Alvarez was born to Cuban parents in Miami, where his father played baseball and his brother Nick was a professional baseball player in the Los Angeles Dodgers organization .
Short track
Alvarez had his first international success as a short tracker at the 2009 World Junior Short Track Championships in Sherbrooke . There he won the gold medal with the relay. He made his debut in the Short Track World Cup in January 2013 in Sochi and finished 24th and 11th over 500 m. At the 2013 Short Track World Championships in Debrecen , he was seventh with the relay. At the beginning of the 2013/14 season he came on the podium for the first time in Shanghai with third place over 500 m in the World Cup. In the further course of the season he took second place with the relay in Seoul and won his first World Cup victory in Kolomna with the relay. At the season highlight, the 2014 Winter Olympics in Sochi, he won the silver medal with the relay. He also took 31st place over 500 m, 19th place over 1500 m and 11th place over 1000 m. In March 2014, he finished sixth with the relay at the 2014 Short Track World Championships in Montreal . At the end of the season he was ninth in the overall world cup over 500 m.