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11.29.07

Game Theory, NFL style

Posted in News, Sports at 11:19 pm by leingang

Shankar Vendatam reported in the Washington Post a while back about the pyschology of football coaches “going for it” on 4th down.

With just over five minutes to play in yesterday’s game against the New York Jets, the Washington Redskins found themselves on their own 23-yard line facing a fourth and one. The team, which was ahead by just three points, elected to do what teams normally do in such situations: They played it safe and punted rather than try to keep the drive alive.

The Jets promptly came back to kick a field goal, tying the game and sending it into overtime. While this particular story had a happy ending for Washington, which won, 23-20, it illustrated the value of an analysis by David Romer, an economist at the University of California, who has concluded that football teams are far too conservative in play calling in fourth-down situations.

You don’t have to be particularly interested in sports to find Romer’s conclusion intriguing: His hunch about human behavior in general was that although people say they have a certain goal and are willing to do everything they can to achieve it, their actual behavior regularly departs from the optimal path to reach that goal.

[…]

New England Patriots coach Bill Belichick is among those who has said he agrees with Romer, and Belichick happens to be one of the more successful coaches in the league. Two Sundays ago, as the Patriots were piling up an astronomical score against Washington, Belichick took a chance on a fourth-down play and got his team seven points instead of the three he might have gotten had the team tried a field goal.

The article goes on to say that most coaches have ignored Romer’s findings. Last week John Madden made a stir when he gave a game plan for the Eagles for their (then) upcoming game against the Patriots:

“I’m not a big guy for going for it on fourth down — but I think you have to go for it on fourth down [in this game] because you have to get touchdowns instead of field goals. It has to be a very, very aggressive approach because offensively, they’re going to take a very, very aggressive approach to you.”

In the middle of the first quarter of the game, the Eagles did go for it on 4th-and-1 at the New England 15. It was basically their first drive, as the Patriots had intercepted a pass three plays into their actual first drive. Generations of coaches have played it safe in similar situations (early in the game, already down 7), kicked a field goal, and tried again on the next drive. But converting the 4th down led to a touchdown which set the tone for the rest of the game: matching scores until the Patriots scored last and forced another two interceptions.

(HT: Sendhil)

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Texify

Posted in Math, LaTeX, Web at 9:42 am by leingang

I installed the LatexRender plugin to my WordPress blog to express myself in mathematical notation that HTML alone can’t handle.  It runs latex on the server side and serves up an image embedded in the text.

For mathematical bloggers who don’t have access to their webservers (or choose not to get their hands dirty with server-side code), there’s Texify, a nice web service that lets you input LaTeX and get a permalink to a graphic that you can include in your web pages.  For instance, I copied-and-pasted some code from a slideshow I’m working on and got this:

\begin{align*} \frac{\partial f}{\partial x_i}(x_1, x_2, \dots, x_n) &= \lambda \frac{\partial g}{\partial x_i}(x_1, x_2, \dots, x_n) & \text{for each $i=1,\dots,n$}\\ g(x_1, x_2, \dots, x_n) &= 0.\end{align*}

I’m impressed that they seem to have enabled the amsmath packages in their backend, so some of the more sophisticated mathematical constructs can be used (I’m using an align* environment and the \\text command up there).

The site also provides code to copy-and-paste into BBCode posts such as you’d find on forums, and even Google Docs!

(HT: Michael Tsai)

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11.16.07

Social bookmarking for courses

Posted in Education, Web at 3:02 pm by leingang

I was at the monthly web pegagogies free lunch sponsored by the Bok Center today and we talked a little about using social bookmarking sites like del.icio.us to collect bookmarks as a group. (There was also a nice demonstration of Facebook by two students, but I’ve already blogged about a similar presentation they made last Spring). I like the idea, but I’m wondering about the methodology.

In the examples of this that I’ve seen, a delicious account is created and the password is given to all the students in the group. The account is given a course-specific username like “history1667″ Then students use that account to save tagged bookmarks relevant to the course. Then to view all the bookmarks tagged by the group you go to the group’s user page.

I think this unnecessarily confuses the distinction between a user and a tag. It seems to me that people in the group should use their own delicious accounts to add a “history1667″ tag to their bookmarks. Then you can view the collection of pages tagged for the course by looking at that tag’s page.

That would certainly result in more links as students who already use delicious regularly wouldn’t have to log out/log in to do their research (delicious integrates well with browsers and can be hard to extricate). And it means that people could add links to that collection even after they left the course, and new students would have at their fingertips all the old links, without having to worry about passwords. And the entity “History 1667″ seems more to me like an attribute of the link than an agent in and of itself.

I’ve started doing this for my courses. If I’m looking at a page that might be useful for my Math 20 or Math 21b course, I can just tag it. I don’t have to re-login. I can tag the same page for as many of my courses as I want. And if my students want to do the same, the bank becomes richer.

There are, I suppose, reasons for having a controlled account. There might be another course numbered History 1667 at another university. Well, make the tag less common (I almost said “more unique” there) by calling it “HUHist1667″ or “HUHist1667Fall2007″ (then, if you want a fresh batch every semester you just change the tag). Most delicious interfaces feature tag-completion so you don’t even have to worry about it being easy to remember. Or, you can just apply the philsophy of folksonomy: don’t worry about it. Tag clouds make sure that the most important (as defined by user activity) links bubble up. It’s only going to become a problem if the tag is used by two groups equally frequently, which is unlikely and can by choice of tag name be made even less likely.

Another worry might be that outsiders might start using the tag to randomly bookmark irrelevant things like, as someone suggested, a picture of a cat. Again, I think the response is don’t worry about it. A basic tenet of semantic web philosophy is that anybody should be able to declare anything about anything, and it’s up to another layer to endow the trust. In this case, the user him/herself is the trust layer by visually weeding out the irrelevant links, and the tag cloud by making pages more users have marked with the same tag more connected to that tag.
A third objection might be that we don’t want to force students to create accounts on third-party services if they don’t want to, or to open up their use of a third-party service to a class. I can kind of see that, although delicious is for sharing bookmarks, so if you don’t want to share them with the world, why are you using it? But I can see wanting to share different things with different groups (and under different identities). So then maybe you have a group account for those who don’t want one, or encourage users have don’t want to use their “private” delicious accounts to create another one specifically for coursework.

So there’s a tradeoff between openness and quality, but I say, the more the merrier.

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11.14.07

Spirit Airlines markets to math geeks

Posted in Math, Funny, News at 11:34 am by leingang

Spirit Airlines is running a promotion based on the Fibonacci Sequence.

The image “http://www.airlinepins.com/ftp/i1341187269.jpg” cannot be displayed, because it contains errors.

Cheapano Fibonacci wants you to take advantage of his latest Fabulous Fibonacci Sale. Fares are as low as $1* each way. …$1, $2, $3, $5, $8, $13, $21, and some $34 and $55 fares must be booked on spiritair.com between 12:00 PM ET on November 13, 2007 and 11:59 PM ET on November 14, 2007 for travel on the dates as specified by individual market and by market direction…. Please see the terms and conditions for complete restrictions and details.

Asterisks abound , and you can’t fly any day you want, but the deal is legitimate. For instance, you can fly (if you book today)

  • from Fort Lauderdale to Nassau for $1
  • from Fort Lauderdale to Orlando for $2
  • from Fort Lauderdale to Freeport (Bahamas) for $3
  • $5 and $8 fares seem to be missing!
  • from Fort Lauderdale to Grand Cayman for $13
  • from Boston to Myrtle Beach for $21 (now we’re talking!)
  • from Atlanta to Las Vegas for $34
  • from Detroit to Cancun for $55
  • from Orlando to Agudilla, PR for $89
  • from Orlando to Kingston, Jamaica for $144
  • or first class for $233

Even though the Fibonacci sequence grows (asymptotically) exponentially, this is still my favorite airline promotion based on an integer sequence.

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