# Daily Archives: March 30, 2011

## How likely is VCU’s run to the Final Four? A VCU professor and sports nerd reflects on the likelihood of her school’s path to the Final Four

I am thrilled that VCU made the Final Four this year.  My school’s team had an unlikely path to the Final Four, so unlikely that only 2 of 5.9 million ESPN brackets correctly picked all Final Four teams.  Sports nerds unanimously agree that VCU’s run has indeed been unlikely.

• Nate Silver at the NY Times tweeted that “VCU reaching Final 4 may be least likely event in the history of the NCAAs. Penn in ’79 is close. So is Villanova winning it all in ’85.”  He wrote an excellent article that summarizes that the numbers show that VCU was indeed less likely to make the Final Four than the other 11 seeds in the tournament.
• Before the tournament began, Wayne Winston gave VCU a 1-in-1000 chance of reaching the Final Four (using the Sagarin ratings) and a 1-in-5000 chance of winning the entire tournament.
• Andy Glockner at Sports Illustrated summarizes a few stats about how likely VCU’s run has been.  According to Ken Pomeroy, VCU had a 1-in-3333 chance of making it to the Final Four and a 1-in-203,187 shot to win the title, one of the worst odds of the teams in the field.
• Slate’s Hang Up and Listen sports podcast discusses the Final Four odds and statistics.  This enjoyable podcast sheds light on quite a few quantitative factors that relate to the tournament and provide several good links for further reading.
• This Final Four has the highest seed total ever, and it is the first time since 1979 that no 1 or 2 seeds are in the Final Four.

VCU making the Final Four is not “proof” that we should throw out the expert advice from sports nerds since anything can happen.  While anything can indeed happen, each outcome is not equally likely.  Most outcomes are so unlikely to occur that we will not see them in our lifetimes (the probability that all four 16 seeds comprise the Final Four would occur once every eight hundred trillion years on average).  It’s like monkeys randomly typing away. Given enough time, they will rewrite Shakespeare, but don’t expect to see it happen any time soon. However, even though most of the potential tournament outcomes have an infinitesimally small chance of occurring, when you add them all up, there is almost a certain chance that a few unlikely things will occur (which is why we always see a few upsets in the first two rounds).

On the contrary, the excellent analyses from sports nerds will produce the best predictions that work on average.  That is, averaged over a large number of tournaments, their predictions will yield the best results (meaning that brackets produced using advice from the experts who have crunched the numbers will win the office pool most frequently).  That is because the numbers point to the outcomes that are most likely to occur.  There are an enormous number of potential outcomes in the tournament (2^67 ~= 1.5 x 10^20, which is way, way more stars than there are in the Milky Way!), and it helps to have some quantitative advice to prune most of the unlikely outcomes, nearly all of which are even less likely to happen than VCU making the Final Four!  Even the most likely outcomes rarely occur:  we would expect all four one seeds to comprise the Final Four, for example, to occur every 39 years (it has happened once).  The problem is, things don’t average out in a single year–we have just one tournament this year.  In any single year, something unlikely–like VCU reaching the Final Four–has a chance of occurring (albeit a small one).

Now that VCU is in the Final Four, what are their odds of winning the tournament? VCU may have initially had an infinitesimal 1-in-203,187 chance of winning the tournament, but given that they have made it to the Final Four, their odds of winning it all is not unlikely (they’ve completed the hard part of being one of four teams left).  Wayne Winston estimates that they have a 0.11 chance (a 1-in-10 chance) of winning the tournament.  Using past tournament outcomes, Sheldon Jacobson has shown that seeds don’t matter after the Sweet Sixteen round, which means that VCU essentially has a 1-in-4 chance of winning the tournament.  The truth is likely somewhere in between, which means that VCU has an excellent chance of being the national champion. Let’s go Rams!