At first glance, it seems like something of a mismatch. Uniqlo, the Japanese fast fashion brand, is paying $300 million over 10 years to replace Nike Inc. as the kit sponsor for Roger Federer.

The Swiss might be the greatest male tennis player ever, but at 36 his best years are behind him. From a commercial perspective, he seems to have aced it. And Uniqlo looks like it’s paying an awful lot for a sportsman who isn’t too far off from retirement.

A less cursory look tells a different story. Uniqlo parent Fast Retailing Co. Ltd. is enduring slowing growth in its home Japanese market, which accounts for more than half of all revenue. It’s therefore accelerating a push into both international markets, which it wants to overtake Japanese sales this year, and e-commerce.

The problem for the $18 billion-revenue company is that, as much as it wants to present itself as a big-data whiz kid, the price it charges for its products rules out a fully digital response.

It can cost about $25 to acquire a new customer with a digital advertisement push or paid search results. For the likes of Hugo Boss AG, whose cheapest t-shirts can still cost $40, that cost is relatively easier to stomach. For Uniqlo, whose t-shirts sell for as little as $6, it’s harder to make the economics of a digital campaign add up.

Of course, Fast Retailing will still use digital ads, but it will get the most bang for its…