The relationship of price to wine-quality scores

This is a topic that I have periodically addressed before. For example:

Quantifying value-for-money wines - part 1
   — issues with quantifying value for money
Quantifying value-for-money wines - part 2
   — empirically comparing wines within a specified wine group
Quantifying value-for-money wines - part 3
   — formulae for assessing individual wines against a baseline wine
Quantifying value-for-money wines - part 4
   — empirically comparing wines across wine groups
How many wine prices are there?
   — Everyday wines, Better, Premium, Affordable Luxury, Luxury, Icon, Dream
Luxury wines and the relationship of quality to price
   — Bordeaux pricing
Calculating value-for-money wines
   — identifying wines that are good and poor value for their assessed quality

In particular, I have shown that the expected relationship between wine price and wine quality is mathematically known as exponential, as shown in the graph above. This means that the price increase exceeds the quality increase at an ever-increasing rate — value for money is never to be found among high-price wines. Was it ever otherwise?

The Wine Enthusiast data

In my last post, I discussed a dataset from the Wine Enthusiast, covering the years 1999–2017. For our purposes here, there are c. 121,000 wines with both a quality score (80–100) and a price (in $US). We can thus look at the relationship between these two variables using a simple graph, as shown below.

In this graph, the quality points are listed on the horizontal axis, with the prices shown vertically, so that each point in the graph represents one wine. Note that the price axis is logarithmic, so that the exponential relationship will form a linear pattern in the graph. The exponential relationship can thus be shown by the straight lines super-imposed on the points. [Note: if you want to see the same data plotted the other way around, then you can look at: Visualizing wine reviews.]

The interesting thing about these data is that they cover a much wider range of assessed quality than do other data sets that I have looked at, all the way down to 80 points — most other datasets do not bother with wines <85 points (even though many of us are very happy to drink these as everyday wines).

What the graph shows is that below c. 86 points, there is very little increase in price associated with an increase in quality score. I have not seen this point made before, and yet it seems to be an important one, at least for wine buyers. Why buy an 80-point wine when you can get an 86-point wine for pretty much the same price?

Beyond 86 points, the price starts to increase rapidly, as expected. Here, the value-for-money wines will be those that are the furthest below the straight line, and the rip-offs will be those furthest above the line. The graph seems to indicate that there are actually some good-value wines in the vicinity of 91 points. This is slightly higher quality than I have reported from previous analyses, where the best values were around 89 points, instead.

There are a few caveats to the analysis that I have presented here. The main thing is that the dataset combines all of the numerical variation due to different times (eg. price inflation over 18 years), different tasters (eg. different interpretations of points), and different wine types (eg. countries, grapes). In one sense, this is a “good thing”, because any general data pattern that can be detected among all of this variation must be an important one. In this sense, the graph above is very revealing.

On the other hand, we might learn a lot more from the dataset if we start to subdivide it. In this case, we might discover different patterns through time, or differences among the critics or the wine types. I hope to look at this in future posts.

Biases in the quality scores

Using the same dataset, we can also look at another topic that I have addressed before. This is the distinct bias almost everywhere in the wine world towards awarding 90 points instead of 89. For example, see:

• Biases in wine quality scores
• Awarding 90 quality points instead of 89

This bias is quite blatant in the Wine Enthusiast data, based on the c. 130,000 quality scores in the dataset, as shown in the next graph. The scores are arranged horizontally, with the vertical bars indicating the number of wines with each score.

In previous posts I have used the Weibull frequency model as a comparison to evaluate this bias. In this case, it indicates that simply swapping the frequencies for 89 points and 90 points would produce an unbiased dataset. I conclude from this that it is actually arbitrary whether a wine gets awarded 89 or 90 points!

This seems sad, in one sense. Presumably it matters for the sales of any wine whether it gets 89 or the magical 90 points, and yet there is apparently no objective basis for distinguishing between these two choices. What, then, is the role of the wine critics? They are just tossing a coin, for this pair of points.

Perhaps it is worth noting that this type of bias is not detected among those people who use a 20-point quality scale — there is no magical number!