Comments on: The long tail tagging the dog http://www.econometa.com/archives/12 The economy of stuff about stuff Sat, 12 Jun 2010 21:22:21 +0000 hourly 1 http://wordpress.org/?v=3.0.1 By: EconoMeta » Blog Archive » Turning rankings into graphs http://www.econometa.com/archives/12/comment-page-1#comment-14 EconoMeta » Blog Archive » Turning rankings into graphs Tue, 14 Jun 2005 01:30:48 +0000 http://www.econometa.com/?p=12#comment-14 [...] ly cleared up what was bothering me about those long tail graphs, prompted by Phil’s comment and helped a lot by this article. The issue is that long tail graphs have an x axis com [...] [...] ly cleared up what was bothering me about those long tail graphs, prompted by Phil’s comment and helped a lot by this article. The issue is that long tail graphs have an x axis com [...]

]]> By: Adam http://www.econometa.com/archives/12/comment-page-1#comment-13 Adam Fri, 10 Jun 2005 16:18:48 +0000 http://www.econometa.com/?p=12#comment-13 Yeah, something still bothers me about that too. But the classic "long tail" is that of Amazon: products are ranked by sales, and significant overall sales volume comes from the many products that don't sell much each. So I think that this is the right graph, but I agree people sometimes forget that the X axis doesn't really represent an independent value, and start talking about bell curves, etc. In fact, I think the "power law" terminology itself lends itself to such confusions. Firstly, it's really an <em>inverse</em> power law. But also, a 1/x graph has a "tail" that is equal to its "head," but if you want a graph with a "heavy tail" you'd be looking at something like 1/x^.5; even "inverse power law" usually means something like 1/x^2. Plus the idea of comparing "areas" under these curves is problematic since integrals of all such functions are divergent... Yeah, something still bothers me about that too. But the classic “long tail” is that of Amazon: products are ranked by sales, and significant overall sales volume comes from the many products that don’t sell much each. So I think that this is the right graph, but I agree people sometimes forget that the X axis doesn’t really represent an independent value, and start talking about bell curves, etc.

In fact, I think the “power law” terminology itself lends itself to such confusions. Firstly, it’s really an inverse power law. But also, a 1/x graph has a “tail” that is equal to its “head,” but if you want a graph with a “heavy tail” you’d be looking at something like 1/x^.5; even “inverse power law” usually means something like 1/x^2. Plus the idea of comparing “areas” under these curves is problematic since integrals of all such functions are divergent…

]]> By: Phil http://www.econometa.com/archives/12/comment-page-1#comment-12 Phil Wed, 08 Jun 2005 11:01:55 +0000 http://www.econometa.com/?p=12#comment-12 The graph ideas look interesting; I hope someone with more time and better access to the data picks them up. I'm still uncomfortable with using ranking as an X-axis variable, though; in effect, both axes are carrying the same piece of information ("that bar's the tallest *and* it's the first!") This may be a trivially obvious point, but I do think it's been overlooked by a lot of the people who have spread the 'power law'/'long tail' image; people have even contrasted 'power law' distributions with the 'bell curve' of a normal distribution, which (of course) you can't possibly get if you're using ranking along the X axis. The graph ideas look interesting; I hope someone with more time and better access to the data picks them up. I’m still uncomfortable with using ranking as an X-axis variable, though; in effect, both axes are carrying the same piece of information (“that bar’s the tallest *and* it’s the first!”) This may be a trivially obvious point, but I do think it’s been overlooked by a lot of the people who have spread the ‘power law’/'long tail’ image; people have even contrasted ‘power law’ distributions with the ‘bell curve’ of a normal distribution, which (of course) you can’t possibly get if you’re using ranking along the X axis.

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