But let's be honest: there are lots of facets to being a good basketball player, and Rudy surpasses Bayless in the majority.
Skill: player who's better
3 point shooting: Rudy
Passing: Rudy
Post Feeding: Rudy (he was our best player overall at this last year)
Court awareness (and general BBall IQ): Rudy
Ball-handling: Bayless (although Rudy knows his limits, and I haven't seen him dribble the ball out of bounds off his foot, like Bayless)
Getting fouled: Bayless
Defense: Bayless tries hard, but is pretty clueless (and stumpy-armed), Rudy is sneaky but easily pushed around. Both are non-ideal, but at least...
Steals: Rudy (this is something Rudy has really excelled at this year)
Clutchness: Rudy
Big-time international experience: Rudy
Hops: probably Bayless, but Rudy's no slouch
Hair highlights: Rudy
Designer stubble: Rudy
the list just goes on.
Interesting. Let's try this exercise with some different players. Prime Shaquille O'Neal and prime Allen Iverson.
Skill: player who's better
3 point shooting: Iverson
Passing: Iverson
Post Feeding: Iverson
Post Scoring: Shaq
Court awareness (and general BBall IQ): Iverson
Ball-handling: Iverson
Defense: Both are non-ideal, but at least...
Steals: Iverson
Blocks: Shaq
Clutchness: Iverson (he's hit more game-winners, I believe, than Shaq, plus his free throw shooting close-and-late is much better)
General excitement: Iverson
the list just goes on.
So, hmm...a scientific proof that Iverson was a superior player to Shaq. He "wins" many more categories. The Lakers probably would have won more championships with Iverson instead of Shaq. After all, every arbitrary "facet of the game" is equally valuable and should be given equal weight.
Ultimately, it's about effectiveness, not breadth of skills. Shaq had a few skills (post scoring, rebounding, help defense) and those were so overwhelming that he didn't need anything else to be one of the most impactful players in the game. Many, many perimeter players had "more" skills, but they didn't add up to anywhere close to the same total effectiveness.
So, the exercise is really pretty meaningless in determining who the better player is.
Rudy, despite his court awareness, passing ability and three-point shooting skill, is simply not that effective. He has a fatal flaw to his game, the inability to handle the ball well (by NBA standards). That weakens the effectiveness of all his other tools. Being a stand-still three-point shooter has only limited application. Being a stand-still passer is even worse...great play-makers have to be able to dribble, force the defense to react and then pass to exploit that defensive reaction. Rudy can't do that.
Bayless has less natural passing talent/flair than Rudy, but his superior ability to handle the ball gives him equal or better potential as a play-maker for others. He's already a more dangerous and effective scorer, because he can create his own shot. Rudy can't (the limitation of being stand-still shooter). And while neither is ideal on defense, right now, Bayless has the better lateral quickness and strength, giving him the chance to be an average or plus defender in the future. I don't think Rudy will ever be anything but a liability in man defense, though he does provide some value in team defense with his ability to generate steals.