Why Is It So Hard to Estimate Crowd Size?

(Aug. 30) -- Size matters. At least it does when it comes to reporting crowd estimates.

Take Glenn Beck's "Restoring Honor" rally, held Saturday on the Lincoln Memorial -- the anniversary and site of Dr. Martin Luther King Jr.'s "I Have a Dream Speech." Besides being an important illustration of the scope of Beck's popularity, the number of attendees also poses a test for mainstream news operations. Will they be able to stand by their figures, or be forced to retract them? (As has been the case countless times when crowd-inflation or miscounting has been exposed.) Plus, at least in this case, there's a fairly high-profile bet riding on the outcome, between Beck and his Fox News colleague Bill O'Reilly.

But whatever the event, if it's held in Washington, it's hard for the estimate of crowd size to not become heavily politicized. Those with a stake in the answer often accuse the other side of misrepresenting the number to achieve a certain goal: overemphasizing or downplaying the number of people who feel sufficiently strongly enough about an issue, person, or platform to congregate at a specific time in the first place.

So far, the estimates for Beck's "Restoring Honor" audience have, predictably, varied considerably depending on the source of the information. Here's Surge Desk's roundup of the numbers, in descending order, by source:

1.8 million -- The number mentioned by National Park Service spokesman "Dan Bana," aka "Dan Barna." That was the number of people who attended the Obama inauguration and was mentioned by the spokesperson as a benchmark for measuring the size of the Beck crowd but erroneously cited and reprinted as the actual size of the Beck crowd by several blogs, according to Washington Monthly's Steve Benen.

1 million -- The minimum number cited by attendee and speaker Rep. Michele Bachmann, R.-Minn., according to The Washington Post (via MinnPost).

300,000 to 500,000 -- The number attributed to Beck himself, on the day of the rally, according to The Washington Post. He extended this range to between 300,000 and 600,000 on "Fox News Sunday," notes The Hill. On his radio show Monday, he called other, lower reports "hilarious." The first range cited was also repeated by Sarah Palin on her Facebook page.

300,000 -- The number another National Park Service official gave to NBC News, unofficially (since the Park Service doesn't do official estimates anymore after the 1995 Million Man March, as MSNBC: First Read blogger Carrie Dann points out). Also the number that was listed on the permit granted to Beck and the event's organizers, according to CBS News.

87,000 -- According to a crowd estimate from AirPhotosLive.com, which was commissioned by CBS News.

"Tens of thousands" -- The Associated Press

Just how could the estimates in this, or any case, range so widely? After all, there are plenty of aerial photographs of the event circulating. Shouldn't it just be a simple matter of using a variance of the classic gumball jar estimate contest? According to many crowd analysts (most of them journalists, tellingly), it is easy, mostly. The basic method is accredited to Herbert A. Jacobs. From a 1967 Time article on the Berkeley Vietnam War protest crowds:

"Estimating the size of a crowd may be the last area of fantasy in the newspaper business," observed Herbert A. Jacobs, 63, a longtime Wisconsin newspaperman who now lectures at the University of California. Jacobs set out to make a more scientific calculation. ...

By doing a little arithmetic, Jacobs arrived at what he calls the "Jacobs Crowd Formula," pace off the length and breadth of any crowd, add the two figures, multiply by seven for a slack crowd, by ten for a dense one.

Sounds simple, right? The problem is, even Jacobs recognized that there were inherent limitations with his method:

Jacob admits that his formula is not flawless. Some crowds will not conform to the norm. If a crowd is composed primarily of women, for instance, some allowance must be made for greater hip girth. Or if the crowd is largely coeducational, he adds, it is conceivable that people might press closer together just for the fun of it.

Other challenges have been noted by journalists abroad. For instance, Giovanni Tapang of the Philippine Daily Inquirer wrote about a protest last year:

Crowd density is usually not uniform, except in very crowded areas, and will taper off from the hub of activity. The time the estimate was made is also important, as crowds are dynamic systems. Over a period, the crowd size can swell or ebb due to people coming in and out of the assembly area. Making an estimate at only one point can lead to a different count if it is taken at the peak or near the end of the event. Assigning marshals to monitor people coming in and out of the hanay (line) would keep a contingent relatively organized.

Indeed, the deceptive simplicity of crowd arithmetic is precisely the reason that the National Park Service is discouraged from publishing official crowd estimates. It had used a version of Jacobs' method to estimate the attendees at the "Million Man March," initially coming up with 400,000 but later retracting this estimate after facing criticism from Nation of Islam leader Louis Farrakhan, who threatened to sue the agency, citing racism behind the count.

Since Jacobs' time, many other mathematical and computer-assisted methods for estimating crowd size based on photography have been proposed. The problem? They are highly specialized, and require equipment and the time and resources of research groups, which, of course, do not come cheap. So unless a media organization or another interested party is willing to pay to hire such specialists, their work is rarely applied in the field and in real time.

As for estimating the racial and demographic makeup of a crowd? Another ballgame entirely, but one that is clearly no less politicized.