Monday, July 23, 2018

Calculating value for money wines

The prices of wines rarely seem to go down. Indeed, at the top end of the market, they seem to go up rather alarmingly. It has often been noted that the Baby Boomer generation has been willing to pay much more for good wines than the Generation X and Millenial generations are currently doing. This means that the latter groups are looking for wines that are seriously good value for money.

I have previously provided a summary of various quantitative methods for assessing value for money (ie. in addition to personal judgment): Quantifying value-for-money wines - part 1, part 2, part 3 and part 4. The fact that there are seven different methods discussed in that blog series tells you just how seriously people have taken this issue. In all cases, the crucial relationship is between the quality score and the price (QPR) — for any given wine quality we need to estimate the price that is considered to be good value for money.


I thought that it might be interesting to present a real example of one way in which this value can be obtained. Indeed, it is the one that I use myself.

How I do it

Needless to say, in practice I use the method that works best for me. It is described in the post Quantifying value-for-money wines, part 2, although the most detailed discussion is in The relationship of wine quality to price. For it, I need a data set consisting of as many wines as possible, for each of which I have both a quality score and the price — the more wines the better.

I have previously noted that, due to the economics of how the government-owned liquor chain Systembolaget operates, Sweden has mid- and high-quality wines at a cheap price, but has no discount wines (Why is wine often cheaper in Sweden than elsewhere?). This means that I need to optimize the QPR — I can't just go down to a store and see what wines are on special, because there are no such wines. I have also noted the way in which new wines become available (Wine monopolies, and the availability of wine), and that the most interesting wines appear in Systembolaget's "Small quantities" assortment (små partier), which is where I focus my attention.

The wine-quality scores that I use come from Jack Jakobsson, who regularly does the Systembolaget wine tastings for BKWine Magazine. He produces a monthly report of all of the new-release wines that he has been able to taste (some wines are in too small a quantity to be made available to the media). He uses a 20-point scale, including half-points. His scores during 2017 ranged from 11 to 18.5 (see the graph at the bottom of the post). Wines that would score higher may exist, but they are not available for media tastings.

I standardize the prices to those for 750ml bottles of table wine (red, rosé, white, sparkling) — that is, excluding fortified wines, which tend to exist on a different price scale, and also other-sized bottles (halves, magnums, etc).

This first graph shows the scores for the 1,691 "Small quantities" wines that Jakobsson tasted during 2017, with the single-bottle price shown vertically and the quality score shown horizontally (each point represents one wine). You can convert the Swedish crown (krona) into US$ by dividing by c. 9 (eg. 175 kronor ≈ $20).

Wine prices in Sweden during 2017

What I need to do now is derive the QPR relationship for these wines. That is, I need to calculate the "expected" or "average" price-quality relationship. I do this by fitting some mathematical model to the data (as explained in An introduction to data modeling, and why we do it). I have to do this only once, so it it no big deal.

As I have discussed before (eg. The relationship of wine quality to price), an exponential model is usually the best fit to economic data, and this is shown in the next graph. Note that the vertical axis is logarithmic, which means that the model can be represented by a straight line. The fit of the data to the model is quite good (60%), especially compared to some other price-related data sets that I have looked at.

Fitting the exponential model to the wine data

The line on the graph may look like it is a bit too low, but that is only because there is a mass of points in the lower part of the graph — half of the points really are above and half below the line.

Since the fit of the model and data is quite good, we can now proceed to identify the value-for-money wines. [If the fit is poor, then the exercise would become pointless!] The next graph shows three dashed lines, representing three different QPR criteria.

Identifying the value for money wines

The wines below the pink line are the best 5% in terms of value for money, while those below the blue line are the best 10% — these are the wines we should think about purchasing if we want to get the most for our money. The wines above the black dashed line are the worst 5% in terms of value for money — these are the rip-off wines, because I can get the same wine quality for a lot less money.

You will note that the best bargains are usually in the 15-16.5 points range (which is approx. 88-91 points on the 100-point scale). This is a very nice quality range if you happen to like good wines — there is no need for me to pay more than the equivalent of US$25 for a "90-point wine".

The practical result of this analysis is that I now have a separate price noted for each quality score, which I can use to assess the value for money of any new wines that are released — new wines that are selling for less than that price are good value for money. For example, I always take a close look at any new wines that are below the prices represented by the pink line on the graph.

Conclusion

The procedure outlined here possibly looks cumbersome, but it is quite straightforward to anyone used to a bit of quantitative analysis. It works well, in practice; and it could be applied to a set of scores for any set of wines.

Jakobsson's scores

Finally, in accepting to use the scores provided by Jack Jakobsson, it is of interest to look at whether there are any biases in his scores, such as I have discussed in previous blog posts (eg. Biases in wine quality scores). The next graph compares the frequency distribution of Jakobsson's scores (in blue) with that expected from unbiased scores (in maroon).

There are few biases in the quality data

Interestingly, his scores are remarkably unbiased, compared to the situation discussed in my previous posts for other collections of wine scores. There is a slight under-representation of 15.5 compared to a score of 15 or 16, along with a small over-use of 14 and 14.5 compared to lower scores, but that is about all. Perhaps this is a result of using a 20-point scale, where there is no temptation to over-use scores like 90 on the 100-point scale.

Jakobsson also helpfully provides an indication of the likely best period during which to enjoy each of the wines. This is a topic that I will return to in a future post. On the flip-side of the coin, the most obvious downside to his reviews is his apparent disdain for rosé wines — they rarely get good scores, even when they taste pretty good to me.