Microsoft and the Long Tail of search

A former senior Microsoft manager (he didn't want his name used) emailed me with an interesting perspective on the Long Tail of search:

As you know, search engine query logs have a Zipfian distribution (Rank * Frequency = Constant).  When I presented this concept to senior execs at Microsoft, including BillG, they never quite got it.  I would draw the graph just like the logo on your site, but it just wouldn't sink in.  I realized that the size of the X axis was the problem.  People see a graph, but they don't comprehend the scale of the X axis. 

Looking at your logo, for example, it looks as if the (yellow) long tail is what, 4x, 5x the size of the red portion?  And it is, if you are comparing the integral of the yellow portion (i.e. query volume) compared to the red.  But the X axis, on a linear scale, extends almost infinitely to the right, and no visual can communicate that.   In essence, in order to represent the long tail in graphical/visual form, you implicitly have to represent the X axis logarithmically, as you know, and people (generally) don't comprehend logarithmic / exponential scale.

He eventually found a way to explain the curve using stacks of pennies, which ends up with a few high stacks followed by a trail of single pennies extending out the door, down the hall and, if you have enough pennies, as far as the eye can see.

He also found a handy rule of thumb to estimate the consequences of this distribution:

Loosely speaking, if you divide the number of queries by 4, you'll get the frequency of the most popular query, and if you divide by two you'll get the number of queries that occurred only once over whatever time period you are measuring.

Finally, it turned out that Zipf distribution turned up in all sort of unexpected places at Microsoft:

A second example refers to what the external world knows as Windows Crash Analysis but what inside Microsoft is known as Watson or Dr. Watson (of "come here, Watson, I need you" fame) because that's what it was first called.  Anyway this is the dialog that appears when a Windows application crashes on Windows XP -- an alert appears and offers to send the information to Microsoft.  Back at Microsoft, they compile that information in a SQL Server database, indexed by application name, module name, module version, and the internal address where the crash occurred.  Back in 2001 or 2002, they started showing off a graph of all the application crashes, with Rank on the X axis and Frequency on the Y axis.  Internally they called this the "Watson Curve," even in front of Gates. 

When I saw the curve, I smiled, because it looked familiar.  I asked one of the guys on that team to do me a favor and plot the results log-log.  He got back to me a few days later and said "wow, it's a straight line!"  I wasn't surprised.  I don't think they call it the Watson curve anymore because it's just yet another example of a Zipfian distribution at work.   

For more, check out this amazing site, which is all about the many Zipfian distributions found in the real world.

Comments

[Barry Ritholtz]

That's Fascinating stuff to a numbers geek (like me) -- I would hope you include it in the book.

Of course, the more math, the less copies you will sell.

Whaich raises a question: Which part of the fat head/long tail do you hope the book occupies?

[ecolson]

Very interesting stuff. However, regarding this stat:

"Loosely speaking, if you divide the number of queries by 4, you'll get the frequency of the most popular query..."

My research shows that 4 is much too small of a constant to characterize the Search Head. That is to say, the head is not nearly that large - rather, you would need to divide the total queries by a number like 100 to 400 to get the frequency of the most popular query.

I would be curious to see where the stat came from.

[Mathew]

For the best on the long tail, Zipf, etc,
Try reading Mandelbrot and Taleb:
http://misbehaviorofmarkets.com
http://fooledbyrandomness.com

[chris anderson]

Barry,

Well, I'd like to put a good bit of math into the book and accept my inevitable place down the tail. But my publisher, whose money is paying the rent, would rather that I not. At the moment, there is exactly one equation in the book (unsurprisingly, y=ax^k), but we'll see if that survives the editing.

[Adam Marsh]

Funny, I just wrote a post on this exact topic:

"Loosely speaking, if you divide the number of queries by 4, you'll get the frequency of the most popular query."

This says that in a Zipfian distribution, the top bin gets 25% of the total. As I detail in my post, the percentage of the total in the top bin depends upon the number of bins, assuming that the distribution follows an exact inverse power law. According to this reasoning, if the top query gets 25% of the total queries, there were less than 100 queries!

Of course, in fitting real data to a power law all kinds of offsets, etc. are swept under the rug, so this isn't really a fair thing to say -- but it is an interesting topic in general. You can find more on similar long tail / power law stuff here, here, and here.

[Michiel]

Doesn't have a lot to do with the Tail, but dr. Watson: I turn it off. On all workstations. People don't get it, or get annoyed. They are much happier when the application just crashes and they can restart it.

[MelbournePhilosopher]

I came here from out-of-context. Frequency of *what*, measured in units of what, according to whom?

Cheers,
-MP

[Mendy]

This says that in a Zipfian distribution, the top bin gets 25% of the total. As I detail in my post, the percentage of the total in the top bin depends upon the number of bins

[Arik]

That is to say, the head is not nearly that large - rather, you would need to divide the total queries by a number like 100 to 400 to get the frequency of the most popular query.

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