Monday, 1 May 2017

Do sales by US wine companies fit the proverbial "power law"?

The short answer is: almost.

The Power Law is used to describe phenomena where large events are rare but small ones are quite common. For example, there are few billionaires while most people make only a modest income; there are few large cities but many small towns; there are few very frequent words (such as "and", "the") but many rare words.

Mathematically, Power Laws are of interest because of what is known as "scale invariance", as well as the fact that there is no well-defined average value. You can read about this in Wikipedia.

For the rest of us, Power Laws are of interest because of their practical consequences. For example, the 80:20 Rule (or Pareto Principle) is one example of a Power Law, which says that for many events, roughly 80% of the effects come from 20% of the causes. You can also read about this in Wikipedia. For a discussion of this idea, see What is the 80/20 rule and why it will change your life. [Sometimes, it is also 90/10; for example, it is usually estimated that 90% of wine consumption in the USA is by 10% of the people.]

Power Laws are considered to be universal, and so there is no reason why they should not exist in the wine industry. One of the more obvious places that we might expect to find them is in the size of wine companies. Size might be measured by amount of wine produced or by monetary income, for example. Either way, there will be a few very big companies and lots of little ones.

So, let's look at a specific example. In its February 2017 issue (p.48), Wine Business Monthly compiled its fourteenth annual ranking of the top 30 U.S. wineries by case sales (in 2016). You can see a copy of the list in Big Wine takes over.

Wine Business Monthly notes:
Though there are now 9,091 wineries in the U.S., the WBM 30 companies represent more than 90 percent of domestic wine sold by volume. The three top wine companies by themselves represent more than half of all case sales.
This sounds like a classic case of a Power Law; and so it is worth checking this possibility.

One special case of the Power Law is known as Zipf's Law, which refers to the "size" of each event relative to it's rank order of size. This is what we are looking at here. For each wine company, the "size" is the number of cases of wine sold during 2016, and the WBM 30 companies are listed in rank order of their sizes (largest to smallest).

The standard way to evaluate the Zipf pattern is to plot the data with both axes of the graph converted to logarithms. Under these circumstances, the data should form a straight line. Here is the graph of the WBM 30 data. The three largest wineries are labeled.

A Power Law fitted to the sales by US wine companies

As you can see, almost all of the data lie roughly along a straight line, and thus do indeed fit a Power Law. That is as expected; and the Power Law is thus not proverbial in this case.

However, there is one exception — the largest company, E&J Gallo Winery, did not produce enough wine to fit into the same pattern as the other 29 wineries. Indeed, to fit the Power Law, the top-ranked company would need to have sold about 260 million cases during 2016, which is c. 3.5 times as much wine as E&J Gallo actually sold.

This is an interesting finding. The Power Law suggests that the biggest US winery (and thus the biggest wine company in the world) should dominate the US industry to a greater extent than the Gallo winery currently does. That is, having one-quarter of the US wine market is not enough! The current degree of industry dominance has been held by Gallo for at least the past quarter-century, but it seems unlikely that it has ever dominated sufficiently to fit the Power Law. Apparently, it is rather hard to dominate US wine sales in the way predicted by a simple Power Law model.

This "under-performance" by Gallo may be a good thing for the consumer, of course, since Diversity is usually a better thing than is a Power Law — the Power Law actually represents a rather extreme situation.

For comparison, the biggest-selling imported wine in the USA is Yellow Tail (from Casella Wines, in Australia), with more than 8 million cases shipped to the US per year. This would place it at no. 9 in the WBM 30 list. This will be the subject of a separate blog post.

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