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The Unlikeliest Final Four

Posted by Neil Paine on March 28, 2011

Just how unlikely is this year’s Final Four of Kentucky, UConn, Virginia Commonwealth, and Butler?

Well, going by one measure, the odds of it happening were 0.00003% — only two entries (out 5.9 million) correctly picked the four teams in’s Bracket Challenge. But I decided to see how this year’s improbable group matched up against other inexplicable Final Fours since the tournament expanded to 64 teams in 1985. Here were the Final Fours with the highest average seed # since then:

Year Team A Seed Team B Seed Team C Seed Team D Seed Avg #1s
2011 KEN 4 CONN 3 VCU 11 BUTL 8 6.50 0
2000 UNC 8 FLA 5 WISC 8 MICS 1 5.50 1
2006 GEOM 11 FLA 3 LSU 4 UCLA 2 5.00 0
1986 KAN 1 DUKE 1 LSU 11 LOU 2 3.75 2
1992 IND 2 DUKE 1 MICH 6 CIN 4 3.25 1
2010 MICS 5 BUTL 5 WVIR 2 DUKE 1 3.25 1
1985 STJO 1 GTWN 1 VILL 8 MEM 2 3.00 2
1990 ARKA 4 DUKE 3 GEOT 4 UNLV 1 3.00 1
1996 MIST 5 SYRA 4 UMAS 1 KEN 1 2.75 2
2005 LOU 4 ILL 1 MICS 5 UNC 1 2.75 2

Aside from 2011, two other years stand out at the top of the list: 2000, when two 8-seeds crashed the Final Four, and 2006, when no #1 seeds made it (but George Mason did). In terms of pre-tournament likelihood, how do those years stack up to 2011?

To answer that question, I simulated each tournament from scratch ten thousand times using the seed-based win probability formula I introduced here. In my 10,000 simulations, here’s how often each team made the Final Four:

Year Team Count Probability
2011 KEN 1194 11.9%
2011 CONN 1631 16.3%
2011 VCU 24 0.2%
2011 BUTL 174 1.7%
2006 LSU 1140 11.4%
2006 UCLA 2261 22.6%
2006 FLA 1649 16.5%
2006 GEOM 50 0.5%
2000 FLA 749 7.5%
2000 UNC 192 1.9%
2000 MICS 3028 30.3%
2000 WISC 211 2.1%

Multiplying the probabilities together, we find that the 2006 Final Four had a 0.00213% chance of happening based on seeds, the 2000 Final Four had a 0.00092% chance of happening, and the 2011 Final Four had a staggering 0.00008% chance (about 1 in 1,229,650) of happening. Since the field expanded to 64 teams, I think it’s safe to say that this year’s Final Four is easily the most improbable.

8 Responses to “The Unlikeliest Final Four”

  1. Dave Says:

    How does it compare if you take out the play in game that VCU had to play?

  2. Neil Paine Says:

    If you take away the play-in, VCU’s expected path would be the same as George Mason faced in 2006 (about 0.5%), so the likelihood of the 2011 Final Four would become 0.00017%. That still would make it the most improbable Final Four of the 64-team era, though.

  3. AHL Says:

    What’s sad is that we all saw this coming. Everyone was all “none of the 1 seeds strike me as strong favorites” and yet in that uncertainty many more people went chalk, including national media talking heads (Obama lol). Yet even the more advanced “pick Texas to hedge your bets” analysis didn’t work out so hot. Is there an expected time when someone finally picks the Perfect Bracket?

  4. BSK Says:

    Does this include VCU’s “play in” game?

    I’m also reminded of a thought experiment I read about (the name eludes me, but I’m sure someone here knows it). The premise was that if a lottery exists such that any individual ticket had such infinitesimal odds of winning as to consider them zero, could it still be assumed that SOMEONE was guaranteed to win the lottery? Basically, if no one had a practical shot to win, then is it possible that no one wins? To apply it here, if we assumed that no Final Four was likely, could we conclude that maybe the Final Four just won’t happen??? I SURE HOPE NOT!

  5. deron Says:

    This has been one the strangest tournaments I’ve ever seen. VCU’s win sets up a historic game with Butler, two unranked teams in Final Four game. This occurrence says a lot about college basketball today, anyone can win it all.

  6. David Zukerman Says:

    Anyway to determine if the eight TV timeouts a game have an impact? Seems to me, the flow of the game goes for no more than a bit more than five minutes before there is a pause of four minutes. Then another four minutes or so, and pause of four minutes,
    another four minutes of play or so. Paise again four minutes. Then less than four minutes to the half (or end of regulation play).

    These pauses — this interference with the normal momentum of play, this removal of the flow of game from control of coaches and players — all this has no impact on results?

    Where does the money go? For coaches pay and recruiting costs?

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