The team that has recorded the most points at the end of a game is declared that game's winner.
NBA
Most points in a career: Kareem Abdul-Jabbar (38,387 pts) http://www.nba.com/statistics/default_all_time_leaders/AllTimeLeadersPTSQuery.html?topic=4&stat=1
Highest career points per game: Michael Jordan (30.12 ppg) http://www.nba.com/statistics/default_all_time_leaders/AllTimeLeadersPPGQuery.html?topic=4&stat=0
Most points by a player in an . http://www.nba.com/history/records/regular_points.html
Most points averaged by a player in one season: 50.4 by Wilt Chamberlain (1961-62)
Most points by a player in one season: 4,029 by Wilt Chamberlain (1961-1962)
Most points by a player in one half: 59 by Wilt Chamberlin
Most points by a player in one quarter: 33 by George Gervin
Most points by a player in one overtime period: 16 by Gilbert Arenas