Based on what each did for KU:
1 Allen--put KU on the map.
2 Brown--put KU back on the map
3 Self--kept it on the map and won a ring.
4 Williams--kept it on the map, didn't win ring.
Best head to head with equal talent?
Larry Brown would win the most games against all of these other great KU coaches. There are only three guys Larry could not consistently beat with equal talent in all of basketball history: Red Auerbach, John Wooden and Phil Jackson.
The least talented of these four?
That's easy. ROY WILLIAMS. Roy has never built anything in his life. He has been a coat tail rider his entire career. Roy has proven he can't win any rings at all without superior talent delivered by petroshoeco regimes and an EST whistle. There's just no doubt. If Roy had not started at KU with the apparent petroshoe connection from UNC and the nucleus of players like Randall that Brown left him, he probably would have been a .600 coach at best at KU. Roy has wasted more great talent at KU and UNC than the other three great KU coaches have ever had COMBINED. Roy is a good coach, not a great one, that has won multiple rings once he got a huge edge and even then he has choked frequently. Roy only wins when he holds the most aces.
The above sounds too harsh about Roy. Roy is a fine coach with a gift for getting players to play incredibly hard. In comparison to other UNC coaches, it's pretty clear Roy is their best coach now. But this list of KU coaches is a murderers row! And Roy just wasn't as good in his time at KU. In Roy's defense, when he does hold all the aces, he tends to "get her done." Lots of coaches that have held them haven't. LB blew it with his best KU team. So: to take Roy down a notch here is not so harsh as it may sounds. But bottom line? Every guy on this list ahead of him has built a program and "got her done" with LESS aces than an opponent had, but not Roy.
By comparison, Brown won his ring with when he equal or less talent, and Self won his ring beating a more talented UNC team and a Memphis team full of ringers.
Of all the coaches, the jury is still out on Self. He could still surpass Brown and Allen, but the clock is his opponent now. It appears he will never be allowed to sign OAD 1s and 5s.
...unless Self and KU give up the gravy train shoe contracts and regain apparent full access to the lion's share of available talent at 1 and 5.
Go, Bill, go!