Thursday, 24 March 2011

Micro Four Thirds lens pricing

The pricing of some Micro Four Thirds lenses have caused some discussion. For example, the Panasonic Leica 45mm f/2.8 macro and the Panasonic Lumix G 14mm f/2.5 are seen as expensive lenses. And the Panasonic Lumix G 45-200mm is seen as a bargain.

Just for the fun of it, I decided to see if there was any patterns to be found when it comes to lens pricing. I used the US prices, since the US is a big market.

First, one might think that weight is important. After all, glass is heavy, and also expensive to produce. Here is the relationship between the lens weight in grams and price in dollars:

We see rather easily that there is a relationship between weight and price, but it's hardly significant (R2=0.28). There are many outliers, for example the 45mm macro lens, and the 45-200mm tele zoom.

One could also guess that fast lenses are more expensive. So let's look at price versus the maximum aperture of the lens:

What we see, though, is the opposite. Faster lenses are less expensive. However, this is because some of the slower lenses are expensive special lenses, like the wide angle zoom Panasonic Lumix G 7-14mm f/4. We also have long zooms and superzooms in this category. Again, the fit is not very good, R2=0.06.

It is quite obvious that to explain the price, we need to include several parameters, not just the weight or the aperture.

One way to identify interesting variables, is to use Principal Component Analysis (PCA). This is a way to find which variables that best cluster the observations. Here is a plot of the first two principal components:

What we see here, is not surprising, but the presentation is somewhat interesting. First of all, we see that the pancake lenses are fundamentally different from the rest, as they occupy one large part of the image.

Another binary variable is premium. I've put the Lumix 45mm macro, the Lumix 14-14mm HD superzoom, and the Olympus 75-300mm tele zoom lens in this category. However, this variable does not appear to be important in grouping the lenses. It is correlated with other variables, like length, weight, number of lens elements, lens groups, filter thread, and maximum aperture.

Some lenses are still outliers, like the basic kit zooms (since they are light, but have many lens elements).

However, when using the first two principal components to fit the price, there is still a lot of unexplained variation:


What this all boils down to, is that there are too few observations. With more observations, i.e., more lenses, we might be able to fit the price to lens characteristics in a better way. And this is a conclusion we all can agree with, I am sure, that we need more Micro Four Thirds lenses.

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