Category: Maths

Should Statistical Sampling Be Used in the United States Census?

January 29, 2015

“Statistics—the mathematical science of analyzing numerical information—is vital to the practice of all the empirical sciences. No modern science tries to account for the complexity of nature without using statistical methods, which typically provide investigators with a numerical outcome along with an analysis of the margin of accuracy of that outcome. With the help of computers, statistical techniques for collecting and analyzing large, complicated data sets have become very sophisticated and have proved to be reliable and effective for scientific researchers, inventors, and engineers working on problems in such diverse fields as economics, physics, and pharmaceuticals.”

http://www.scienceclarified.com/dispute/Vol-2/Should-statistical-sampling-be-used-in-the-United-States-Census.html

The unexpected power of baby math: Adults still think about numbers like kids

January 28, 2015

“A new study has found new evidence that educated adults retain traces of their innate sense of numbers from childhood — and that it’s more powerful than many scientists think. The findings could contribute to the development of methods to more effectively educate or treat children with learning disabilities and people with brain injuries.”

http://www.sciencedaily.com/releases/2014/01/140122134231.htm

The problem of really big numbers

January 28, 2015

“If you were around during the last technology boom and bust cycle of the early 2000s you were likely exposed to the concept of really big numbers. Countless business plans for all manner of ill-conceived ideas began with “If just 0.00001% of all internet users visit our site…” and used that as the core foundation of their revenue model. While it all seemed logical at the time, the logic of really big numbers had two fundamental failings.”

http://www.techrepublic.com/blog/tech-decision-maker/the-problem-of-really-big-numbers/

Op-ed piece on swimming pools vs. guns as the most dangerous weapon

January 28, 2015

What determines how much we fear something? Is it based on the actual risks posed? Or do our emotions lead us to fear the wrong things and weigh risks differently than we should?

Interesting piece comparing the relative risks of swimming pools and guns and how much we fear each.

http://scienceblogs.com/deltoid/2001/07/27/levittpoolsvsguns/

4th Down Bot. Live analysis of every N.F.L. fourth-down decision

January 28, 2015

4th Down Bot copyThis is a clever program that does an analysis of every 4th down play in every professional football game. It determines based on mathematical expected value whether teams should go for it, punt, or kick a field goal. It breaks down the math behind its decision making. What’s interesting is how often the mathematical decisions are not the ones followed by the people on the field. Who is right in a case like this? What happens when the “common sense” approach is different from the mathematically “true” approach?

http://nyt4thdownbot.com/

How Oregon Coach Chip Kelly Can Spark ‘Moneyball’ Revolution In NFL

January 28, 2015

“Those fourth down calls epitomize Kelly’s aggressiveness but what the average football fan doesn’t realize is that Chip’s play-calls (the fourth down tries, fake punts, two-point conversions, etc.) are almost always the correct mathematical decision. Like Paul DePodesta and Billy Beane did in baseball, Kelly’s genius comes from exploiting arithmetic that other coaches are too naïve to acknowledge.”

http://www.thepostgame.com/blog/men-action/201211/how-oregon-coach-chip-kelly-can-spark-moneyball-revolution-nfl

Using Math to analyze baseball. Sabermetrics

January 28, 2015

Popularized in the book and later on the movie, Moneyball, Sabermetrics is “the search for objective knowledge about baseball.’ Thus, sabermetrics attempts to answer objective questions about baseball, such as ‘which player on the Red Sox contributed the most to the team’s offense?’ or ‘How many home runs will Ken Griffey hit next year?’ It cannot deal with the subjective judgments which are also important to the game, such as ‘Who is your favorite player?’ or ‘That was a great game.'” -Bill James.

Sabermetrics has caused tremendous controversy among sports analysts and enthusiasts because of the positions they take on questions such as: How do we reconcile mathematical knowledge that contradicts our intuition? What if our eyes tell us one truth and our numbers tell us a different one?

Some people complain that the reliance on numbers takes away from the “magic and mystery of the game.”

The baseball organizations themselves have adopted the data driven approach to analyzing players. With the success of the Oakland Athletics (a team that was an early adopter of the mathematical methods known as Sabermetrics) and later on the Boston Red Sox, most if not all teams use these analytical methods.

The first link below is an introduction to the basics of sabermetrics and below that are two disagreeing with its use.

http://sabr.org/sabermetrics

http://www.hardballtimes.com/death-to-sabermetrics/

http://www.foxsports.com/mlb/story/sabermetrics-moneyball-stat-geeks-are-ruining-sports-092211