The following season saw Wright play slightly more one-day cricket, but slightly less first-class cricket. After playing in four of Tasmania's opening five Pura Cup matches, Wright did not appear in the competition again until the final two matches of Tasmania's campaign. Of his 22 first-class wickets in the season, 12 came in the last two matches, with Wright taking four wickets in an innings in both of the matches, against Western Australia and South Australia. His first-class wickets in the season came at an average of 26.95, significantly better than he had managed in previous seasons. In one-day competition, he returned nine wickets, including three wickets in a match Queensland. He spent the Australian winter playing club cricket in Scotland, where he helped Grange Cricket Club reach the final of the Scottish Cup. He also represented Scotland in two Cheltenham & Gloucester Trophy matches. In the first-round match, he made his first half-century in List A cricket, scoring 55 after opening the batting. He made another half-century in the second-round match, and was named as man of the match as Scotland completed a ten-wicket win with Wright remaining 53 not out. First-team regular The 2001–02 season saw Wright become a regular member of both Tasmania's first-class and one-day sides, playing all of their matches in both formats of the game. Wright continued to show an improvement with the bat, averaging 34.08 in the Pura Cup, making four half-centuries. The first of these—his maiden first-class half-century—came in Tasmania's opening Pura Cup match of the season, when he scored 50 exactly before being trapped leg before wicket in a high scoring draw. In his next match, Wright was named man of the match after taking two wickets and conceding only 22 runs in his ten overs, helping to restrict Western Australia to 195 to set up a five-wicket victory for his state. Wright finished with identical figures in his following one-day match against the same opponents, but Western Australia secured victory thanks to a century from Michael Hussey. He was selected to play for the Prime Minister's XI against New Zealand in a 50-over contest, and claimed the solitary wicket of Mathew Sinclair and conceded 51 runs in his nine overs. Later in the season, he helped his team to an innings victory over Western Australia in the Pura Cup thanks to a first-innings score of 63 with the bat, and