Category Archives: Fun with Statistics

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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Open Source MatLab Clone, Graph Theory and Anaysis Tools

SciLabdeveloped by a scientific consortium based in France, is an open source MatLab clone that can ingest MatLab code. Worth a look if you are MatLab savvy and want a open source alternative. Also has a simulation module.

Gephi is a similarly supported open source graph analysis software for complex systems and dynamic networks.

Tableau an interesting interactive data display tool.

This one is a pay product, but looks interesting

Flying logic (Hat tip to Chris Weuve) planning and course of action analysis tool.

Check them out!

Net oil product exporter, but are we past “peak oil”??

This WSJ article reports that the U.S. is poised to be a net oil product exporter in 2011. This seemed to be a rather interesting claim so I went to the source document: from the Energy Information Administration.  I searched for the 753.4 million barrels exported and found it in table 52 as the totel year to date exports of ‘total products’. Next the 689.4 million barrels imported is found on table 40 similarly under ‘total products’. Possibly good news, but the problem is we still were a net importer of 3.13 BILLION barrels, when you include crude oil.

WONDERFUL! We are exporting more oil productsthan we imported so far this year by some 76 million barrels. But where does this put us comparatively speaking? Lets go back 5 years and look at 2006. The 2006 report for the same period had us at 994 MB of products imported and 3.77 Billion barrels total. Our total exports were only 354M Barrels.

So our total imports are down about 17%, our product imports are down 31% and our product exports are up 113%

The big question will be can we keep ourselves weening off oil, as we are arguably past “peak oil” production (there is some question whether when sand and shale oil finishes ramping up we will hit a new peak…). Bulk biofuel is still about 4 times oil see this danger Room post

So the other question is where are these product exports going? Here are the big jumps (over 100%). (First number is 2006, second is 2011 in M bls) turns out that Canada and Mexico mostly, but huge increases in Central and South America as well. So is this a NAFTA win? Seems so.

Argentina       2.4, 10.7

Brazil             11.8, 40.7

Canada         36.9, 64.0

China              3.5, 13.1

Columbia      1.6, 15.2

Dominican Rep 3.9, 11.4

Honduras    4.3, 12.4

France          3.7, 14.5

Mexico         67.9, 150.6

Morocco       2.3, 8.1

Netherlands 22.4, 64.7

Panama         11.7, 27.3

Peru                 2.1, 8.2

Singapore    12.2, 34.8

Turkey            3.8, 14.0