Does bottle price have anything to do with cellaring desirability?

I recently asked the question: How soon is wine consumed after purchase? This inevitably involved the topic of cellaring wines, since most wine production seems to be intended for consumption within 1—3 years of bottling. Indeed, only c. 10% of the people surveyed said that they preferred to cellar their wines.

Having a wine collection seems to be associated with a certain amount of wine snobbery, although we might prefer to see this as "wine interest", instead. Another aspect of snobbery is, of course, cost. Having expensive bottles in the cellar is much "better" than having cheap ones, as explained in Leonard S. Bernstein's 1982 classic The Official Guide to Wine Snobbery.

The obvious question, then, is: Does the wine price have anything to do with cellaring desirability?

One possible source of data to answer this question comes from Wine Ark, one of Australia’s leading wine storage companies. You can read a bit about the company in: A conversation with Wine Ark.

Wine Ark periodically releases a list of Australia's Top 50 Most Collected Wines, based on how many customer bottles they have in their storage. So, I have had a look at Australia’s Most Collected Wines 2019. These are graphed below (in order from the top), along with the Wine-Searcher "Avg. USD Price (ex-tax)" for the most recent vintage release. Note that the price uses a logarithm scale in the graph.

Well, it seems to me that there is not a very strong relationship between cellar popularity and price. For example, the three most expensive wines are ranked 1st, 15th and 21st, while the three cheapest are 8th, 37th and 40th.

However, the top 25 wines are, on average, 50% more expensive than are the bottom 25, at US$121 versus US$88. Furthermore, the rank-order correlation between cellaring and price is 0.274 (p=0.056, for those of you who want to know), indicating a general decrease in price with fewer stored bottles.

So, the answer to the question posed in the title is: Yes, more-popular cellar wines do tend to cost more than less-cellared ones. However, even within a single company wine price does not always correlate with cellaring (eg. the Penfolds wines, and the Wynns Coonawarra Estate wines).

Also, there is not much relationship to availability. Some of these wines are produced in quite large commercial quantities, and are available world-wide (eg. the Wynns Coonawarra Estate wines), while others are much more specialist (eg. the Yarra Yering wines, or the Mount Mary wines).

This leads me to wonder whether it is only Australians who behave like this, or whether this is a much more general cellaring pattern. After all, many people think that an Australian wine cellar must look something like this: