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Comparing National Championship and Final Four Odds

Rob made a very good point in the comments of yesterday's "Final Four Odds" post:
"I agree that Sportsbook did not really make any assumptions regarding seed. In fact, I think these odds are simple extensions of their odds to win the title...Simply, it looks like they are dividing the odds of winning the title by a factor between 4.5 and 5."This is very true. It is also an awful way to go about creating these Final Four odds. Let's take a look at the Final Four and National Championship odds of the 14 longshots that have F4 odds listed.

The first three columns should be self explanatory (all odds taken from Sportsbook). The final column is their implied odds of winning the title should they reach the Final Four. For example, Indiana is 8:1 (11.1%) to reach San Antonio, and 40:1 (2.4%) to win the title, so their final column is .024/.111, or 22.0%.

For these two sets of odds to be equal, each of these teams would have to have between a 22% and 23.5% chance of winning two F4 games. None of them are even close to that number. Take Purdue, for instance. Let's give them a 30% chance of winning either game in the F4 (this is being generous). That puts them at 9% to win both. If they are 22:1 to reach San Antonio, they should be at least 250:1 to win it all. They are 100:1. You...

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