The latter goal is becoming less realistic with every loss for the Crimson Tide, but Randolph is still faring well in his first season as the team's undisputed leader.
The Tide graduate student and team captain is easily having his best season after playing largely a supporting role to guard Trevor Releford for much of his career. He's averaging career-highs of 14.6 points and 4.9 rebounds while leading the team in scoring, assists and steals - and also finished his first semester of grad school with three A's and a B in the fall.
Alabama (13-8, 3-5 Southeastern Conference) has lost five of its last six games, a huge blow to its bid to make the NCAA tournament for the first time since Randolph's freshman season in 2012.
''That's been our motivation since Day 1,'' Randolph said Tuesday. ''We've never lost track of our vision, our hope.''
He and the Tide play Missouri on Wednesday night in a rematch of his best game. Randolph posted career-highs of 33 points and five 3-pointers against the Tigers last season.
Alabama won't have No. 2 scorer Ricky Tarrant for a second straight game with a lower right leg injury and Tide coach Anthony Grant isn't certain when he'll be able to return.
He has been able to count on Randolph's presence for 122 consecutive games, all but 15 of them starts. Teammates unanimously voted Randolph team captain before the season, the first player to hold that role during Grant's tenure.
The 6-foot-5, 208-pound Randolph ranks among the SEC's top 10 in steals (fifth), free throw percentage (seventh) and scoring (ninth).
Randolph is also averaging double figures in points for the first time in his career, but he still takes the mentality of a hard-working role player.
''On the court, as a basketball player you have to be more versatile, you have to be able to do multiple things,'' he said. ''It's not all about scoring. You have the loose balls, hustle plays, effort and intensity. The intangibles that you have to bring every day.
''My teammates do a really good job of helping me, and I try to help them.''
That includes forcing himself to be more vocal on the court and in the locker room, when he was more comfortable pulling teammates aside in the past.
''He challenges us on and off the court to be the best player and person that we can be,'' Tide guard Retin Obasohan said. ''He really models that in everything he does, obviously starting academically and athletically. He's been a great role model and leader for our team.''
If making the NCAA tournament is Randolph's chief goal as an Alabama player, the marketing grad student also has long wanted to be the Tide's first Academic All-American.
''Our freshman year, I went into the academic center,'' Randolph said. ''They have a wall with all the Academic All-Americans, and there wasn't one for basketball. Every other sport had one except basketball.
''So I was like, `I do well in school.' I just tried to make it a prime goal to become the first.''