Baseball aficionados in Minnesota cringed last month when their home-state baseball star Joe Mauer laid down a bunt with runners at first and second and no outs. However, a self-styled ‘Twin’s Geek’ supported this decision with an interesting statistics grid called the “expected runs matrix” published by Pete Palmer and John Thorn in The Hidden Game of Baseball. I came across this today in the Gameday program for the contest between the Minnesota club and the Toronto Blue Jays (Twins win! :)). If you are a baseball nut like me and enjoy digging into all the stats, check out this case made for making the sacrifice. In a nutshell, statistics compiled over 75 years of major league baseball indicate that Mauer’s success in advancing two runners made the out moot – the expected runs did not change. The Twins’s Geek (TG) thinks that Mauer, the reigning American League batting champ, thought he might get a surprise bunt hit, which would have increased the expected runs by a big margin. However, TG notes that the sacrifice may have gone in vain by not advancing runners (force at third, for example) or created a disastrous double play (pop to the pitcher and double up at first). What made this really interesting for me was the juxtaposition of situational stats provided by Gameday in this same issue. It shows that Joe Mauer is the premier clutch hitter on the Minnesota Twins and possibly all of baseball. For example, he bats nearly .400 with runners in scoring position! Therefore I must say: Joe, give it a go – swing away and make our day!

Researchers from my alma mater, the Carlson School of Management at the University of Minnesota, have discovered that many people become confused when dealing with more than one percentage at a time. For example, when a store offered 25 percent off on top of a 20 percent discount, they enjoyed significantly more sales than the equivalent offer of a 40 percent reduction. Evidently most shoppers simply add the two discounts together — 25 plus 20 in this case.

I recall someone saying they saw an item that went on clearance for 50% off and after going unsold got marked down another 50%. They brought the item to the checkout only to be told by the clerk that this could not be right because then there would be no charge — 50 minus 50 is obviously zero! The shopper demanded that the store manager be called in to resolve the matter. However, after much deliberation, the superior declared that the clerk had it right and refused the sale because the store would go broke by giving away products for free.

Here’s a puzzler that will weed out those who do not deal well with percentages. Imagine you buy a stock for 100 and it shoots up 40 percent but then drops back by 30 percent. How much profit will you make by then selling this stock? See this report by UMNnews for the answer.

In today’s Ask Marilyn® column in Parade magazine, a reader questions whether a commuter might get to work earlier by leaving home later. Beam me to my cubicle Scotty!

I’ve never considered this idea as a possibility, but I have experimented on varying times of departing for my daily commute of 20 miles to the Stat-Ease office in Minneapolis. My goal is to precisely predict the rush periods and avoid them while working within our flex-time rules for full-time workers. The graph shown here illustrates my theory on traffic around the Twin Cities (I drive through Saint Paul from a suburb to the east – Stillwater, Minnesota).* My belief, based on decades of daily commuting and not refuted by these experimental results, is that cars congregate in waves due to differences in working hours – some drivers working the 7 AM factory shift and others expected to be at their desks by 8 AM, for example. For me the most desirable departure is at 6:34 AM,** which maximizes my sleep time and hits a trough in the waves of traffic – still 35 minutes on the road for my average commute. I call it the “hole” and when I hit it right, my car is like the container you put into the drive-through receptacles of the bank – it whooshes me into Minneapolis. My statistical colleagues question my theory due to the sparsity of recorded data, so if any of you can provide support, I’d appreciate it. It boils down to this: Obviously one can leave later and get to work faster, but the trick is not to be late.

*For all the details, see the One-Factor RSM [Response Surface Methods] Tutorial for Design-Expert® version 7 software.

** Refer to the One-Factor RSM Tutorial (Part 2 – Advanced topics) for details on how Design-Expert’s numerical optimizer found the most desirable combination for leaving at the latest, minimizing drive-time and making the results least susceptible to variations in departure via propagation of error – POE.

Professor Scott M. Stanley of the University of Denver in his keynote address to the 2002 Smart Marriages Conference,
What is it with Men and Commitment, Anyway?, cited a survey saying that 85% of divorced couples blamed their breakup on “lack of commitment.” Nadeem Irfan Bukhari, Lecturer on Pharmaceutical Technology for the School of Pharmacy at the International Medical University (IMU), Kuala Lumpur – Malaysia, offers this cartoon that speaks on this vital issue. Nadeem worked for about 10 years as a political cartoonist for the National daily press. I am very pleased that he has consented to contribute cartoons like this with a statistical bent. Thank you Nadeem — very enjoyable!

PS. Having been married now nearly a third of a century, I must counteract my training in statistics that one must never, ever say you are certain about anything. For the record, when my wife asks me this question, I always say “Yes — 100 percent!”

In the latest issue of American Scientist magazine, Howard Wainer, an adjunct professor at Wharton, makes a case for how ignorance of how sample size affects statistical variation has created havoc for nearly a millennium – and continues to do so today. Simply put, the variance of sample means increase as the sample size decreases. Wainer deems Abraham de Moivre’s 1730 discovery of this mathematical relation The Most Dangerous Equation .

The article details a major investment by Bill and Melinda Gates Foundation and others to provide better education via smaller schools. Statistics showed that among high-performing schools were an unrepresentatively large proportion of smaller ones. However, the Wainer found that the same can be said for low-performing schools – smaller ones are over-represented. This finding agrees with De Moivre’s equation – smaller schools display greater variance of test score averages and thus over-populate the extremes. Wainer presents statistical evidence that “overall bigger schools do better…not unexpected, since very small high schools cannot provide as broad a curriculum or as many specialized teachers.” He concludes that “Spending more than a billion dollars on a theory based on ignorance of de Moivre’s equation – in effect serving only to increase variation – suggests just how dangerous that ignorance can be.”

Wainer provides another example showing how U.S. cities rank for automobile safety. Smaller cities come out on top and bottom – again demonstrating how variance increases as sample size decreases. How often have you seen tables like this in the popular media that rank areas by some criterion and seen the same result – smaller cities coming out on top and bottom? Perhaps some of the investments for improving education ought to be directed toward basic statistics!

Subject matter expertise from a technical guru often works wonders. For example, consider Charles Steinmetz of General Electric, who learned his trade from Thomas Edison. Steinmetz invented more than 200 electrical devices. It’s said that after he retired, GE hired Steinmetz to solve a particularly difficult machine problem. He looked here and there, tested various parts, and then marked an “X” on a specific spot. The GE engineers were amazed to find a defect precisely at the Steinmetz mark. Later they got a bill for $1,000. The itemization read: “For making one chalk mark – $1. For knowing where to put it – $999.”

Many years ago (40!*) as a pre-teen I read the story “Eleven Blue Men” by Berton Roueché. This and other true stories about medical detectives fascinated me. Given the popularity of the television show House, I am not the only one who appreciates experts that make astoundingly accurate diagnoses based on a few facts and fantastic leaps of intuition.

Dr. Jerome Groopman in his book on How Doctors Think says that “The mind acts like a magnet, pulling in clues from all directions.” However, Groopman advises experts keep their guard up against these common biases:
– Availability – the tendency to reach for the easiest plausible explanation and reject all others,
– Confirmation – see only evidence that fits preconceived notions,
– Commission – the rush to action when doing nothing would be best.
(If you never want to believe any expert opinion again, see an exhaustive list of cognitive errors in diagnosis compiled by Dr. Pat Croskerry (Dalhousie University Faculty of Medicine, Halifax, Nova Scotia, Canada).)

Groopman suggests that patients who fear they are not getting a good diagnosis ask these simple questions: “What else could it be? Could two things be going on simultaneously?” This strikes a chord with me as a specialist in the field of experiment design. It seems that the toughest problems for those who rely on intuition, or heuristics as Groopman calls it, are those where factors interact to create an important effect.

By the way, Groopman has some interesting caveats about the new approach of “evidence-based medicine,” which you can see in an excerpt from his book posted along with the sound track of an interview by NPR’s “Morning Edition” radio show. He warns, “Statistics embody averages, not individuals.”

*PS. Yes, I do feel old, but age may provide some benefit via the accumulation of experience. For example, the March 22nd issue of Wall Street Journal says that age 53 is best for financial decisions. “The age of reason” they call it. Guess how old I am. It’s funny how one notices stuff like this that confirms a prior notion.

Hmmm, the French philosopher Camus would not approve, but I have some odds and ends left over from my previous blog on happiness and well-being.

1. The New York Times published a much fancier graphic on happiness by country than mine but with out-dated stats (’95) on per capita income.

2. In their article titled “Reversal of Fortune,” this month’s issue of Mother Jones magazine (March/April 2007) refutes the axiom “Make money, get happy.” They report that money consistently buys happiness right up to about $10,000 income per capita – what an average Mexican earned in 2006 while achieving the second ranking in the World Values Survey on happiness and well-being.* Folks at the poverty level get a great lift from even a small reversal of misfortune. The author, Bill Mckibben, calls this the “Laura Ingalls Wilder effect” after the writer made famous by “Little House on the Prairie”. One of my favorite stories is Wilder’s reminiscence of Christmas on the banks of Plum Creek near Walnut Grove, Minnesota, in 1875. Her parents could only afford to give less than a dozen pieces of hard candy to each of their children, but this sufficed to create great happiness in the prairie-dwellers’ dugout. This really puts things in perspective!

* Evidenced in Figure 1 presented by Ed Diener (University of Illinois, Gallup Organization) and Martin E.P. Seligman (University of Pennsylvania) in their article Beyond Money Toward an Economy of Well-Being. It shows that “Over the past 50 years, income has climbed steadily in the United States, with the gross domestic product (GDP) per capita tripling, and yet life satisfaction has been virtually flat.”

3. The San Francisco Chronicle (12/24/00,Science Tracks the Good Life ) offered this list of the most important sources of personal happiness from researcher Michael Hagerty:
— Close ties to friends and family;
— Wide political freedom*
— High income, and
— A narrow gap between rich and poor.
According to Hagerty’s analysis, the United States is the fifth-happiest nation, a fact that baffled him because for the most part, the top-rated countries are small and homogeneous. That may explain Puerto Rico’s positive feelings of well-being.

*(See also Democracy and Happiness: What Causes What? by Ronald Inglehart (University of Michigan).)

4. Here are some other topical references I found on the internet, but after I reached a point of diminishing happiness trying to find the secret to happiness (Camus was right!):

a. The Reliability of Subjective Well-Being Measures by Alan B. Krueger (Princeton University) and David A. Schkade (University of California, San Diego).

b. A Simple Statistical Method For Measuring How Life Events Affect Happiness by Andrew E. Clark (CNRS and DELTA, Paris, France) and Andrew J. Oswald (Department of Economics, University of Warwick, UK).

(Photo of Guatemalan girl by K. M. Anderson)