Salary Cap Circumvention

In a heretofore unprecedented (?) move, the National Hockey League has rejected a contract between a player and a team.  In this case, the NHL is trying to void the 17-year, $102 million contract between Ilya Kovalchuk and the New Jersey Devils.  The NHL isn’t commenting right now, but they obviously see this contract as specifically designed to circumvent the spirit of the NHL’s salary cap.  The gaming of the system in this manner has been going on for several years.

The salary cap is essentially a yearly limit on how much a team can spend on its players.  The amount that an individual player counts toward this limit (that player’s “cap hit”) is easy to compute:  it’s the total value of that player’s contract divided by the total number of years on that contract.  In other words, a player’s cap hit is the average salary per year of his contract.

You don’t have to think very hard to figure out how to game this system:  instead of signing a player to a 10-year, $100 million contract, pay them the minimum possible salary ($500K) for 4 extra years and sign them to a 14-year, $102 million contract.  Now, instead of a $10 million cap hit per year, the player has a $7.3 million cap hit per year, allowing the team a lot more financial flexibility.  Do the Devils really expect Kovalchuk to play in year 17 of his contract, when he’s 44 years old?  Probably not.

You could drive a zamboni through this loophole.

Water Ellipses?

A funny thing happened on the way to the graphing utility.

I thought I’d use Geogebra to estimate the equation of the water parabola I saw at the Detroit Airport.

So I pasted the photo into Geogebra, dropped five points on the arc, and then used “Construct Conic Through Five Points”.  The results are on the right.

Now the weird part:  the equation is not a parabola, but an ellipse.  I thought that perhaps I had done a poor job of selecting points, but no matter how I chose the points, the equation came up as an ellipse.

Note the presence of both an x² and a y² in the equation below.

Ellipse.Equation

Is this a limitation of Geogebra?  Is this an anomaly caused by rendering the digital picture?  Or is the assumption that the path of the water is parabolic faulty?

Related Posts

 

Water Parabolas

It’s not easy to see, but at the right is a picture of the famous water parabolas at the Detroit Airport.  The parabola certainly is a favorite among the fountain designer.  I wonder why?

Upon closer inspection, I’m not sure it’s a parabola!  Check out my attempt to find the equation of this parabola using Geogebra.

And here is a lovely video of the water feature in action:  http://www.youtube.com/watch?v=VSUKNxVXE4E

David Blackwell

David Blackwell was a highly-regarded statistician and mathematician who taught at UC Berkeley for 30 years.  Apparently he was the kind of mathematician who could become interested in a new topic, learn about it, and then quickly produce profound results.   Then he’d move on.  Blackwell died on July 8th:  his obituary in the NYT can be found here.

Among other things, Blackwell was a strong proponent of the Bayesian approach to statistical inference, and he produced results in Game Theory regarding bluffing and dueling.

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