Odds and probabilities – Super Bowl innumeracy…

This ESPN story demonstrates how not understanding probability and expectation can lead to saying some REALLY dumb things…

The story here, supposedly, is that the Packers, 9-5 favorites with a 32% overall probability estimate of winning the Big Game are “weak enough on defense to make it more likely that another team will prevent them from repeating as champions”. “The story is not how prohibitive of a favorite they are, but the fact that they are being given less than a one-in-three chance…the Patriots and Saints combined have a better chance than the Packers.”

Wow, how many times as the odds been so heavily stacked for single team going in to the playoffs, that the odds for them winning were greater than all the other teams COMBINED. Its not clear what the probabilities were, but there have only been a few times that a team came into the playoffs and “coulnd’t lose” since there has been a 4 round playoff system (1978): The Bears in 85 and the 49ers in 89. The times since then it came close (The Packers in 1997, the Rams in 2001 and the Pats in 2007 – all lost the Super Bowl!)

OK, lets take a look at the numbers here. There are 12 playoff teams, so if all things were equal, each team would have a 1 in 12 chance or a bit over 8% chance of winning.

The odds according to the sourced website are (seed in parentheses)
Packers (1) 32%
Patriots (1) 18%
Saints (3) 15%
Ravens (2) 10%
Steelers (5) 7%
49ers (2) 7%
Giants (4) 4%
Falcons (5) 2%
Lions (6) 1.5%
Texans (3) 1.5%
Bengals (6) 1%
Broncos (4) 1%

So yes the odds are that the Packers will not win the Super Bowl. But based on these probabilities the Packers are nearly 4 times more likely to win than assuming the teams were equal strength. Yes the Patriots and Saints Combined have an equal chance, but that is only because the Packers chances are nealy twice as good as either one individually. Again, if teams are assumed equal, any two teams should be TWICE as likely to win, not “equal” to another team. The Packers chances are nearly equal to to that of other NINE teams combined! To have to roll up the bottom NINE teams to get odds greater than that of the favorite, that is a pretty strong endorsement of that team!

If the last 21 years (since the current playoff systems started) are any indication, top 2 seeds have lost 17 times, and won 15 (though top 2 seeds played each other 9 times). But there has not been a SB in that span that did not include at least 1 top 2 seed.

1 seeds: (9-12) 2009 Saints(W), 2003 Patriots(W), 1999 Rams (W), 1998 Broncos(W), 1996 Packers(W), 1995 Cowboys (W), 1994 49ers(W), 1993 Cowboys(W), 1991 Redskins (W), 2010 Steelers, 2009 Colts, 2007 Patriots, 2006 Bears, 2005 Seahawks, 2004 Eagles, 2002 Raiders, 2001 Rams, 2000 Giants, 1994 Bills, 1991 Bills, 1990 Bills
2 seeds: (6-5) 2008 Steelers(W), 2004 Patriots(W), 2002 Buccaneers(W), 2001 Patriots(W), 1992 Cowboys(W), 1990 Giants(W), 1998 Falcons, 1997 Packers, 1996 Patriots, 1995 Steelers, 1994 Chargers
3 seeds:(1-1) 2006 Colts(W) 2003 Panthers
4 seeds: (2-3) 2000 Ravens(W), 1997 Broncos(W) 2008 Cardinals, 1999 Titans, 1992 Bills
5 seeds: (1-0) 2007 Giants(W)
6 seeds: (2-0) 2010 Packers(W), 2005 Steelers(W),

So yes, the odds are the Packers will not be Super Bowl champs, but their odds are FAR better than any other team. However, this has happened at least 5 times in the past and the “team that couldn’t lose” has lost 3 of 5 times… So I would not be too quick to blame the packer D for only a “1/3 chance of winning”. I will refrain from saying any more about the Packer chances – good or bad, until this years playoffs play out. I’ll take a 1/3 chance hope it comes through!

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About Paul Vebber

"If you read about something, you have learned about it. If you can teach something, you have mastered it. Designing a useful game about something however, requires developing a deep understanding of how it relates to other things."

Posted on January 4, 2012, in Fun with Statistics. Bookmark the permalink. Leave a comment.

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