Through Math for America, I am part of an on-going collaboration with the New York Times Learning Network. My latest contribution, a Test Yourself quiz-question, can be found here:
http://learning.blogs.nytimes.com/2011/05/4/test-yourself-math-may-4-2011/
This question is based on a recent article about the dwindling consumer support for “Green” products. Just how much does it cost us to “Go Green”?
This website aims to evaluate the accuracy of various weather-prediction services while providing its own forecast:
Using composite indices and statistical methods, data from sites like Accuweather and Weather.com is analyzed and rated.
This is a good resource for an interesting group or individual project in statistics: how accurate are the various services? What is a “good” prediction? How valuable is this information? How can we use statistics to evaluate these questions?
Several years ago I read this post from the Freakonomics blog: it details an informal study conducted by a man and his daughter who looked at seven months of TV weather forecasts in Kansas City and evaluated their accuracy. The entire article is interesting, but the bottom line is best summed up in a quote from someone from one of the TV stations: ““We have no idea what’s going to happen [in the weather] beyond three days out.”
I’ve had some fun playing around with old CDs and CD cases recently.
In addition to demonstrating Cavalieri’s principle both with discs and their cases, I’ve found some other mathematical uses for these objects.
Here I’ve used a stack of cases to demonstrate the difference between some geometric solids.
On the left, we have a right rectangular prism. Give that prism a slight push in a direction perpendicular to a side and you get an oblique rectangular prism.
And if you give that original prism a push along a diagonal of the base, you’ll get one of my favorite geometric objects, a parallelepiped. It may not be the perfect parallelepiped, but I’ll take it!
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After posting some thoughts on the mathematics of NFL Draft Pick Valuation, let’s take a look at what actually happened during the 2011 NFL Draft and see just how much credence NFL teams put into to the Trade Value Chart.
A quick re-cap: the Trade Value Chart estimates what should expect in return for trading their pick. The valuation of picks resembles exponential decay, and the draft format may also play a role in determining a pick’s value.
There were thirteen trades of draft picks during the first two days of the draft (Rounds 1 through 3), so I collected all of the data and tallied up the nominal values of the picks based on the chart. Here are two examples of a trades: the Picks row contains the picks that the team traded away; the Total Value row contains the sum of the values of the picks based on the Trade Value Chart.
In both cases, the larger total value is a little bit more than 10% of the smaller value. Here is a summary of all the trades in Rounds 1 through 3.
A couple of notes: first, when future picks were involved in a trade, I assumed that the future pick would be the same pick number as this year’s pick, and I valued it as such. That is, I assumed that the 2012 first round pick Atlanta sent to Cleveland would be number 27 overall, and therefore its value would be 680 points. For percent difference, I measured the difference relative to the smaller total value.
The relative values seem close enough to suggest that the teams are using the Trade Value Chart as a guide, a conclusion also reached by @EmergentMath in his interesting analysis of past Draft day deals.
The notable exceptions in this year’s draft both involve New England, a team that is highly regarded for its skillful draft management. They have a exceptional record for team-building, so maybe some serious mathematical analysis of draft strategy has paid dividends!
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The sun’s projection of one set of axes looks like a translation of another set.
