Growing up in Wisconsin, Looney was named the top high school player in the state as a senior in 2014. He also received national recognition as a five-star prospect and earned All-American honors. In his only season at UCLA, he led all freshmen in the nation in double-doubles, recording double figures in both points and rebounds in 15 games. One of the top players in the Pac-12, he was also named to their all-freshman team. As a rookie with Golden State, Looney's playing time was limited after undergoing surgery on both of his hips. The following season, a strained left hip sidelined him for most of the playoffs during their championship run. Finally healthy in 2017–18, he became a regular in the Warriors' rotation as an undersized center, helping them win a second straight championship.
Looney was born in Milwaukee, Wisconsin, to Doug and Victoria Looney. As a youngster, he watched his older brother Kevin, who was six years older, play pickup games. Like his brother, Looney became a Los Angeles Lakers and Kobe Bryant fan, and would watch tapes of Bryant and copy the Lakers star's moves.
Looney was the best player on his high school team at Alexander Hamilton High in Milwaukee. He was already being recruited by colleges as a freshman, receiving offers from in-state schools Marquette and Wisconsin. In his sophomore year in 2012, he was named Player of the Year of the Milwaukee City Conference after averaging 20.9 points, 8.6 rebounds and 2.0 assists per game. As a junior, Looney averaged 26.1 points, 12.4 rebounds, 7.0 blocks and 3.1 assists per game, and led a team of mostly unproven players to a runner-up finish for the conference title.
In his final season, he averaged 27.9 points, 12.7 rebounds, 7.0 assists and 8.0 blocks per game; both CBS Sports and The Post-Crescent called his averages "nearly" a quadruple-double. Though he was Hamilton's tallest player, he was also their best passer, and played mostly at point guard. Hamilton went undefeated in conference play to win its first league title in four years, and Looney earned his second City Conference player of the year award. He gained national recognition, becoming just the second player in Milwaukee Public Schools history, and the sixth ever in Wisconsin, to be named a McDonald's All-American; he was a Parade All-American as well. Looney was named Wisconsin Mr. Basketball by the Wisconsin Basketball Coaches Association, and Gatorade and the Associated Press named him their state player of the year. He was listed as a five-star prospect by Rivals.com, ESPN.com and Scout.com, who ranked him nationally as the No. 10, No. 12, and No. 15 player, respectively.
Looney announced on Halloween in 2013 his decision to attend the University of California, Los Angeles (UCLA). No recruiting analysts at 247Sports.com had predicted his decision, which was a secret to everyone including his parents. Looney liked California, and called UCLA the "most beautiful campus I had ever seen." He was impressed with UCLA coach Steve Alford's vision for the team. The Bruins did not guarantee Looney a feature role as a freshman, but sold to him that he would be allowed to play both inside and outside and show his versatility, much like Kyle Anderson did for the Bruins in 2013–14.
Upon his arrival at UCLA, Looney suffered a hip injury. He rested for two-to-three weeks before the season and did not exhibit any related issues the rest of the season. Playing power forward for the Bruins, he was one of the top freshman in the country in 2014–15. In the season opener, he debuted with 20 points, nine rebounds and three assists in a 113–78 win over Montana State. CBS Sports called his performance "one of the more impressive freshman debuts in UCLA's rich history." He followed up with double-doubles in his next four games, and became the first freshman in UCLA history with at least four double-doubles in his first five games.[a] Soon, pundits began projecting Looney as a freshman lottery pick should he decide to enter the National Basketball Association (NBA). He had seven double-doubles in the Bruins' first 10 games, before scoring in double digits just once during a five-game losing streak for UCLA, which included an 0–2 start to their Pac-12 Conference schedule. Looney helped the team end their streak with career highs of 27 points and 19 rebounds in an 86–81 double-overtime win over Stanford. He was one of 14 players named to the midseason watch list of the United States Basketball Writers Association (USBWA) for the Wayman Tisdale Award, presented annually to the nation's top freshman. He was also one of 16 finalists for the inaugural Karl Malone Award, given to the top power forward in Division I men's basketball.
UCLA rarely called plays for Looney, and his scoring typically came off putbacks, fast breaks, and open shots. A natural at rebounding, his shooting improved as the season progressed. After making just nine of 28 of his three-point field goals in the first 24 games, Looney was 11 of 17 in the last seven games of the regular season. Still his scoring tapered off, with only one game over 15 points since his career-game at Stanford. In the 2015 Pac-12 Tournament, Looney exited mid-game after he took an arm to his left cheek during UCLA's quarterfinal win over USC. He was a game-time decision to play the following day against Arizona, when he was cleared and fitted with a protective mask just 90 minutes before the contest. Though impaired by the mask, he played 30 minutes but was limited, finishing below his season averages with only five points and four rebounds. The Bruins lost 70–64, but the close match helped them secure a bid into the 2015 NCAA tournament. Looney continued to play wearing the mask as UCLA advanced to the Sweet 16 for the second straight season.