BEAVERTON, United States — With European soccer's annual transfer window drawing to a close and star players from Alexis Sanchez to Virgil van Dijk changing hands at values higher than ever, Nike Inc. has a boots-on-the-ground advantage over rival Adidas AG.The combined value of the 100 most expensive players in the professional leagues of England, France, Germany, Italy and Spain has hit 8.97 billion euros ($11.2 billion), according to a study by the CIES Football Observatory in Neuchatel, Switzerland. Adding data on individual shoe sponsors reveals that 57 percent of that value comes from players wearing Nike boots — including Sanchez and van Dijk — compared with 33 percent from those wearing Adidas. The balance comes from a handful of athletes in footwear from Puma SE and Under Armour Inc.Over five years, the price tag of a player with the same characteristics has doubled, said Raffaele Poli, who heads the institute.In addition to its strength as measured by top-player value, Nike recently had an edge over its German rival as the shoe of choice among players in Europe’s five biggest leagues. The Beaverton, Oregon-based company provided cleats for 60 percent of those players last season, up from 48 percent three years earlier, according to data provided by German sports-business consultancy PR Marketing. Adidas fought back, however, turning that trend this season, and it maintained its lead in overall soccer gear.“There is an arms race for the top players and a dramatic increase of sponsorship money,” Poli said.The inflation in player value comes in large part from booming sporting-goods sales: Nike seeks $50 billion in revenue by fiscal 2020 and Adidas about 26 billion euros, meaning their combined marketing spending, typically 10 percent to 12 percent of sales, may hit as much as $10 billion then.Part of that money helped Manchester United, which has a 10-year jersey deal with Adidas worth a guaranteed minimum of 750 million pounds ($1.1 billion), secure the services of the Chilean winger Sanchez from Arsenal this week. Chelsea paid Adidas a penalty of 67 million pounds in 2016 to end a long-term deal prematurely for a more lucrative arrangement with Nike, worth 900 million pounds over 15 years.Fueled also by foreign investors, transfer prices have been pushed to new levels, with the record-breaking 222-million-euro fee that sent Neymar Jr. to Paris St. Germain quickly followed by FC Barcelona reinvesting the proceeds into French striker Ousmane Dembele from Borussia Dortmund and attacking midfielder Philippe Coutinho from Liverpool. The latter team this month paid a world-record fee for a defender in signing van Dijk from Southampton for a reported 75 million pounds.What do those players have in common, besides fat bank accounts? They all play in Nike shoes.By Richard Weiss; editors: Eric Pfanner and John J. Edwards III.