I comment on this all the time, but I thought I would sum it up again. I believe you need not just a top offense, but one of the best offenses to win it all. You also need a top defense to go with it, not just a good one. Looking at the final kenpom efficiency numbers of the past 10 champions.
2003 Syracuse AdjO (11) AdjD (19)
2004 UConn AdjO (4) AdjD (5)
2005 UNC AdjO (1) AdjD (5)
2006 Florida AdjO (2) AdjD (5)
2007 Florida AdjO (1) AdjD (12)
2008 Kansas AdjO (2) AdjD (1)
2009 UNC AdjO (1) AdjD (16)
2010 Duke AdjO (1) AdjD (4)
2011 UConn AdjO (16) AdjD (14)
2012 UK AdjO (2) AdjD (9)
Average AdjO (4.1) AdjD (8.4)
> 7 of the past 10 champions have an adjusted offense of #1 or #2 in the nation. 1 champion (2008 Kansas) has a top 2 defense (1st) and they happened to also be 2nd in offense as well
>2 of the 10 champions ranked outside the top 10 in offense. 2003 Syracuse (Carmelo Anthony) and 2011 UConn (Kemba Walker). One could describe them similarly with superlative individual stars surrounded by decent college supporting players.
>Neither list has a single team that did not finish in the top 20 in both categories. UCLA in that time span has done this just once in 2008 finishing 7th in offense and 3rd in defense. We got dropped that season by Memphis who as 4th in both categories. Definitely our best team and the hardest game to watch because we should not have been that overmatched.
>UCLA has only ranked under 20 in a single category in 3 other seasons. 2006 with the 28th AdjO and the 3rd AdjD and in 2007 with the 23rd AdjO and 2nd AdjD.. both times getting waxed by a better Florida team that was ranked higher in adjusted offense and lower in adjusted defense. In 2009 UCLA had the 3rd AdjO and the 44th AdjD resulting in another ugly loss to Villanova (22nd off, 15th def)
Statistically the point here is you need to be really good in both. And by really good I mean at minimum a top 20 in both categories to be a have a chance. I would argue top 10 or even 5 in both to be a serious contender with an emphasis on offense that has 4.2 avg being a little more important than the 8.4 avg of the past 10 champions on defense.