But fate intervened and now the two most polarizing figures in Thursday's 2012 NBA draft will be forever linked for their battles on the court and their remarkable stories off it.
As for Robinson, he is a self-made millionaire in every sense of the word. His journey to basketball's grandest stage was nothing short of the ultimate struggle.
On the court, he patiently waited for his turn behind the Morris twins (Marcus, now with Houston, and Markieff, now with Phoenix), providing Self with steady high-energy off of the bench for his first two seasons.
Off the court, Robinson was forced to deal with unrelenting tragedies culminating with the loss of his mother and his new responsibility to raise his younger sister, Jayla.
But he faced those demons and accepted those challenges, emerging as one of the strongest figures in the sports world and one of the strongest forces in college basketball.
As for Davis, his climb to the top of the NBA draft board was every bit as unique as Robinson's was tragic.
Four years ago, Davis was a 6'4" sophomore point guard playing for a widely-ignored team in the lower division of Chicago high-school hoops. He was considering an offer from Cleveland State because, frankly, that was about the extent of interest from the collegiate level.
By his senior season, though, Davis had a new 6'11" frame and a new standing atop recruiting rankings everywhere. Like many top recruits, he was soon Kentucky-bound to headline coach John Calipari's latest coup.
Great NBA rivalries often begin on the collegiate level, and this one got its start in the national championship game on April 2, 2012.
Davis' Wildcats were a coach's dream, with six great options (all part of a record six Kentucky players selected in the top 46 picks) and a 37-2 record coming in.
Robinson's Jayhawks, meanwhile, were simply that: They were Robinson's. The top scorer (17.7) and rebounder (11.9) had carried his teammates through the postseason save for occasional help from senior (and 41st pick) Tyshawn Taylor.
The game was one that had been played so many times during basketball's rich history. The young, athletic Wildcats raced out to a 14-point halftime lead, before the veteran Jayhawks clawed within a five-point deficit with 1:30 remaining before finally running out of steam.
Robinson gave Self everything he could, finishing with a team-high 18 points and a game-high 17 rebounds.
But Davis stole the show, despite scoring just six points. The rest of his stat line read: 16 rebounds, six blocks, five assists and three steals.
Draft-lottery hopefuls salivated. Sports analysts were in awe.
But not Robinson. "He's not Superman, he's just a great player," he told reporters after the game. "I'm not going to sit here and give all my praise to someone I go up against."
Nearly three months later, Robinson's still not impressed. After Davis wore a shirt bearing the phrase "Check my stats" to the draft combine interviews, Robinson told Sports Illustrated's Sam Amick that if executives were to go check the stats then he, not Davis, would be the draft's top pick.
Either stats do not hold the same weight for executives, or they just had a different way of reading them than Robinson did. Not only was Davis the number one pick on Thursday, Robinson fell to Sacramento as the fifth pick.
But that could be a blessing in disguise. Sacramento is certainly not the NBA's version of the Kentucky Wildcats, but they appear to be a lot closer than Davis' Hornets.
Both franchises took major steps in bringing these two on board. They could be the building blocks for some terrific Western Conference playoff matchups down the line as this budding rivalry continues to grow.