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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 – . . . → Read More: Were the San Francisco Giants #1?

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 . . . → Read More: Playoff Probabilities


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 . . . → Read More: Moneyball

Scoreboard Stats

A couple of weeks ago I noticed this article on the Yahoo Sports page, which highlighted a statistically rare event that occurred in the American League on Sunday, May 8th. On that day, 7 baseball games were played on the AL schedule, and in all of those games one team scored exactly 5 runs. The post then links to this article from the AP, which gives this rare event the following context:

It was the first time in 18 years that such a quirky thing happened with a full schedule. On Aug. 10, 1993, all seven NL games featured one team scoring precisely two runs, STATS LLC said.

The last time it occurred with five or more runs was July 20, 1955, when all four AL games had at least one team score exactly six, STATS LLC said.

When I read this article, some questions immediately came to mind: exactly . . . → Read More: Scoreboard Stats

Optimal Base Running

Now that the World Series is upon is, I thought I might take a moment to discuss the latest results in the field of optimal base running. On the face of it, this may seem like a non-issue; after all, as any decent student of geometry will tell you, the shortest distance between any two plates is a straight line.

In a game of baseball, however, it’s more important to minimize time, not distance. Given this, running a path that consists of four straight lines connecting each base is not optimal, because the runner must slow down to make the sharp turns at each base. Of course, baseball players already know this, which is why they often swing out in their path before crossing first when they are confident that they can reach second or more. But still, the question remains: are these trajectories optimal?

According to a trio of . . . → Read More: Optimal Base Running

The Housekeeper and the Professor

Some time ago, I heard about a book from Japan called The Housekeeper and the Professor, written by Yoko Ogawa in 2003 and translated by Stephen Snyder last year. As the title suggests, the book centers on the relationship between a housekeeper, her son, and a math professor. The main conceit of the book is that the Professor suffered an accident some years before that impaired his memory, so that his short term memory only lasts around 80 minutes. In other words, every day the housekeeper and her son come to visit the professor, it is as if they are meeting him for the first time. He copes by clipping small notes to his clothing, and in spite of his disability he still dabbles in mathematics.

One part Memento, one part A Beautiful Mind, the book was named a New York Times Book Review Editors’ Choice, and was popular . . . → Read More: The Housekeeper and the Professor

Mathematics Awareness Month 2010

As April comes and goes, so too does Mathematics Awareness Month. Every year, the Joint Policy Board for Mathematics swirls mathematics with a different delightful discipline: last year it was climate, and the year before was voting.

This year’s theme is mathematics and sports, a topic which has inspired a number of articles here on this site. As usual, there are a number of essays that discuss this theme from various perspectives; while usual suspects such as football and baseball play a central role in many of the essays, other sports get to mingle with mathematics as well, including track, golf, and tennis (also NASCAR, if you consider that a sport).

This dude always thinks about math when he is golfing.

There are too many articles to discuss, so I’d encourage you to go take a look and see if anything strikes your . . . → Read More: Mathematics Awareness Month 2010

Ballpark Mathematics

Like the dawn of a new day, the start of the baseball season carries with it tremendous promise. These first few weeks provide a reprieve from the breakneck pace of March Madness, where every team is burdened with the knowledge that one loss is all it takes to prevent it from total victory. Instead, the major leagues are a product of the season in which they begin, and just as the warming weather invites us to spend weekend afternoons on grassy knolls looking for shapes in the clouds, so too do the opening games of the baseball season encourage us to let our hair down and reacquaint ourselves with this traditional American pastime.

The American Dream personified?

However, eventually Spring must give way to Summer, and Summer must give way to Fall. As the days grow shorter, so does the window of opportunity for a team to make it into . . . → Read More: Ballpark Mathematics