## Archive for February, 2009

### Statistically Significant

February 4, 2009

Today’s xkcd is a good one:

The mathematical humor is spot on, as usual, but the comic also has some linguistic interest.  Language Log (a longtime fan of the strip) has a great post that starts by discussing the phrase “statistically significant”, and ends up using the words “cepstrum” and “quefrency”.

Quefrency is my new favorite word.

### Dimension Confusion

February 2, 2009

So how about that Super Bowl?   Having analyzed the game here yesterday (OK, not the actual game, but potential scores) it’s time to reflect on the commercials.  The sense seems to be that the commercials were…OK.  Some pretty funny ones, but not one of the absolute best years ever for commercials.

And from a math perspective, one commercial stood out.

Although come to think of it, the 1D version of Chuck might be really entertaining!  The ultimate stick figures.

### Predicting the Super Bowl

February 1, 2009

It is probably bad form to start off with a disclaimer, but here it goes anyways:  I don’t follow the NFL.  I am aware that the Steelers and the Cardinals are in the Super Bowl, and I am aware that the Cardinals are not from St. Louis, where the Rams play now that they’ve left LA, and the Raiders aren’t in LA anymore either.  (Nor are the Chargers.)  But I’d be hard pressed to name any of the current players for the Steelers or Cardinals, so any opinion I might have to offer about the game will be based on other data.

I am going to a Super Bowl party this afternoon, and there is likely to be discussion (or perhaps -ahem- a “party game” with prizes and such) focused on the final score of the contest.

What strategy would one employ in order to be most likely to predict the final outcome?

After perusing the final scores of 12,595 NFL games (from 1922 to the present), I’ve found a few patterns:

• The most frequently occurring scores for an individual team are:
• 17 points  (7.2% of all scores),
• 14 (6.3%),
• 7 (6.1%),
• 24 (6.0%), and
• 10 (5.9%).
• The least frequently occurring total scores [under 20]  are:
• 1 point (which never can happen under NFL rules),
• 4 points (which happened once:  Racine 10, Chicago 4, on November 25, 1923),
• 5 points (18 times in NFL history),
• 2 points (31 times), and
• 8 points (36 times)
• It is possible for a team to score exactly 1 point under NCAA Football rules, but I haven’t had a chance to search through that ocean of data to see if it has ever happened.  [If a team is attempting a PAT, and a safety occurs, the defending team gets 1 point under the NCAA rulebook [see page FR-108.]
• The most frequently occurring final scores are:
• 20 – 17 (211 times),
• 17-14 (162 times),
• 27-24 (153 times),
• 13-10 (141 times), and
• 24-17 (125 times).
• Modulo 10, the most frequently occurring team scores are:
• 0 (19.3%),
• 7 (19.1%),
• 4 (15.1%), and
• 3 (12.3%);
• The least frequently occurring team score modulo ten is 2 (3.1%).
• Modulo 10, the most frequently occurring pairs of scores are:
• {0,7} (8.1% of all games), followed by
• {4,7} (6.8%),
• {0,3} (5.8%),
• {0,4} (5.2%), and
• {3,7} (4.5%).
• The least likely combinations modulo 10 are:
• {2,2} (0.024% = 3 times in NFL history), followed by
• {9,9} (0.10%),
• {5, 5} (0.14%),
• {5, 9} (0.25%), and
• {2, 8} (0.26%)

My own Super Bowl prediction?  Cool ads and lots of fun chatting with friends.