Photo: Jeff Chiu, Associated Press

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Golden State Warriors forward Draymond Green (23) reacts after scoring next to guard Klay Thompson (11) during the second half of an NBA basketball game against the Denver Nuggets in Oakland, Calif., Saturday, Dec. 23, 2017. (AP Photo/Jeff Chiu) less

Photo: Jeff Chiu, Associated Press

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Golden State Warriors forward Draymond Green (23) reacts after scoring against the Houston Rockets during the second half of an NBA basketball game Saturday, Jan. 20, 2018, in Houston. (AP Photo/Michael Wyke)

Photo: Michael Wyke, Associated Press

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Golden State Warriors' Draymond Green, left, passes against Cleveland Cavaliers' LeBron James in the first half of an NBA basketball game, Monday, Jan. 15, 2018, in Cleveland. (AP Photo/Tony Dejak)

Photo: Tony Dejak, Associated Press

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Golden State Warriors' Klay Thompson (11) scores past Chicago Bulls' Robin Lopez (42) and Jerian Grant during the first half of an NBA basketball game Wednesday, Jan. 17, 2018, in Chicago. (AP Photo/Charles Rex Arbogast) less

Photo: Charles Rex Arbogast, Associated Press

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Golden State Warriors guard Klay Thompson is defended by Cleveland Cavaliers guard Kyle Korver in the second quarter Monday, Jan. 15, 2018 in Cleveland, Ohio. (Leah Klafczynski/Akron Beacon Journal/TNS)

Photo: Leah Klafczynski, TNS

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Forward Draymond Green and guard Klay Thompson were named reserves Tuesday for the NBA All-Star Game next month in Los Angeles, making the Warriors the first team in league history to have four All-Stars in back-to-back years.

Green and Thompson, who were selected by NBA head coaches, join teammates and All-Star starters Stephen Curry and Kevin Durant.

Per the league’s new All-Star Game format, Curry and LeBron James — the players from each conference who received the most fan votes — will choose rosters from the pool of players voted as starters and reserves. On Thursday, TNT will announce the team rosters Curry and James select. Curry has said that, if possible, he’d like to pick Durant, Green and Thompson.

This marks Green’s third All-Star Game selection and Thompson’s fourth. Green, the reigning Defensive Player of the Year, is averaging 11.3 points, 7.9 rebounds and 7.6 assists per game through Monday. Perhaps more importantly, he is the emotional leader of a Golden State team loaded with mild-mannered personalities.

Thompson is averaging 20.6 points, four rebounds and 2.5 assists per game. A catch-and-shoot maestro, he is within striking distance of the 50-40-90 club, the gold standard of efficiency for shooters. Thompson is shooting 48.6 percent from the field, 45.3 percent from three-point range and 88.1 percent from the foul line — all while regularly guarding the opponent’s top scorer.

The rest of the Western Conference reserves are the Timberwolves’ Karl-Anthony Towns and Jimmy Butler, the Spurs’ LaMarcus Aldridge, the Trail Blazers’ Damian Lillard and the Thunder’s Russell Westbrook. The Eastern Conference reserves are the Pacers’ Victor Oladipo, the Wizards’ Bradley Beal and John Wall, the Celtics’ Al Horford, the Cavaliers’ Kevin Love, the Knicks’ Kristaps Porzingis and the Raptors’ Kyle Lowry.

There have been four players from the same team named All-Stars in the same year nine times in NBA history. Before Curry, Durant, Green and Thompson were named All-Stars last season, the last team to have four All-Stars was Atlanta in 2015 (Kyle Korver, Al Horford, Paul Millsap and Jeff Teague).

Connor Letourneau is a San Francisco Chronicle staff writer. Email: cletourneau@sfchronicle.com. Twitter: @Con_Chron

Warriors’ Draymond Green, Klay Thompson named All-Star reserves

Updated 4:33 pm, Tuesday, January 23, 2018