Green won a Gold Glove Award and Silver Slugger Award in 1999. On May 23, 2002 he hit four home runs in one game. He also led the league in extra base hits, doubles, and total bases. He holds records for most home runs in a game, most extra base hits in a game, most runs scored in a game, most total bases in a game, and more. He was one of the best known Jewish baseball players of all time. Green retired in February 2008. He played and coached for Israel in the 2013 World Baseball Classic qualifier.