I am kind of bothered by a single-elimination tournament purporting to crown a national champion; most years it would be very reasonable to expect that you could play the tournament ten times before crowning the same champion twice. A team has a bad day or runs into a team that just "matches up well" with them, and that team is eliminated. What I'm about to propose mitigates that, and, while it ends with a single-elimination tournament, that single-elimination tournament will have most of the best teams in the country.

We take 48 teams (even if we keep the automatic bids, this leaves 18 at-large, which is sufficient) and divide them into three sections of teams seeded 1-16; we'll call them Red, White, and Blue.
1-16 4-13 5-12 8-9 2-15 3-14 6-11 7-10
1-8 4-5 9-16 12-13 2-7 3-6 10-15 11-14
1-4 2-3 7-11 8-12 5-9 6-10 (13-16) (14-15)
1-2 3-8 4-7 (11-12) 5-6 (9-14) (10-13) (15-16)
This table is read in the same way as the "gauntlet" tables elsewhere; teams switch seeds if there is an upset, so that if you beat number 1 you become the top seed for the purposes of pairing the next round. This table is really just the standard tournament setup, except, of course, that I don't throw teams out of the tournament after they lose a game. This is carefully constructed so that, as with all of the tables I construct, the teams that win more games end with better seeds, no two teams ever play each other twice, etc.

Incidentally, a note on practicality: currently, in the NCAA, each region has two sites for the first two rounds, and the matchups in the first two rounds here don't preclude the tournament being broken up that way with the additional games. The last two rounds, however, now have eight games each, and would also want two sites; this can be done, taking seeds 1, 2, 3, 4, 7, 8, 11, and 12 at one site and the other eight at the other site. No matchup occurs that pairs any of these eight with any of the other eight in the latter two rounds. This is indicated in the table; first four games in a line are at one site, the other four at another.

R1 ----- ----- ----- -----
N1
W3 -----
B3
B2 ----- -----
R5
W2 -----
R4
W1 ----- ----- -----
B5
R3 -----
B4
B1 ----- -----
W5
R2 -----
W4
I've exceeded my HTML capabilities here, but hopefully you get the idea. R1 is the team from the red section that ends with the one seed; W3 is the team from the white section that ends with the three seed. N1 is the NIT champion, or something similar (perhaps an asymmetrical fourth bracket). Note that with this addition we now have 16 teams.

If no team loses to a team that appears below it in the chart, then no team would lose to a team that entered with a lower seed (eg R2, a 2 seed, beats W4, a four seed, which is lower than a two seed); in addition, no two teams from the same division would play. This latter characteristic is, in fact, robust to a single upset; if there are two upsets, bets are off. (The exception to this final point is that, for example, if B3 beats R1 and B2 beats W2 the two blue teams play each other; the robustness requires that one consider B3 beating W3 an upset, as it is listed on the chart.)

Note that, with 18 at large bids at the beginning, the NIT champ may well be the twenty-fifth best team or so; in any case, a team that has just won five games against respectable competition. Most of this field of sixteen should be pretty competent.

(Projected for the 1999 tournament.)