Football Calculator

football calculatorIn an ESPN blog-post, Bill Belichick’s decision to go for it on 4th down against the San Diego Chargers was analyzed, and the ultimate conclusion was that, by a few percentage points, this was wrong decision.  Last season, Belichick was second-guessed after a similar decision led to a Patriot loss to the Colts.  Interestingly, a similar analysis deemed that particular decision to be correct.

The idea of applying serious risk-reward analyses to football seems to increasing in popularity, even though a rigorous study by a world-class economist was conducted nearly 10 years ago .

The author at ESPN utilized a Win Calculator at the Advanced NFL Stats website.  It’s a pretty cool idea–input the current score, time remaining, quarter, field position, down and distance, and the calculator returns Win Probability, Expected Score, and some other projected data.

Of course, the devil’s in the details–that is, the algorithms–but it’s cool to see the quantitative analysis of sports continue to spread.

Paul the Octopus, 2008-2010

octopus2_1675213cPaul the Octopus, whose prognosticating skills captured the imaginations of World Cup viewers everywhere, died this week at the age of 2.5.  He died of natural causes.

Paul defied probability by correctly predicting the results of all of Germany’s seven World Cup matches.  After making it through the tournament with a perfect record–during which he received death threats and had a stamp printed in his honor–Paul retired from predicting.   Rediscovering his British roots, Paul was appointed an official ambassador for England’s 2018 World Cup bid, a post he held until his untimely demise.

Apparently there have been many copy-cats, so to speak, including “a saltwater crocodile named Dirty Harry, who predicted Spain’s World Cup final win and called the result of Australia’s general election by snatching a chicken carcass dangling beneath a caricature of Prime Minister Julia Gillard”.  But Paul will always have a special place in our hearts.

Wireframe Torus

wireframe torusThis is a cool example of wire-sculpture:  a single piece of wire woven into the shape of the torus.

http://makezine.com/2010/10/24/math-monday-wire-torus-challenge/

(I doubt you can play pool on this one, though.)

The author of the blog post, George Hart, is the proprietor of the soon-to-be Math Museum, and it seems he is something of a sculptor himself.  According to the article, this piece was on display at a conference held by the European Society for Mathematics and the Arts.

Poking around their website and admiring the the multitudinous mathart is a pleasant way to pass a little time.

Coffee and Cream

I was recently reminded of an excellent math problem involving mixtures.

Imagine yourself sitting in front of a cup of coffee and a cup of cream.

coffee and cream solution 1Suppose you take a spoonful of cream, pour it into the coffee, and stir it up. Now once that’s thoroughly mixed, you take a spoonful of the mixture and pour it back into the cream. Then you mix that up.  After all of this, is there more coffee in the cream, more cream in the coffee, or equal amounts in both?

I encourage you to think about the problem before perusing the several solutions below!

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Paddling Upstream

canoeThe Canoe in the River problem is an algebra classic.  You know how it goes:  “Paddling upstream, it takes Betty Boater 6 hours to travel up the river to Point Apex.  It takes only 3 hours for the return trip downstream to Point Bellows.  If the distance between Point A. and Point B. is 15 miles, what would Betty Boater’s speed be in still water?” 

Below is wonderful retelling of the Canoe in the River problem created by Dan Meyer.  Using a video camera, an ipod, a quiet morning in a mall, and some great editing, this problem is brought new life in this modern and engaging context.

dmeyer -- boat in river

Check it out at http://blog.mrmeyer.com/?p=7649.  Meyer seems to be focused on modernizing mathematics curricula, and the more stuff he does like this, the better.

And for Betty Boater’s speed, click here.

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