No Russian opposition rally and protest march is truly over, it seems, until there has been an Internet flame war over the strength of its attendance. By now it's a formulaic ritual: pro-government bloggers cite official police reports which minimize the number of protesters and thus their relevancy, while members of the opposition claim to have witnessed a much larger showing. The low and high estimates usually vary widely, while the truth, as it often happens, is somewhere in the middle.
The January 13, 2013 “March Against Scoundrels” was no exception — if anything, there was more at stake in the numbers game after a poor showing at last month's unauthorized Lubyanskaya Square rally  [GV]. Leading up to the march people were curious: will this event attract the tens of thousands of people that anti-Kremlin protests did last winter? Needless to say, the speculation started early. Unofficial protest leader Alexey Navalny, for example, was pessimistic  [ru]:
На собрании по поводу митинга я дал свой прогноз численности сегодняшнего марша в 400 – 1200 человек.
At the meeting about the rally I made a prediction of the size of today's march to be 400 – 1200 people.
As people started assembling, however, it was clear that his prognosis was wrong. At 1:00 PM, an hour before the start of the march, BBC Russia correspondent Jüri Maloverjan tweeted  [ru] that there were already “several thousand” people present. Just 40 minutes later Ilya Yashin, Coordinating Council member, estimated  [ru] the column to be around 20,000 strong. At around the same time leftist opposition leader Sergey Udaltsov counted  [ru] 30,000, while young revolutionary Roman Dobrokhotov weighed in  [ru] at 50,000. In a few minutes Yashin updated his count  [ru] to 40,000 “at a minimum.” By 2:30 PM both Yashin  [ru] and Udaltsov  [ru] agreed on 50,000.
Thats not to say that everyone was on the same page. Opposition journalist Oleg Kozyrev, for one, was sure that the numbers were much higher, tweeting  [ru]:
Воможно сегодня самая массовая акция в соаременной истории.
Today's rally is possibly the most numerous in modern history.
Конечно четверть миллиона вряд ли пока была. Но 200000 тоже хорошо
Of course, I doubt there was a quarter of a million yet. But 200000 isn't bad either
Kozyrev explained his rather fantastical estimate (most would agree that Russia's largest mass rallies of the past year have barely topped 100,000 people) by pointing out that  [ru]:
Все, кто пытается считать участников, не ждали хвоста колонны. А я ждал.
Everyone who tries to count the participants didn't wait for the tail of the column. But I waited.
На время протестных акций отбирайте пожалуйста у Олега Козырева твиттер. Сто нашистов так не высмеивают движуху, как один он.
During protests please take twitter away from Oleg Kozyrev. One hundred members of NASHI don't mock the movement the way he does all on his own.
Meanwhile, the official police head-count came in at 9,500  [ru], a number lower than the lowest witness estimates, and certainly at odds with the opposition leaders’ consensus of 50,000. Who was closer to the truth? Never fear, Russian netizens were on the case! Unlike previous marches where estimates were made hand counting people  [ru] on photographs (a very rough method of approximation), this time there were at least three groups that used independent approaches to produce a realistic count.
Photographer and blogger Dmitry Ternovsky, for instance, got together a team of eight volunteers  [ru] to stand by the metal detector frames at the start of the march, the idea being that participants would have to pass through a police operated metal detector to attend. Each volunteer would use a hand operated clicker, or tally counter, to make an exact count of the people passing one metal detector. Since it was impossible for eight people to count all forty-six metal detectors, Ternovsky's team spread out to capture random detectors both in the center and sides of the two rows of frames. They then used the counts to roughly estimate how many people walked through an average detector, and arrived at a total of 24,474.
This result is, of course, likely fraught with inaccuracy at a rate much higher than Ternovsky's self-admitted 5% margin of error. However, elementary statistics does necessitate that such sampling must work on a basic level. And, even with a 20% margin of error, Ternovsky's data would mean that there were between 20,000 and 30,000 people marching — numbers different from those estimated by both the opposition and the police.
Ternovsky's findings were corroborated  [ru] by another team of volunteers. They used a similar interpolation method to estimate average detector counts and ended up with 21,805. In addition, unlike Ternovsky, who apparently has been loosely tied to pro-Kremlin groups in the past, Dmitry Ionov, the leader of the second team, has opposition “credentials,”  [ru] being an active participant in Citizen Observer and other election observer programs.
Finally, if these two counts aren't convincing enough — there is a third. Analtoly Katz, a computer scientist, used a completely different method to make his estimate — based on footage he shot from an apartment window  [ru] overlooking the march route and then ran through a proprietary piece of software. Katz describes  [ru] his methodology:
Мы зафиксировали фотокамеру в одном месте, и делали примерно один снимок в секунду, пока вся толпа проходила мимо нас. Если мы знаем скорость и плотность толпы в каждый момент, суммируя эти данные по всему времени шествия, мы получим общее количество пришедших.
We fixed a camera in one place, and made around one photograph per second, while the crowd walked past us. If we know the speed and density of the crowd at each moment, summing these data over the time of the march we will get the total number of participants.
Katz's program counted 24,500 people, very much in line with the other two estimates. He has also produced his data for independent verification.
In the end, however, those who are sure that there were fifty or one hundred thousand participants won't be convinced by counts, no matter how independent. Why try to explain the loss of popular support by the opposition, when it's much simpler to call anyone who says so a Kremlin stooge? A few days after the march Roman Dobrokhotov, who made the first estimate of 50,000 people, brushed off  [ru] Katz's analysis when cited by Ternovsky:
@dternovskiy да это жулик очевидный, он из твоего доклада цифру и взял.
@dternovskiy well he's an obvious crook, I bet he just took the number from your report.
Truly, faith brooks no argument.