Fun with statistics

I have seen a lot of talk in the last couple days about Big Ten championships and National Title contention, and I have to agree that I'm as excited as anyone about what's happened so far this year.  After Saturday's win I'll admit I had one hand on the crazy straw and one hand on the refrigerator door, eyeing up the Kool-Aid...but before I go completely insane, here is some sobering statistical analysis...

DISCLAIMER:  I expect this post to be boring to many (most) and I realize I'm a nerd.  Try to stay awake.  This could be informational.

To be favored in a game, your chances of winning are predicted to be over 50%, nothing ground-breaking there.  And Penn State has 7 to go in this regular season.  We could well be favored in every game from here on out, but how far over 50% are our chances in each remaining game?  For starters, let's blindly say we have a 70% chance of victory in each individual game left this year:

Our chances to run the table are then 0.7^7 (0.7*0.7*0.7*0.7*0.7*0.7*0.7, one for each remaining game), or 0.082.  Using this logic, we have an 8.2% chance of running the table and (obviously) a 91.8% chance of going down to somebody.  Assuming a national title game appearance is a lock if we go undefeated (it isn't, but it's probably close) and that game would be a toss-up, our chances of bringing home the crystal football are 4.1%.

This simplifies things quite a bit, of course, because we have a greater chance of losing on the road to a Wisconsin or Ohio State than at home to Indiana.  If anyone wants to get really techinical, you could predict what you think the line will be for each of our remaining games, then do some research to see what the success rate has been in the recent past based on that spread.  But, using an easy formula like this you can see that our chances are not great for a national title game appearance.

I don't mean to be a total doom-and-gloom guy, just trying to offer some perspective, and here's some more:  USC and Texas were considered head-and-shoulders above their competition in 2005 but even still, running the table as preseason #1 and #2 was a once-in-a-lifetime event, no matter how much more talented they were than their competition along the way.  Consider this:  even if you said USC would beat each of their opponents 9 out of 10 times in 2005 (a reasonable assumption?), that leaves them with a 0.9^12 = 28.2% chance of running the table.  Saying the same for Texas that year, we need this 90% chance to hold for 24 games, or 0.9^24 = 8%.  And that assumes USC and Texas were expected to dominate each and every team on their schedules that year.  The moral of the story?  THIS NATIONAL CHAMPIONSHIP GAME STUFF IS HARD!!!!  It's hard to get there! It's even harder to win!!!  And, get this:  (as much as I HATE tOSU) It's WAY harder to get to two title games in a row and lose both than it is to get to one and win!!!

IMPORTANT PARAGRAPH:  At this point, Penn State has the best shot of winning the Big Ten, statistically speaking.  PSU will be favored this week against Purdue, and if victorious, again next week at Wisconsin.  If I had to put money on anyone to win the conference right now, my money would be on Penn State...but I'm smart enough not to put money on it.  The moral of the story?  It's awesome to dream, and I'm as much a dreamer as anyone, but realistically we have a LONG way to go.  Buckle up.  It's going to get bumpy.  There are twists and turns.  Oh and, no Kool-Aid on the bus.