was said matters more than how many people heard it. And thus I present Jon Stewart’s 12 minute closing remarks below – the highlight of the rally in my opinion.

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Jon Stewart’s 12 minute impassioned closing words are worth hearing: