Monday, September 30, 2013

Long Tails and Fat Heads

Sometimes words or phrases are used in MATH and then spread to the REAL WORLD. I have blogged about how the terms Prisoner's Dilemma has become a real-world-phrase here and speculated about the terms Venn Diagram, Zeno's Paradox, and n+1 here.

I recently came across a pair of words that are related--- one of them seems to be (like Prisoner's Dilemma) going from MATH to THE REAL WORLD. The other one is very odd in that I've seen it in the REAL WORLD but it SHOULD be in MATH.

Long Tail: A Probability distribution has a long tail if there are MANY items that have a SMALL but NON-ZERO prob of happening. This is a term in probability. However, I have seen it used in the REAL WORLD as in Amazon has a long-tail strategy meaning that they will sell LOTS of DIFFERENT things even if the number of people buying some of them is small (like this which is ranked 9,578,520- though I doubt they can be that precise). This article from the Atlantic Monthly points out that ESPN used to have a long tail strategy (e.g., showing Billiards and others sports that are not that popular, but ALOT of them) but then abandoned it for... see next definition. Note that the term Long Tail is used for both a type of Prob Dist and a marketing strategy related to it. How common a word is Long Tail? It gets 66,500,000 hits on Google. The first page has the definition above only. The 10th page had about half of the hits with the def above.

Fat Head: A strategy where you concentrate on just a few items. ESPN is doing that by covering just a few sports, but the most-watched ones (too bad, I was hoping they would cover my favorite sport, chess boxing). This SHOULD be a math term for a Prob Dist with just a few points of high prob. I asked my friends in the ML community and he assures me that NO its not a math term--- but it SHOULD be! How common a word is this? It gets 2,300,000 hits on Google. The first page seems to have NOT have ANY reference to the definition above.

SO- this COULD be a case where a term used in the REAL WORLD migrates to MATH with essentiallythe same meaning. This isn't that uncommon (the term Continuity comes to mind) but this timeI will have predicted it! Maybe I should do Machine Learning.


  1. yeah "long tail" got popularized somewhat in wired articles by anderson, who is a great popularizer of theoretical concepts. eg lately datamining. also nicholas taleb has a lot to say about the "long tail" & he got a lot of attn after the 2008 crash. long tail has a lot to do with web-based retailing models which make it feasible or even profitable to stock/ship "long tail" type items. eg amazon, netflix, etcetera. also, note these are statistical concepts. statistics is really in the limelight lately with datamining. (some musings on datamining, more to come.)

  2. Not sure what Amazon does now but a decade ago I heard from an insider that below a certain level of sales, their sales rank was randomly assigned.

  3. "A Probability distribution has a long tail if there are MANY items that have a SMALL but NON-ZERO prob of happening."

    More precisely, when these rarely appearing items together constitute a large part of the whole probability mass. My favorite example is a famous quote from an Amazon exec: "We sold more books today that didn't sell at all yesterday than we sold today of all the books that did sell yesterday."

  4. Interesting observation! "Long tail" tends to have a mathematically defined distribution of lognormal or power law distribution. What would be the mathematically defined distribution for "fat head"?

  5. Hum...I never thought about this in specifics. I wonder which is more structurally safe for a company, Fat Head or Long tail.
    P.S. Chess Boxing may be my new favorite sport.