Baseball Bailouts

Baseball MoneyThere’s an interesting article in the NYT about the economics of baseball’s revenue-sharing system.

The revenue-sharing system is essentially a robin-hood style redistribution of baseball income, taking money from the most profitable teams and dividing it up among the least profitable.   The system, in theory, gives smaller-market teams a chance to compete with their big-market brethren by providing them with addtional cash to invest on players.  But are the recipients of these baseball bailouts really using the money to improve their teams?  Thanks to an anonymous leak last summer, the public was given an unprecedented look at some MLB financial information.

It was quite interesting to see that the Pittsburgh Pirates, who not only have posted a league-record 18 consecutive losing seasons but also rank near the bottom of the MLB in both popularity and team payroll, have actually been quite profitable the past few years.  For example, in 2007 and 2008 the Pirates, who routinely traded away their best players, not only made around $30 million in profit but also collected around $70 million in revenue sharing payouts!

Maybe the owners of the Pirates have figured out that spending their yearly $35 million bonus on players doesn’t increase revenue enough to make it worthwhile.  Why not just take the safe money?  Not a bad year for a business that hasn’t seen success in two decades.

By patrick honner, ago

Testing the Testers

mc testThe SAT has long been a thorn in the side of students, parents, and teachers everywhere.  At some point it became the standard for establishing academic potential, and we’ve been forced to deal with it ever since.

It’s almost too easy to loathe the SAT and its administrative body, the College Board:  they rake in billions in revenue for providing an assessment that is of debatable value; they have helped create a mindset and industry around the idea of “test prep”;  and the College Board has positioned itself as a significant voice in education policy.  Worst of all is that, at their heart, they are a secretive entity accountable to no one.

Which makes stories like this all the sweeter.

http://abcnews.go.com/GMA/ConsumerNews/teen-student-finds-longer-sat-essay-equals-score/story?id=12061494

A smart high school student, Milo Beckman, had a hypothesis about the essay component of the SAT:  he thought that longer essays earned higher scores, independent of quality.  So he took a poll of his classmates, correlated the length of their essays with their eventual scores, and ran a regression analysis on the data.  The results?

Milo says out of 115 samples, longer essays almost always garnered higher scores.

“The probability that such a strong correlation would happen by chance is 10 to the negative 18th. So 00000 …18 zeros and then (an) 18. Which is zero,” he said.

And Milo’s hypothesis seems in line with the opinions of some other prominent SAT critics.

Maybe these important exams are being so closely examined?

By patrick honner, ago

Gumdrop Solids

gumdrop solidsThis is a nice little video demonstrating how to use gumdrops and toothpicks to create Platonic Solids.

http://www.youtube.com/v/5QgIJOy7T7Y

A Platonic Solid is basically the 3-dimensional version of a regular polygon.  A regular polygon is a 2-dimensional figure whose sides and angles are all congruent.  A Platonic Solid is a 3-dimensional figure whose faces are all congruent, and the faces are put together at every vertex in the same way.

The most common example is the cube:  it has six identical faces (squares), and each vertex is formed by putting three squares together at right angles to each other.

Quite remarkably, there are only five Platonic Solids:  the tetrahedron, the cube, the octahedron, the icosahedron, and the dodecahedron.  There are many other solids with interesting properties, but only five that satisfy the above conditions.

Our video-maker wasn’t ambitious enough to construct a dodecahedron.  Or maybe she just didn’t have enough gumdrops.

By patrick honner, ago

The Art Gallery Problem

I recently attended a function at the Museum of Modern Art hosted by Math for America.  In typical MfA fashion, the invitation was designed around a relevant mathematical idea, in this case, the Art Gallery problem.

art galleryThe Art Gallery problem (aka the museum problem) basically asks “What is the minimum number of guards required to keep an entire region under watch?”.

We make the usual idealizing assumptions for the purposes of elegant mathematics.  For instance, we assume that the guards can see infinitely far, that there are no obstructions (other than the walls), that the guards can see everything in front of them, and the like.

So looking at the map at the right, how many guards would be needed to watch over the fifth floor at the MoMA?

The Art Gallery problem is a classic question from computational geometry, and its solution involves a lot of great ideas from graph theory and graph coloring.

There are a number of fun extensions to this problems, too, including the watchmen route problem (one watchman guarding the entire museum) and the fortress problem (guarding the exterior, rather than the interior).

The Art Gallery problem is the best kind of math problem:  easy to state and understand, surprisingly rich and complex, and lots of fun to play around with!

By patrick honner, ago
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