New Delhi, Sept. 23 -- Kylian Mbappe left Nike this month for Swiss sportswear company On on a deal that mixes cash with equity. Football treated it as a shock kit switch. The closer read is a business sequel. In 2019, Roger Federer did not simply endorse On. He bought in, helped design a tennis line from scratch, and only then took the brand onto tour in a match shoe it had never made. Mbappe is now being asked to do the same job in football.

Before November 2019, On was known for CloudTec running shoes and Swiss engineering, not Grand Slam courts. Then Federer joined as an investor and what the company called a co-entrepreneur. The New York Times described him as an investor, contributing designer, and representative. Notably, an endor...