Coincidently, it seems long tail topics got popular both in English blogosphere and Japanese blogosphere.

In Japanese blogosphere, those articles are best.

• "Long Tail and Basic-law of the Internet Businesses" by Mr. Satoshi Watanabe

• "About Long Tail Theory by Mr. Mochio Umeda

BTW, at the recent session of "Power-law and the net trust money talking night," Mr. Ichiro Nakagawa talked about "Long tail of Self Realisation." His discussion was marvellous.

Hopefully, before continuing to read the rest of this article, please read those discussions or some other articles about long tail theory in English.

I want to discuss weather the long tail phenomena really shows the break of power-law or not.

I was interested in Mr. Asakura's discussion where he used calculus to analyse long tail. As it is possible to approximate Zipf and power-law by exponent function, I thought an exponential index is the key whether 80:20 law by Pareto can be applied to the long tail phenomena or not. I used EXCEL to investigate this problem.

• EXCEL FILE

Let's think we are going to open a virtual book shop where we sale 100 books. There must be a top 20 sales books, or "out of top 20 ranking" books. I made 100 hypothesized data on this EXCEL file, using exponential function as power-law. When you open the EXCEL file, please put some index number into the lined cell on left top column to manipulate how the exponential function index changes sales ranking of those item. Clearly, the ranking of sales shows the 80:20, where top 20 items account for 80% of total sales, to 60:20 or lower. I found the index of -1.21 or bigger (+) number shows the long tail portion of our books sales, which are the sales of 20th and lower sales ranking books, makes 20% or more total sales. Vice-versa, -1.21 and smaller (-) index shows more concentrated sales where top 20 sales books accounts for 80% or more.

Though the "real" net book shops like amazon.com have tremendous number of items, the number of items is still finite. The point is that the holding cost and dealing cost of net business is almost negligible, if you compare it for those of legacy "real" business.

One more point is that our virtual shop has only 100 items and I got the conclusion of index of -1.21. However, the "real" net bookshops have tremendous number of items and the index would be different from our conclusion. Still, those items out of top 100 or 1000 ranking can consolidated sales that exceeds that of top 100 or 1000 ranking items.

<reference>

• Long Tail vs. Lessig @ The Long Tail
• The Mass Age to Common Nitch Age (1) by ck (Japanese)
• The Mass Age to Common Nitch Age (2) by ck (Japanese)