I spend most of my working life researching how collaborative technologies – particularly social media – are impacting business strategy. My academic background is in economics. So when The Economist does a special report on something like social networking, it always gets my attention. And as with most articles in the publication, I always find a treasure trove of interesting statements and facts to think about. Over the next little while, I’m going to be exploring a few of them here.

Today I’m going to start with something very, very simple – the statistics they provided on Facebook usage in their lead article. Specifically, each of the following three stats were presented in relation to Facebook becoming so popular:

• 350 million users
• 55 million updates a day
• 3.5 billion pieces of content shared each week

Each is unquestionably a big number, that seems to indicate popularity – but a simple calculation of per-user stats seems to be telling me a slightly different story. For example, 55 million updates a day, across 350 million users, works out to just over one update per week, per user. That doesn’t actually seem like very many – particularly given that, at least from what I have seen, there is a reasonable number of people that update their status quite regularly. Spun a different way, if 15% of people were providing one update per day, that would leave 85% never providing an update at all. I’m not exactly sure how the exact distribution plays out, but in general it appears that providing an “update” on Facebook isn’t something most Facebook users do that often – and certainly less than once a week.

I also find it interesting to contrast the 55 million daily “updates” with the 3.5 billion weekly – or 500 million daily,  just under 1.5 per user – pieces of content shared. So for every update people opt to provide to their network, about 10 other pieces of content are shared. When you think about Facebook as a place where people share with their network who they are (and what they’re thinking), that means personal identity can be defined far more by the types of content being posted then quick little statements.

I’d really like to see a breakdown of what exactly this content is (are such numbers floating out there somewhere?). My initial hunch is that photographs account for a significant chunk of this, but there’s obviously also a lot of news links, videos, events, etc. But again, a VERY unscientific study (basically scanning the recent activity of my own friends) seems to indicate that, unsurprisingly, this activity is very skewed. I’m assuming that, for example, the 52 photos my friend just posted counts as 52 pieces of content… and I notice a handful of people seem to post multiple things daily, while a huge chunk are relatively inactive.

Which all takes me back to one of the research themes I’ve been exploring for awhile. When it comes to social media, a lot of attention is paid to the active people that create a lot of content – and share a lot of information. And since so much attention is paid to them, many social media strategies (often inadvertently) have an underlying assumption that everyone is like that. A lot less attention tends to be paid to the legions of people that are, more or less, relatively passive members of various social networks – perhaps absorbing some of the information from others, but doing little else. The reason I think this is important is that I’ve often heard customers are no longer passively absorbing information, thus the broadcast media model is dead – but the behavior of many people on social networks indicates the reports of death might be premature. Instead, they might just be listening to a different broadcaster, which is a very different story.

Today my favorite writer – The Sports Guy – wrote an excellent column about Bill Belichick’s “reckless” call to go for it on 4th and 2 when his team was up by 6, on their own 28 yard line, with just over 2 minutes left to play. Much of the article goes into great detail on the problems inherent with relying on statistics in such a situation (see: Insane angle #1: Statistically, it was right move). But in Insane angle #2, he can’t help but pull out his own statistics to “justify” why the Pats shouldn’t have gone for it.

Unfortunately, The Sports Guy made an all-too-common mistake while doing so – providing a reminder that however dangerous putting blind trust in statistics can be, the problem is that much worse if you don’t understand them properly.

His argument was simple. Indianapolis had already completed two long touchdown drives in the 4th quarter. By punting, New England would have forced them to do it a third time. So, to “prove” his point, he asked someone to crunch the numbers on “the number of times a team started and completed three touchdown drives in the fourth quarter to erase a double-digit deficit and win an NFL game since 2005.” The answer he found was 4 – it happens less than once per season. He then started banging his head on his desk.

It sure looks like a perfectly reasonable, statistically-based argument, but there are some major flaws. The one I’m going to focus on here (another big one is switching from %s to a raw count of a known rare situation, which is almost always an easy but meaningless thing to do) is tied to what’s called the “Gambler’s fallacy” – the belief that deviations from expected behavior in the past are likely to be evened out by opposite deviations in the future. The common example is coin flips, but I’m going to use a basketball analogy – since that’s the Sports Guy’s favorite sport.

Let’s say your playing the Cleveland Cavaliers, and for no obvious reason whatsoever they run a play to get a three-point shot for Shaquille O’Neal – who has only even attempted one such shot in the last decade or so. The defense is so confused by this that they foul him, and he steps to the line. Even though he’s only a 50% FT shooter, he hits the first two. What are the odds of him hitting the third?

The correct answer is 50%. The fact that he’s just hit his first two has absolutely no bearing on the probability he’ll hit his next one. But if you follow the underlying logic of the Sports Guy’s argument, you’d determine the answer is 12.5%. After all, that is the odds that he hits three free throws in a row. But that number goes out the window, because the first two have already been made.

That’s the Gambler’s fallacy in action, and underlies the logic of the Sports Guy’s argument. He tried to use statistics to argue down the probability of an event happening, based on that same event happening twice before.  Marching 70+ yards down the field may be difficult, but just because you’ve done it twice already in the quarter doesn’t make it more difficult the third time (and things like “how many times it’s happened to three times to win a game, etc., etc.” don’t matter much at all). If anything, it would be the opposite – and I’ve got the stats to back it up.

Just kidding – I don’t really. But since I’m writing, there is another interesting thing to point out here in terms of common statistical / analytical mistakes.

The question of the day is whether the team should have gone for it. But in his analysis, the Sports Guy brings in the particular offensive set the coach chose. Now it’s perfectly valid to question this in terms of “does the coach suck?”– but from an analytical standpoint, you really should keep the two decisions separate. Whether he made the right play call for the 4th down conversion and whether he should have gone for it on 4th down are two very different things.

Why is this distinction important? Well let’s say you’re watching a game where the coach for one team is absolutely terrible. Andy Reid in any given 4th quarter will do. On third down and six, for whatever reason, he opts not to block the defensive team’s best pass rusher, who breezes in untouched for a sack. It’s now 3rd and 12. In turn, using the above logic, you can argue that he shouldn’t have gone for it on third down, because the probability of success was so low, given the play call. But it’s not the strategy that was wrong – it was the execution. Or for a non-sports analogy, hitting on the single girl at the bar might have been a good strategy… but throwing up in her drink was poor execution. Hitting on the girl with a huge fiance standing beside her was probably a bad strategy, regardless of execution. Different things, different lessons to be learned.

The reason I’m writing about all of this is because we see variants of this situation come up all the time. Arguments for why a person, team, or company should or shouldn’t do something rage, any many people throw lots of stats and other “facts” behind them. Some have bad information. Some have information from biased samples. Some interpret it incorrectly. Some confuse strategy with execution. Some make too much from too little, others too little from too much. It’s really, really easy to do – but from my experience it usually stems from trying to over-complicate things.

In cases such as the Pats game (with so many variables in play, and a low relevant sample size to draw from), I prefer simple, back of the envelope type calculations. My “best guesses” at the percentages indicate going for it was absolutely the right call. And personally, I believe the long-term benefits to the team if they had made it (demoralizing the opposition after showing them no “respect”, increased confidence, etc) outweigh the downside here (where the coach, not the players, shoulders most of the blame). I could be wrong – particularly since you can’t really quantify the latter at all.

But what I think really doesn’t matter. To repeat the important lessons: thoughtful analysis can often be more important than the underlying data for complex circumstances such as this one (in this case, most of the Sports Guy’s best points have no numbers tied to them whatsoever). And if you want to respond to a poor use of statistics with your own statistical analysis, you should probably make sure you get it right.