## Mathalicious Post: To Foul Or Not To Foul

Greetings, mathletes. As some of you know, I’ve recently joined the crew of good folks at Mathalicious. Consequently, the blog work here is in a bit of a transition, but don’t worry! I will still be around, though the focus may shift somewhat.

How Math Goes Pop! will be changing is the subject for another post. One thing’s for sure, though: I’ll be contributing to the Mathalicious blog regularly. My first post, on whether or not it makes sense to foul the opposing team at the buzzer in a close basketball game, went live last week. Here’s a small sample:

A three point shot by Sundiata Gaines turned a two-point loss for the Jazz into a one-point win. No doubt that’s a tough defeat for Cavs fans and players alike, but in such a situation, there’s really nothing the defense could’ve done to change the outcome.

Or is . . . → Read More: Mathalicious Post: To Foul Or Not To Foul

## Were the San Francisco Giants #1?

Last month, I posted a review of a new book titled “Who’s #1?” on the mathematics of ranking and rating – if you’re interested, you can purchase a copy via the Amazon sidebar on the right.  Today I’d like to study the San Francisco Giants with one of the techniques used in this book: the offense-defense rating method.

Why the Giants?  It’s really just a personal preference.  For the non-Giants fan, though, it’s worth pointing out that the Giants won the World Series in 2010, but failed to even make the playoffs in 2011.  Let’s try to investigate why this is the case.  Baseball fans may have their own explanations for this observation, but for a moment let’s focus on the math.

Let's go Giants!

As the name suggests, the offense-defense rating method rates a team’s offensive and defensive capabilities.  Of course, these two things are highly interdependent – if a baseball team . . . → Read More: Were the San Francisco Giants #1?

## Math in Books: Who’s #1?

In an earlier post, I closed by hinting at the mathematics of ranking.  In this modern era, the topic is particularly relevant: the ranking algorithms are hard at work whenever you type something into a search engine, rate a movie on Netflix, or look at a product on Amazon.  It’s also a popular area of study among sports enthusiasts, for whom accurate rankings of the relative strengths of teams can make all the difference in a fantasy league or a betting pool.

Because of all of these accessible applications, it should come as no surprise that the mathematics of ranking is the subject of a new book, titled Who’s #1? The Science of Rating and Ranking.  Written by applied mathematicians Amy N. Langville and Carl D. Meyer, the book tackles a variety of methods used to extract ratings or rankings given some collection of input data.

Front Cover!

This book is chock full . . . → Read More: Math in Books: Who’s #1?

## Run for the Ranking

This Saturday, folks from all over the country will be tuning in to the 138th Kentucky Derby.  In fact, this year the Kentucky Derby falls on the same day as Cinco de Mayo; undoubtedly the result of this intersection will be a plethora of parties celebrating the melting pot that is America (tacos and mint juleps make for a wonderful combination, I’m sure).

Whenever racing comes up, mathematics can’t be far behind.  Gambling is always a popular topic: how are the odds for the different racers determined, for example?  But this is a question I will save for another time.  Today, inspired by horse racing in particular, I’d like to discuss the following classic logic puzzle.

Suppose you have 25 horses and a 5 lane race track.  You have no way to record the finishing times of the horses, but you can race up to 5 horses on the track at once and . . . → Read More: Run for the Ranking

## Are the 49ers skilled, or just lucky? Part 2.

In my previous post, I asked whether the San Francisco 49ers’ improbably successful season was due more to luck (say, by being granted a relatively easy schedule), or due to real improvements in the skill of the team.  By comparing the 2011 season with the 2010 season and correcting the schedule for the number of wins and losses each team accrued, I concluded that the level of difficulty of the team’s schedule year over year was roughly the same, and therefore more of their success should be attributed to skill rather than luck.

In this follow-up, I’d like to dig a little deeper into measurements of the 49ers’ skill, in an attempt to further bolster the above claim.  If you are a football fan, then you are fortunate to have me write two football-themed posts in a row.  If you are not a football fan, fear not; with the season having come . . . → Read More: Are the 49ers skilled, or just lucky? Part 2.

## Are the 49ers skilled, or just lucky?

Fans of the two football teams who face off in the Super Bowl will no doubt spend the weekend filled with nervous anticipation – hopeful that their team will emerge victorious, but certain of the knowledge that there can only be one champion.  For the rest of us, we must hang our heads with relative degrees of shame, and bide our time until the next season brings with it the promise of new opportunities for all 32 NFL teams.

For a San Francisco 49ers fan like myself, most of the last decade has been spent in a fairly constant state of disappointment.  But after ten years without a playoff appearance, the team blossomed this season under the influence of new head coach Jim Harbaugh, and came within one game of their first Super Bowl appearance since 1995.

This poster hangs proudly in our apartment.

Despite a great season, in which the team won . . . → Read More: Are the 49ers skilled, or just lucky?

## Playoff Probabilities

Continuing with last week’s theme, and since we are in the midst of playoffs, I’d like to take a moment now to discuss another link between baseball and mathematics.  This link is particularly timely since the scuttlebutt on the internet suggests that next year the playoff rules for baseball will be changed: the number of teams competing for the World Series will increase from 8 to 10, and because of that, another round of playoff games will be introduced.

Currently, the playoffs consist of three rounds.  The first round is the Division Series, in which eight teams compete in a best-of-five match-up (equivalently, a first-to-three match-up, i.e. the first team to win three games wins the series).  The second and third rounds, better known as the Championship Series and World Series, are composed of four and two teams, respectively, but are both best-of-seven (equivalently, first-to-four).  Because of these three rounds of several . . . → Read More: Playoff Probabilities

## Moneyball

This weekend, mathematics played a supporting role to Brad Pitt in one of fall’s first critical darlings, Moneyball. Based on the Michael Lewis book of the same name, the film profiles the Oakland A’s during their 2002 bid for World Series glory.  What allegedly separates their story from the story of other teams during that season is the way General Manager Billy Beane, played by Brad Pitt, deals with the budget constraints imposed on him by the team’s owners.

With a payroll roughly a third the size of the Yankees’, Beane understood that the playing field was not a level one from an economic standpoint.  What’s more, at the end of the 2001 season, three of the A’s star players left Oakland for bigger paychecks.  To fill the void, the film (and book) show how Beane took a more analytic approach, and used statistical analysis to uncover . . . → Read More: Moneyball