BP: Billions to Pay

“You have been invited to the Facebook event, ‘NO BP GAS UNTIL THE LEAK IS STOPPED.’” This strident call for action reached me in early June, when the British Petroleum oil spill had become daily fodder for political commentary and fervent activism. Outraged social networkers have flocked to the event, reaching a total of 110,275 confirmed attendees. Another 23, 519 have indicated possible attendance, and the event awaits a response from yet another 211,221 Facebook users.

If we extrapolate from these numbers, BP stands to lose millions of dollars from loss of confidence alone. And this loss is only a fraction of the total economic cost of the spill, once clean-up costs, legal fees, income compensation and long-term industry and environmental impact are taken into account.

The Value of Stephen Strasburg

The average salary of a Major League Baseball player is about $3 million, but in 2009 the first pick in the draft broke through that ceiling. Earning $3.7 million per year, Stephen Strasburg’s $15.1 million over the next four years also shattered USC phenom Mark Prior’s $10.6 record contract in 2001.

In the past, star draft picks have not also has successful careers, and pitchers the most risky prospects of all. In a newsletter for the SABR, Victor Wang found that 62% of pitchers who ranked as top 10 prospects turn out to be contributors (on a scale of bust, contributor, everyday, and star) with only 4% qualify as a star during their MLB career. Strasburg’s credentials certainly make him an impressive pitcher heading into his first MLB season, but are they enough to earn such an exceptional rookie contract?
Last August, Washington thought so.

MCG Offers Employment Litigation Risk Management Services Featuring Open Pricing

MCG is pleased to announce that their Equal Employment Advisory and Litigation Support Division (EEA/LS) now offers employment litigation risk management services with open pricing.

One of the top challenges for businesses in 2010 is avidiong employment lawsuits, which are on the rise. By most estimates, the median settlement payout in an employment practice liability lawsuit is nearly $90,000, excluding attorneys’ fees. Recent reports estimate that the average cost of defending an employment discrimination case from beginning to end is approximately $250,000. One way to meet this challenge head-on is to engage in proactive analyses that assess and minimize your risk of employment-related litigation.

Costs and Benefits of Hosting the Olympic Games

There is much debate going on whether it is actually beneficial for a city to host the games. On one side there are all the promises made by politicians regarding the revenue generated for local companies, the flows of tourists who spend large sums of money and the improved image of the city, on the other side one might think that the legacy of the games is underutilized stadium and heavily indebted local authorities. This article looks at some of the costs and benefits, and call attention on some of the common mistakes made when evaluating the effects of the games.

Loss Analysis: How Much is Haiti Losing?

The Haiti earthquake reminds most of us of images of entire quarters of a city destroyed, only heaps of concrete and dust left behind, and most importantly: enough humans dead to populate a Providence-sized city. Not only is this one of the greatest tragedies of recent years, but it hit a country that has suffered numerous other natural disasters as well as political instability and military coups. In a nation where 50% would be a modest estimation of unemployment and which struggles to finance its debt obligations, events like the earthquake are more painful than anywhere else. This article focuses on a more objective aspect of the natural disaster, the economic losses suffered by Haiti, attempting to give a rough estimation of the economic effects. In this article, I will suggest some possible ways to do so based on the data we have about the loss of infrastructure and lives.

Wason Selection Task

One of the most intriguing instances where our brain goes awry is shown in the Wason Selection Task (also known as the Wason 4-Card Task). Before getting too detailed, though, let’s try it. The goal is to solve this puzzle:

If there is an odd number on one side of the card,
then there is a vowel on the opposite side

Which cards do we need to flip over to verify the rule?

Think you have an idea? Upwards of 90% of adults get this puzzle wrong.

The Gambler's Fallacy

At the roulette table, black comes up six times in a row. The gambler thinks, “Since half the time black comes up and half the time red comes up, the wheel is due to land on red,” and bets on red. This is the gambler’s fallacy.

Why is the gambler wrong? Isn’t it true that half the time the wheel will come up black and half the time it will come up red? These are some loaded questions. It is true that given an infinite number of spins of the roulette wheel, red and black will each come up half the time. Even in only a few spins we expect the wheel to come up red and black relatively equally. However, this certainly doesn’t happen every time. At any given point in time, it just as likely to spin a red as it is to spin a black, regardless of how the previous turns came up. That is, the probability function is memoryless.

So why is it that people expect the wheel to ‘even itself out’?

Quantitative Virtual Reality

Theory and practice make for an interesting relationship. The world would be beautiful if all theory came out true in reality. Of course, some things would be difficult to observe in reality. Can you imagine watching in real-time someone shooting a basketball 1,000 times? Or the number of red beetles that drive by? Just simulate it! Seemingly anything of numerical quality can be simulated; this includes basketball shots, options pricing, and the temperatures of the day. This is called a Monte Carlo simulation when a numerical algorithm is run based off repeated sampling of random numbers. 

Base-Rate Neglect

Here’s a probability problem:

At a university, 15% of students are of legal age to drink (21 or older), leaving 85% illegal. There is one liquor store near the campus. Willis, the owner is very good at detecting a fake ID. 90% of the time he correctly stops a student trying to use a fraud license. Unfortunately, Willis isn’t perfect. He also misidentifies proper ID’s 10% of the time. So he has always has an accuracy of 90% when examining students’ identification. Say a student walks in and hands his ID to Willis, and Willis turns it down. What is the likelihood that this student is under age?

The Hot Hand: Truth or Fiction?

Perception is everything. Whether it’s sports, life, or anything else, the way one perceives things changes his or her thought process. This is especially evident in basketball. Imagine that you’re huddled around your players preparing for a buzzer beater. You have a 55% shooter who has had an off-night, only shooting 1 for 10. On the other hand, you have a 35% shooter shooting an extremely well 8 for 11. Now, the last shot of the game: who do you give it to? Before we tackle that, suppose I tell you that I have a fair coin and an unfair coin that is twice as likely to give heads.

Here is a sampling of flips:

H H T T H T H T H H H H H

Would you say it was the fair coin or the unfair coin? If you said the fair coin, then congratulations, you may do well as a clutch-time basketball coach. Because there are twice as many heads up there, many people perceive the unfair coin as being displayed. However, it’s all part of the randomness of a fair coin.
Now, back to the basketball question.

Disease Screening Fallacy

With modern medicine, there remain very few diseases that are a virtual death sentence. However, the fear of terminal illness still lurks in the shadows. How prominent is breast cancer among women ages 18-25? How likelyis it that Huntington’s will be passed from parent to child? Can Diabetes really be prevented? These are all questions that float around the medical world. But do we ever question the diagnostic tests? We certainly ask for a second opinion, but when those test results come in that say “positive”, do we question it? Maybe we should.

Every screening test has it’s own strength ratings (i.e. how good it is at detecting a disease). These are known as sensitivity and specificity. Sensitivity is the probability that a person who has the disease will test positive (or 1- P(false negative)). Specificity measures the rate at which a person without the disease will test negative (or 1-P(false positive)). For many screening tests, these parameters are extremely high. Does that mean we can trust any outcome we get? Not quite. We tend to disregard the original base-rate of these diseases when evaluating the likelihood of testing positive with the screening test. This is better illustrated through an example.

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.

MCG Works with NGO to Submit Legislative Recommendations to the Cayman Islands Government

A just-released survey conducted in the Cayman Islands has found that about half of the people questioned have been stalked and two out of five respondents have suffered sexual harassment.

The Young Business and Professional Women’s Club (Young BPW) Sexual Harassment and Stalking Taskforce announced the publication of the report, which was completed in April.

Taskforce Chair Joannah Bodden-Small noted that a high number of respondents had experienced inappropriate behavior.

“In the lead-up to launching the survey, members of the taskforce were aware that there were people experiencing stalking and/or sexual harassment in the Cayman Islands, and so in that respect the results of the survey were not surprising in confirming those facts,” she said. “However, what did give cause for concern is the large number of men and women who, based on the results of the survey, are experiencing these issues in the Cayman Islands,” Mrs Bodden-Small added.

MCG Retained to Apply Statistical Rigor to a New Poker Game

Inventor Bruce Paul hired MCG to review his idea for the new poker sensation 2-11. MCG was tasked with undertaking the quantitative and qualitative analysis and providing an overall opinion on the game. That opinion, and an accompanying article will be published in the nationally syndicated BLUFF! poker magazine. The inventor, Mr. Paul, and his team will be providing an exhibition of 2-11 at the Gaming Life Expo in July. The publication of the article will be in the World Series of Poker edition of the BLUFF! magazine. After a poker night where BLUFF! magazine writer Adam Slutsky and Jamie Gold tried their hand at the revolutionary game, the National League of Poker suggested sponsorship of 2-11.

The game, a fascinating derivation of Omaha Hi-Lo, provides players with an additional choice in determining their best five-card poker hand.

MCG Establishes Likelihood that a Miniature Belonged to Abe Lincoln

MCG was approached by a Kentucky investigator with a fascinating proposal: to determine what is the probability that a miniature in their possession portrayed a 33-year old Abraham Lincoln. This concept was especially interest given the fact that, if the individual portrayed in the miniature is actually Lincoln, this would become his earliest known portrait.

The story behind this miniature was equally fascinating, as it was discovered by a couple who purchased a home which, as was later determined, had been owned by a direct relative of Abraham Lincoln. At the time in which MCG became involved in this project, the owner of this artifact had conducted forensic and historical analyses which suggested that it might indeed be portraying Abraham Lincoln… but the analysis was not backed by any quantitative analysis.