A One-in-a-Million Baseball Play

As the 2011 MLB season winds down, there is a slim chance of something very unusual happening:  a three-way tie for the wild card playoff birth!

https://www.espn.com/mlb/story/_/id/7005248/three-way-tie-american-league-wild-card-race-cause-logistical-nightmare

It seems highly unlikely that the Red Sox, Rays, and Angels will actually all finish in a dead-heat, but if they do, it will pose a lot of problems for playoff scheduling.

This is a fun, if complicated, math question to think about:  what are the chances that after a 162-game season, three of the eleven teams ultimately vying for the wild card end up with identical records?

To investigate, the first thing I’d do is simplify the situation.  I’d reduce the number of teams and the number of games, give every team a 50/50 chance to win every game, and then see what happens.  After I’d explored a bit, I’d then consider complicating matters by using more teams, more games, and more realistic winning percentages.

A math challenge that any Strat-o-matic player could love!

By patrick honner, ago

Food Court Number Theory

I recently met some friends for dinner in an open-air food court underneath the New York City Highline.  Much to my surprise, some arithmetic greeted us at the door.

Since beverages could not be purchased in cash, you first had to purchase beverage-vouchers which could then be exchanged for beverages.  The beverage-vouchers only came in two denominations:  $1 and $7.

I guess the food-court operators figured that most of their customers wouldn’t be comfortable solving stamp problems, so they were kind enough to provide some example solutions to common beverage equations.

By patrick honner, ago

Graphing Roomba Paths

This is a great set of photos depicting art made from the paths of Roomba robotic vacuum cleaners:

roomba light paintings

The paths traced out by these self-starting sweepers could provide a novel approach to random walking.  And I wonder how much of the movement algorithm can be reverse-engineered simply by looking at a collection of paths?

It might be fun to perform experiments with roombas.  For example, we could try to determine how long it takes one to completely traverse a floor, or how many times on average they pass through a given point.  Or if working in tandem, what is the probability that two roombas collide?

Of course, we’d have to address the ethical issues of experimenting on roombas without their consent.

By patrick honner, ago

Kickoffs, Touchbacks, and Scoring in the NFL

goalpostsTwo weeks in and my prediction that NFL per-game scoring would be down in 2011 isn’t looking so good.

As predicted, the number of touchbacks on kickoffs has risen dramatically.  In week one, 50 percent of kickoffs were touchbacks, up from around 16% of all kickoffs in 2010.  The increased number of touchbacks, and the consequential reduction in field position, led me to speculate that scoring would drop by a few points per game.

But the numbers tell a different story.  Not only was Week 1 the second highest scoring opening weekend in NFL history, but Week 2 saw even more offensive production.  So far in 2011, teams are scoring a combined 46.63 points per game; in 2010, that number was 44.07.  Thus, scoring is up by about 2.5 points per game.

But I’m not giving up on my hypothesis just yet.  Like a good statistician, I’ll just blame the sample size for the discrepancy!  The season is still young:  let’s see what where we are in January.

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By patrick honner, ago

Mathcircles.org

This is the website for the National Association of Math Circles:

http://www.mathcircles.org/

A Math Circle can be many things, but essentially it is a group of people who get together to have fun with mathematics.  Math Circles exist for young children, older students, teachers, and professionals, and some groups involve all of the above!

There are Math Circles all over the world, and this website aims to create a directory of such circles and provide resources for students and teachers alike.  Use this resource to find a Math Circle in your area; or, start one of your own!

By patrick honner, ago
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