2010: The Year in Facebook Statistics

facebook logoThis is a cool summary of 2010 in terms of Facebook-related statistics:

http://www.siliconrepublic.com/digital-life/item/19778-facebooks-2010-by-the-numb

With 500 million (!) users, Facebook is rapidly becoming a source of seemingly limitless data about how people live and interact in modern society.  Some of the highlights:

  • Nearly 61 million people changed their relationship status to in a relationship / engaged / married
  • Nearly 43 million people changed their relationship status to single
  • Over 6000 pages were liked every second!  (Speaking of which, how about liking my page?)

The potential applications of analysis of this data, both good and bad, are mind blowing.  As previously noted, people have used Facebook data to identify peak break-up times and to predict someone’s sexual orientation based on their various connections and activity.

New NFL Overtime Rules and Strategy

At the beginning of the 2011 playoffs, the NFL implemented a new set of overtime rules that drastically altered how tie games would be decided.  The rules entail many significant strategic consequences, and I’m not sure how well-understood those consequences are.

The old overtime rule is straightforward:  initial possession of the ball in overtime is determined by a coin-toss, and the first team to score is the winner.  Critics of this model argued that since initial possession of the ball was such an advantage, awarding it based on a coin-toss essentially made the outcome of the game equivalent to a coin-toss.  The argument seems reasonable, although whether the data backs it up is a story for another time.

The NFL’s new system tries to counterbalance the advantage of initial possession.  From here on out, let’s call the team that wins the coin-toss, and therefore begins overtime with the ball, Team A.  In the new system, Team A can win the game on its initial possession only if they score a touchdown.  If Team A scores a field goal on their initial possession, Team B will receive the ball and have a possession to then try to win or tie the game.

Here is a diagram illustrating the old system.NFL OT Old RuleThe basic idea here is if Team A scores, they win.  If they don’t, then Team B gets the football and starts at the front of the graph.

Here’s a graph representing the new system.

This system is far more complex.  First of all, Team A now has a great incentive to try for a touchdown on its first possession, whereas under the old system, they had virtually no incentive to do so.  Furthermore, the value of a field goal for Team A on its initial possession has been greatly decreased.  Under the old system, a first-possession field goal won the game.  Under the new system, its value is considerably less.NFL OT New RuleWhat are the consequences of these new realities?

Consider a long field goal on the initial possession.  Make it, and your opponent gets the ball and can beat you with a touchdown or tie you with a field goal.  Miss it, and your opponent will have good field position and now can beat you with a field goal.  Perhaps punting is the better option:  you gain field position and if you defend successfully, you get the ball back and now all you need is a field goal to win.

Even more interesting is a short field goal attempt on the initial possession.  Make it, and your opponent still gets field position and a chance to beat or tie you.  Why not go for a touchdown?   You win outright if you succeed, and if you don’t, not only does your opponent get poor field position, but if you defend successfully you’ll only need a field goal to win.

Because of the altered values of touchdowns and field goals mentioned above, I think 4th down strategies on the initial possession should be modified as well.  As complex as it is, at least the new system reverts to the old ruleset after (at most) two possessions.

As interesting as the many consequences of these rule changes are, I still think the “first to six” idea makes more sense.  We’ll see what happens this weekend! 

Related Posts

 

Metrocard Calculations

metrocard imageThe following article from the New York Times discusses the recent fare increase for public transit in NYC:

http://cityroom.blogs.nytimes.com/2010/10/07/m-t-a-meets-to-increase-transit-fares/

The base fare for a ride on a NYC subway or bus is now $2.25, and price changes have been made both to the monthly unlimited-ride cards and the bulk-purchase bonus rate.

For those of us who live in New York and frequently use public transit, we are faced with the following optimization problem:  is it better to buy the monthly unlimited-use card for $104, or purchase some amount of “single-rides” in bulk and receive a 7% bonus?

The above Times article discusses some of the strategies and factors to consider in making this decision.  In addition, it points the reader to the website www.metrocardbonuscalculator.com that allows the user to experiment with various purchasing scenarios.

Fare hikes have become more commonplace over the past few years, but reliable public transit is still a bargain.  And I’d pay an extra few cents for some additional cleaning crews.

The Packing Problem

Whether it’s spheres in a cylinder, presents in a stocking, cars in a parking lot, or potatoes in a pot, the packing problem is a classic mathematical idea rich in application and complexity.  Here is a nice little article on it, and just in time for Christmas!

https://www.insidescience.org/content/packing-it-all-holidays/876

The seminal result in packing is that spheres, packed cannon-ball style, can occupy around 74% of the available space when you pack them in, say, a cylinder.  The article summarizes some other interesting experiments involving the packing of other solids (including M&Ms!), but none of them can be packed as efficiently as spheres.

Unfortunately, this probably won’t help you get everything in your sleigh for the trip  to Grandma’s house, unless of course every gift you are giving happens to be a platonic solid.

Follow

Get every new post delivered to your Inbox

Join other followers: