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The Tall Tale of Luxury Watch Sizes

Helmets of different size on shelving.
I had the distinct pleasure of recently, and virtually, joining the Horological Society of New York for a lecture this week. The talk was entitled "The Ideal Watch Size: A Curious Case of Misperception and Missed Opportunities." The speaker, Mark Cho, is a men's fashion entrepeneur who co-founded The Armoury (with stores in New York City and Hong Kong). Cho also owns a men's clothing brand in UK: Drake's.

I won't spend too much time describing, in detail, Cho's talk because it is recorded and currently available for HSNY members online (in the near future it will be publicly available on YouTube).
Screengrab from Mr. Cho's talk.
Cho collected some data online, using a survey, about people's perceptions of their wrist sizes as well as their actual wrist sizes. He also compared and contrasted those survey responses. The results are really interesting and worth considering. Plus, Cho mentioned behavioral economics in his talk, which immediately earns points from this economist.

What I'd like to discuss here is a question posed by one of the attendees, Osama Sendi (who himself participated in a WIS-famous HSNY lecture featuring FP Journe). Cho's results seem to suggest that collectors, generally, favor smaller watches. Sendi's question amounted to "why aren't the brands listening and making enough smaller sizes?" It is a fair question. The robust demand for vintage watches may boil down to the fact that collectors can't find the smaller watches they want in autorized dealerships, so they turn to vintage in response.

I want to offer a few reflections, as an economist, on this subject. To begin, I'll observe that Cho is asking a positive question, ie a judgement of what watch size is "best." These are always the most interesting, and also the most controversial, questions. The controversy emerges because different people will use different yard sticks to measure "best." I think we need to begin by asking "what do we mean when we say ideal?" Cho did an outstanding job describing some evidence of demand-side notions of ideal watch size. There are, however, reasons to believe that these don't necessarily match exactly to supply-side notions. I'll explain.

To riff on Ernest Hemingway for a moment, luxury watch buyers are different than the the public at large.
Hemmingway, 1924.
They typically have more money. This is probably obvious, but the implications for the ideal watch size, from a brand's perspective, are far less obvious. To work that out, we need to go to the economics literature. Having more money also tells us something about a person's stature. There is robust international evidence that taller people earn more. We economists refer to this as the height wage premium. I know we can probably name a bunch of short billionaires like Jeff Bezos (5' 7") and Mark Zuckerberg (also 5' 7"). The plural of examples, though, is not data.

The data indicates that, "each extra inch of height is associated with a one-to-two percent increase in average hourly earnings for men and women." There are a lot of explanations for why this happens, but I'm not going to delve into that topic (it warrants a completely seperate post). The point is that, if luxury watch buyers have more money, and watch brands are targeting such buyers, they are also designing watches primarily for people who are typically taller. An interesting question is: how much taller?

To get an answer for that, I turn to Nielsen's 2015 "Luxury Retail Landscape Report."
Top 5 "Established Luxury" markets, 2015 per Nielsen.
The table on page 9 lists the top 10 local markets in the United States for different luxury "segments" (essentially these are a collection of zip codes). The table columns there have fun names like "luxury aspirationals," which is maybe a little too unclear in meaning to me, even though I may very well belong to that group. I decided to focus on the Top 10 "Established Luxury" markets (see figure). I collected the average (mean) household income for these 10 markets and then I averaged that average to arrive at $178,000 (2019). You'll note that I'm using average income (rather than median) because, for luxury markets, we actually want our measures to reflect the upper tail of the income distribution.

That level of income is 52% above the national average. Let's assume that the watch industry wants to target households with half of this income advantage, or 26% above the national average. Estimates vary regarding the height premium, but a 3% increase in earnings for each inch of height is within reason. This implies that brands would end up targeting individuals with a height that is 8 inches higher than average.

The next question is: does taller height translate into bigger wrists? The answer is yes. To arrive at this conclusion, I downloaded the Third National Health and Nutrition Examination Survey (NHANES, 1988-1994) which is conducted by the U. S. Centers for Disease Control and Prevention. Although the data is dated, this is the last time CDC conducted an NHANES survey involving the wrist. It might be the case that American anthropomorphism has changed in the intervening years, but I'll leave that for someone else to explore.

It turns out that height has a very close relationship to wrist "breadth."
Wrist and height relationship.
I present a graph of wrist size and height here (I apply a natural log to both variables first). The line represents a very simple statistical relationship between the two variables. It suggests that height can explain approximately 40% of the differences in wrist size across individuals. This is a highly significant relationship indicating that a 1% increase in height leads to a 1% increase in wrist breadth.

Now we can pin down the implication of designing for more affluent, taller, buyers. As a reminder, we're assuming that watch brands are targeting someone whose income is 26% above average, and evidence suggests that such a person would be 8 inches taller than you might expect. The CDC data implies that a person who is 8 inches taller is 12.3% above average height. Given the estimated relationship between height and wrist breadth, we would expect this taller person to have a wrist that is 12.3% broader, which translates into a wrist that is 2.62 inches wide (for males in the sample).

Now we get into even more difficult territory.
An idealized wrist cross-section.
Wrists are very oddly shaped. One paper I consulted presented a rendering of a wrist "cross section" from MRI scans, presented here. I was pretty suprised by this, for some reason I thought a wrist was basically an oval. But it actually looks a lot more like some kind of asymmetric parallelogram with rounded corners. I settled on a superellipse (aka a Lamé Curve) as an approximation.

While we're conisdering a wrist that is 2.62 inches wide (caliper breadth), we next need to figure out the likely corresponding wrist depth (perpendicular to the plane of a hand).
The parameterized superellipse representing the wrist of a tall male.
I was able to find a publication on carpel tunnel syndrome which suggested that, in a control group, the ratio of width to depth for a wrist is typically .7, giving me a depth of 1.83 inches. I located an online calculator which can generate the circumfrence of a superellipse with these and other parameters (pictured) and concluded that designing for higher income and taller buyers means that a watch should accomodate an approximately 7.5 (7.44) inch wrist. This wrist size is typically associated with watches greater than 40mm in size, for example, Govberg observes "If your wrist circumference is 7.5 to 8 inches, you should be looking at 44mm to 46mm watch cases."

In conclusion, I've suggested here that the height earnings premium is a plausible reason why the luxury watch industry favors larger watch designs. It would be natural to wonder, then, why many brands are starting to offer smaller timepieces. I believe the answer lies in differences in average height around the world. Based upon the literature, the height premium is likely not an absolute. In other words, it is height above average in a country which seems to generate the premium. For this reason, we would expect that if luxury watch demand began to drift towards countries where people are taller (shorter) than averge, watch sizes will increase (decrease). It is clear that the center of gravity for luxury watch demand is shifting towards Asia and, for this reason, brands are offering smaller watches. The implication above, though, is that the brands are probably still making watches than are larger than ideal for the Asian market. The reason? They are targeting those earning the height premium which prevails in that market.


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