The past decade was brutal for American department stores, which were besieged by superstores, off-price retailers, fast-fashion retailers, and e-commerce giants.

Investors usually measure a retailer's growth through comparable-store sales growth, or the revenue growth at locations opened for at least a year. However, we can also measure a retailer's productivity with its average sales per square foot.

A chart of the average sales per square foot of five major U.S. department store chains.

Data source: eMarketer. Chart by author.

Nordstrom (NYSE:JWN), the priciest retailer of the bunch, is crushing many of its peers, which are in a clear race to the bottom. There's also a correlation between a department store's sales per square foot and its revenue growth: J.C. Penney (NYSE:JCP)Sears (NASDAQOTH:SHLDQ)Macy's (NYSE:M), and Kohl's (NYSE:KSS) all posted negative sales growth in fiscal 2016, but Nordstrom reported a 2.9% increase.

Nordstrom's average stores are also smaller than the average Sears, J.C. Penney, or Macy's store. Selling pricier products within smaller spaces boosts a retailer's productivity -- that's why Apple Stores generated a whopping $5,435 in sales per square foot over the past 12 months. Unless American department stores shrink their footprints, they'll keep struggling to boost their overall productivity.

Leo Sun has no position in any of the stocks mentioned. The Motley Fool owns shares of and recommends AAPL. The Motley Fool recommends Nordstrom. The Motley Fool has a disclosure policy.