Conjunction Fallacy

When probability roams the free world, it tends to trip people up. One of its prime offenses is the conjunction fallacy. Take the problem:

Gregory is a very accomplished man. He graduated from MIT with a PhD in Computer Science in only 2 years, and started his own software company. He is now a multi-millionaire.

Which of these explanations is more likely:

(A) Gregory is 19 years old

(B) Gregory is 19 years old and a child prodigy

Many people respond that B is a more likely explanation. Let’s try another:

Victoria has spent a lot of time in the hospital. She has undergone 14 surgeries and suffered from 3 heart attacks. She has also been a keynote speaker for the American Heart Association.

Which of these explanations is more likely:

(C) Victoria is an avid baseball fan

(D) Victoria is an avid baseball fan, but suffers from a congenital heart condition

In this problem, many people choose answer D. The correct answers are A and C. Why, do you ask? 

Simpson's Paradox

Ever seen statistics reverse themselves? Try this on for size:

In 2002 Mo Vaughn batted a .259 batting average for the New York Mets, while Raul Gonzalez batted a .260 (for the New York Mets and the Cincinnati Reds). In 2003 Vaughn delivered a .190 batting average, and Gonzalez batted a .230. Clearly in each year, Gonzalez had a higher batting average than Vaughn. However, between the years 2002 and 2003 seasons, Vaughn had a batting average of .258, while Gonzalez only kept up a .240. How is it possible that across two seasons, Mo Vaughn had a higher batting average? Simpson’s paradox.

Tiger Woods: Blessing or Curse?

In 2008 Tiger Woods underwent surgery on his left knee, thereby producing an 8-month layoff from Golf. His departure from Golf caused many golf enthusiasts to stop watching and some analysts even declared Golf too boring without Tiger. His return in 2009 was stated as “one of the most anticipated returns in sports”. During that time, the media machine began picking up around Tiger. First, ESPN ran a commercial with Tiger entering the clubhouse after his hiatus and the tagline, The Party’s Over. A few months later, Esquire Magazine ran a feature article chocked full of awe. I quote:

“Make no mistake: Tiger is different from the rest. I suspect that he sees colors the rest of us don’t know about, that he senses patterns of heat in the grass, electromagnetism in the earth at his feet. The guy bends the world to his will. This makes him feel alien and repellent to the rest of us.”

MCG Signs Multi-Year Deal with ESPN

Providence, Rhode Island based MCG, LLC signed a multi-year deal today with international sports entertainment firm ESPN for the creation of a March Madness Bracket Optimizer for ESPN.com’s popular Insider program. MCG is a mathematical, statistical and strategic consulting firm that specializes in assisting firms with complex quantitative problems. The firm’s unique blend of quantitative expertise and business acumen has allowed them to work with some of the largest firms in the nation.

ESPN, the worldwide leader in sports, is an international sports and entertainment firm owned by The Walt Disney Company.

MCG Launches Internal Hedge Fund to Take Advantage of Market Turmoil

Today, amidst the turmoil of failing financial institutions and congressional bailout negotiations, MCG launched an internal proprietary hedge fund. “This environment represents an exceptional opportunity to utilize our fresh capital to take advantage of market inefficiencies,” said Head of Mathematical Finance, Barron Gati. Instead of shying away from what appears to be a market rife with uncertainty, the expert analysts at MCG jumped at the opportunity to deploy their capital in the new financial environment. “What better time to prove the efficacy of our strategy than in the midst of the current market turmoil?” asked Gati.