The question at hand - How often does a team win 24 games and NOT make the NCAA Tournament? Or, maybe a bit more on the nose, how likely is a team to make the NCAAs based on their wins, regardless of their schedule strength?
To get at the answer, I looked at all of the 18+ win teams from the past three seasons - 2006, 2007 and 2008 - and whether they 1) made the NCAA Tournament and 2) if they did, whether it was via an at-large bid or because they won their conference tournament. The total sample size included 390 teams with 18+ wins. Team numbers by win total - 19+, 344; 20+, 300; 21+, 254; 22+, 210; 23+, 167; 24+, 130; 25+, 99; 26+, 71; 27+, 54. The number of available NCAA spots for the sample is 192.
Okay, enough of the methodology - On to the percentages:
27 wins or more - 100 percent (54/54)
26 wins - 64.71 percent (11/17)
25 wins - 75 percent (21/28)
24 wins - 61.29 percent (19/31)
23 wins - 62.16 percent (23/37)
22 wins - 53.49 percent (20/43)
21 wins - 38.64 percent (17/44)
20 wins - 23.91 percent (11/46)
19 wins - 13.64 percent (6/44)
18 wins - 13.04 percent (6/46)
Looking at the raw numbers, the cut-off point seems to be 22 wins. If you have more than 22 wins, then you have at least even odds of making the tournament. If you manage 25 wins, then you're practically a lock for dancing.
However, there are two issues complicating the percentages. One, the records are from the END of the season. For example, Air Force finished 26-9 in 2007, but this is mostly because they went 3-1 in a postseason tournament. Prior to that, they lost their last four games. Similarly, in 2008 Massachusetts finished at 25-11, but this was only because of four NIT wins. Neither team made the NCAAs, but their inflated win totals bring down the percentages. Let's re-run the calculations with their records BEFORE factoring in non-NCAA postseason tournament wins.
The other complicating factor for the percentages are some of the automatic bid winners from really weak conferences. Maryland Baltimore County and California State Fullerton both earned automatic bids with 24-9 records, but neither would have made it as an at-large team. Again, with the goal of a more accurate prediction, I'm removing them.
With those two changes, the new percentages:
27 wins or more - 100 percent (54/54)
26 wins - 71.43 percent (10/14)
25 wins - 86.96 percent (20/23)
24 wins - 65.22 percent (15/23)
23 wins - 55.88 percent (19/34)
22 wins - 47.62 percent (20/42)
21 wins - 23.81 percent (10/42)
20 wins - 15.91 percent (7/44)
19 wins - 11.36 percent (5/44)
18 wins - 11.11 percent (5/45)
Ah, that makes the picture a bit more clear. The percentage for 26 wins looks a bit off, but all four qualifiers that didn't make it - Robert Morris, IUPUI, Akron and Stephen F. Austin - played in incredibly weak conferences and lost in their conference tournaments. The same thing applies to the three stragglers at 25 wins - Marist, Appalachian State and Vermont. If you play in a mid-major or above conference, and win 25 games, the at-large bid rate is 100 percent the past three years.
At the 24 win plateau, you start to run into more mid-major teams - Hofstra, New Mexico, Virginia Commonwealth, Utah State and Old Dominion (2006) failed to qualify. However, being in a mid-major doesn't disqualify you from earning a bid at this win level. South Alabama, UAB, Pacific and Old Dominion (2007) qualified. And power conferences teams aren't immune from being left out, as 24-win Syracuse found out in 2007.
As the numbers suggest, it gets to be more of a crapshoot once you only win 23 games. Teams ranging from Big 12 Kansas State to A-10 Massachusetts to CAA Drexel get left out at this level. The first ACC team - Florida State - appears at 22 wins.
However, if you are a mid-major and want an at-large bid, you better win at least 22 games. Creighton and Southern Illinois managed to get in with 22 wins, but once you hit 21 wins in a mid-major conference, no teams except automatic bid earners are in. The Atlantic 10 isn't quite at this level yet - Xavier and St. Joseph's both got in with 21 wins, but that's the low end of the spectrum.
Once you hit 18 to 20 wins, the teams making the tournament are solely those in power conferences - Big 12, Pac 10, Big East and ACC figure in prominently - and automatic bids. The 18-game at-large teams read like a who's who of college basketball: Oregon, Alabama, Stanford, Kentucky and Seton Hall.
For those cheating and skipping to the end, the summary - 25 wins guarantees you a spot in the NCAA tournament, and 24 wins gives you at least a 65 percent chance, and higher once you subtract automatic bids from weak conferences. Anything lower than 24, and the conference you play in becomes substantially more important.