Transfiguring 985 million into 1 billion

short term update: shared by NPR producer, bloomberg, other media and finance and publishing outlets, #2 on redditt statistics, and multiple CEOs including of top marketing firm futures company and kdnuggets

In Mark Zuckerberg's dream Sean Parker whispered "A million users a day isn't cool, you know what's cool?  A billion users a day.  And that's where you're headed, even if you take on bad advice, orchestrate shady psychological experiments, and sustain a lengthy campaign of untrustworthy stunts and specious sharing of your users' private data."  Mission accomplished?  Perhaps.  Yesterday Mr. Zuckerberg (himself with only three million views on the competing Google+) announced the passing of a company milestone:

...one billion people used Facebook in a single day.  On Monday, 1 in 7 people on Earth used Facebook to connect with their friends and family.  When we talk about our financials, we use average numbers, but this is different. This was the first time we reached this milestone...

So this carefully cooked up wording is ripe for inspection, if people are purposefully deceived into believing that one billion people are currently actually logging onto Facebook every day (their original standard for usage), to share with (or spy on) their family and friends and other interests.  They have always presented numbers in the financial statements reflecting daily users that were rising to approach about one billion.  In their latest Q2 earnings, slide 3, they were at 968 million.  But the fine print buried behind it is very revealing in terms of how such a guess is put together.  We'll discuss those considerations and others below.  On net, no, one billion people are not currently on Facebook every day, though it's not outside the realm of possibility to at some point in the future arrive at a "good day" once every few weeks.  Let's explore this headline news, and un-hoodie the difference for them, between the marketed noise versus the actual signal.

Let's look at the eight considerations, which make for an exciting merger of business math and probability theory.  The first thing is that the traffic data captured are always estimates, which devaite around based off of models that are not uniformly precise, from small websites to the largest websites (of which Facebook is one of the largest).  So the number of actual users can never be precisely measured in real-time, but it's rather an estimate built off of a noisy sample.

The second thing is that the estimates that Facebook provides are overestimated by design since they don't have a real way to account for fake people or fake activity, or both.  In slide 25 for example, of the above linked Facebook's earnings, it states:

Our data limitations may affect our understanding of certain details of our business. ... Some of our metrics have also been affected by applications on certain mobile devices that automatically contact our servers for regular updates with no user action involved, and this activity can cause our system to count the user associated with such a device as an active user on the day such contact occurs. ... The methodologies used to measure user metrics may also be susceptible to algorithm or other technical errors. ... We regularly review our processes for calculating these metrics, and from time to time we may discover inaccuracies in our metrics or make adjustments to improve their accuracy, including adjustments that may result in the recalculation of our historical metrics. ... In addition, our DAU and MAU estimates will differ from estimates published by third parties due to differences in methodology. ... The numbers of DAUs, mobile DAUs, MAUs, mobile MAUs, and mobile-only MAUs discussed in this presentation, as well as ARPU, do not include users of Instagram or WhatsApp unless they would otherwise qualify as such users, respectively, based on their other activities on Facebook.

The third thing is that the above commentary, which is quite dreadful for anyone unaware, still doesn't include all relevant disclaimers.  Another point is that an individual can have multiple user accounts.

The fourth thing is that by stating now, at the end of the week, that Monday was a record day, could also reflect "seasonality" within the weekly data.  In other words, we often see a pattern where there is more traffic on some days (e.g., the first workday of the week) which is balanced by suppressed traffic numbers on the other days of the week.  This should be handled by taking a look at the average over a lengthy time frame; not a single day.  This is something noted in their announcement at the top of this article, though they then hypocritically transgressed on the substance of this information.

The fifth thing is that this particular Monday was also informally dubbed China's "Black Monday" due to the Chinese and then global stock market rout.  Of particular note was that this blog site and other news covering market risk and related measures (e.g., New York Times, CNBC) had seen a surge in news reads.  When everyone's net worth was cratering, something other than Facebook was suddenly more important for many more than one billion people.  No other news site (including my blog site), cited a new milestone in readership, as a result of this spectacular (and random) single day shock.  That's common sense.  For someone to, from reading these news sites, simply "Like" an article really shouldn't count as "connecting with friends and family" on Facebook,  The real place people spent quality time was instead on the original news site.  Not on a haphazard "Like", clicked off for fun somewhere.  Just by you getting this far into this article should be verification that quality of time spent sharing information should count, on the margins.

The sixth thing is that there will always be trends that will for a while mirror population growth.  Remember the McDonald's "billions served" jingo?  Served what?  And tallied up by who?  Exactly; and that's why McDonald's dropped this signage long ago.  But at least as the counter and harmful calories swelled higher, we knew it wasn't later subject to volatility and revisions.  But with Facebook data, we can assume that there was some modest growth since the end of Q2.  968 million is now ~985 million.  The trickier part is the uncertainty surrounding what is the daily variation about this statistic.

Which brings us to the seventh thing, concerning the volatility of this estimate.  We know there is a large overlap in the daily user counts, from day to day.  So much overlap that Q2's monthly active user (MAU) total of 1.49 billion is just 55% greater than the daily active user (DAU) count.  We have to track the ratio of DAUs to the total MAUs base to learn more.  Over the past ½ dozen years that the ratio has been erratically building from the low 40% range, to currently the high 60% range.  So we must consider the total variation formula of the expectation of variation [~√(55%*45%/24)], or roughly 10% over the past 6 years.  Plus the variation of expectation, which we noted was just a few percent over this time (the square root of which is de minimis).  If we assume a upper end variation of 1 standard deviation, then we would get ~75% (~65%+10%).  This comes to ~1.1 billion active users on a given day, every few weeks.

But keep in mind the eighth thing that summarizes all of this together.  The ratio of total number of users on only a good day would come to:

(1.1 billion - fake/duplicate user accounts - non-human "activity") / 7.3 billion humans

Sorry if you missed that.  Facebook not only overcounted their users, they also undercounted the global population by 4%.  With both leaders at the helm having also once studied at Harvard, could this have been an innocent oversight?  It is equivalent (from the denominator alone) to taking credit of an additional 40 million or so users that they don't have!  One must be careful as always with people like Mr. Zuckerberg.  Blink for a minute, and a fast one gets pulled.  It's also possible that their statistic is actually even lower (given the language mismatch from the top of this article), but they made up for it by insincerely adding Instagram and WhatsApp usage, as if those were people on Facebook.  Could the real answer be closer to 1:8, or 1:6.5?  None of this fogginess reflects charitably on Facebook.

So sure they are on path to having one billion active users a day, but they are many months away from having this on a continual basis.  None of us should fudge, even by a small amount.  And these sort of impromptu celebrations were premature, just like their historically incredulous first day IPO fiasco.  But we mustn't carp too much.  Mr. Zuckerberg's keeping track of who is naughty and nice.  Don't worship him enough for being CEO, and one day soon you and your friends and family may rudely find yourself unable to take out a loan.