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Butler’s Back-to-Back Championship Appearances a 7,500-to-1 Longshot

Last week, we established that Virginia Commonwealth had only about 1-in-820 odds of winning five consecutive games and reaching the Final Four. Although V.C.U.’s run ended with a loss to Butler in Houston on Saturday, the feat ranks right among anything else accomplished over the course of a single N.C.A.A. tournament; it was about as unlikely as Villanova winning the national title, as a No. 8 seed, in 1985.

But what about over the course of two tournaments? What are the odds that Butler would have reached the championship game two years in a row?

A friend of mine insists that Butler’s is the far more impressive accomplishment; taking even cursory glance at the numbers makes it clear that he’s right. We had Butler with a 0.9 percent chance of reaching the championship before this year’s tournament began. Meanwhile, Ken Pomeroy’s numbers had them with a 1.5 percent chance a year ago.

Multiply 0.9 percent by 1.5 percent and you get 0.0135 percent, which equates to odds of 7,406-to-1 against.

You’ll note that I’m not quite comparing apples to apples, using my model’s estimate on Butler’s chances for this year but Mr. Pomeroy’s for 2010. (The alternative would be to retrofit our model with last year’s data, which would require several hours that I don’t have handy right now). But, although our model tends to be slightly more forgiving than Mr. Pomeroy’s to extremely low seeds like V.C.U., it produces highly similar results for teams that are No. 5 seeds or thereabouts, which is what Butler was last year — so I doubt the figure would have been much different. And even if our model had been several times more favorable to Butler, it almost certainly would not have been enough to overcome the difference between Butler’s 7,406-to-1 parlay and V.C.U.’s 820-to-1 odds against.

You could also probably come to this result intuitively since Butler has had to win 10 games to reach back-to-back finals, as compared to the five wins V.C.U. needed to make it to Houston this year. Although V.C.U. looked markedly worse than either this year’s or last year’s Butler team heading into the tournament, the difference is not enough to outweigh having to win twice as many games.

The only way in which I’ll be a bit of a wet blanket is in noting that, by expanding the criteria from any accomplishment over the course of a single tournament to one over multiple tournaments, you vastly increase the search space, so it’s hard to say whether this is the most impressive accomplishment of its kind. Still, Butler’s accomplishment checked out pretty well against a couple of other possibilities that I tested.

For instance, based on the historical success rates of teams with their seedings, the University of Houston was something like a 250-to-1 long shot to play in three consecutive Final Fours from 1982 through 1984, while Florida had about 225-to-1 odds against winning consecutive championships in 2006 and 2007. And Duke was “only” about a 1,600-to-1 long shot to play in five consecutive Final Fours between 1988 and 1992.

Nate Silver is the founder and editor in chief of FiveThirtyEight.