Archive for January, 2011

Smart Quarterbacks, the Super Bowl, and SAT Scores

This weekend, when the Pittsburgh Steelers take on the Green Bay Packers in Super Bowl XLV, it’ll be a match-up pitting a very smart quarterback against, well, a guy who’s not exactly the sharpest knife in the drawer.

If you’re like most of the world, you probably don’t perceive Ben Roethlisberger to be very smart.  He attended Miami University, but information about what he studied is considerably harder to find, and few would call him intelligent. After all, he rides his motorcycle without a helmet, frequently fraternizes with underage co‑eds, and associates with people who occasionally urinate in public. So it will come as no surprise that Roethlisberger scored lower on the Wonderlic test — the 50‑question, 12‑minute exam administered by the National Football League to measure the problem-solving ability of players who will enter the draft — than Aaron Rodgers.

The maximum possible score on the Wonderlic test is 50. Roethlisberger scored 25, Aaron Rodgers scored 35. (Wanna know how you compare? Try a sample Wonderlic test for yourself.)

So, does this mean that Rodgers has an advantage in Sunday’s game? Not necessarily.

Below is data from the last ten Super Bowls. The winning quarterback is listed first, and his Wonderlic score is given in parentheses. (Sorry, I couldn’t locate the Wonderlic score of Brad Johnson.) But for the other nine games, the team whose quarterback had a higher Wonderlic score won four times, the team whose quarterback had a lower Wonderlic score won four times, and last year, the two quarterbacks had the same score.

Super Bowl XXXV – 1/28/01
Trent Dilfer, Baltimore Ravens – Fresno State (22)
Kerry Collins, New York Giants – Penn State (30)

Super Bowl XXXVI – 2/3/02
Tom Brady, New England Patriots – Michigan (33)
Kurt Warner, St. Louis Rams – Northern Iowa (29)

Super Bowl XXXVII – 1/26/03
Brad Johnson, Tampa Bay Buccaneers – Florida State (unavailable)
Rich Gannon, Oakland Raiders – Delaware (27)

Super Bowl XXXVIII – 2/1/04
Tom Brady, New England Patriots – Michigan (33)
Jake Delhomme, Carolina Panthers – Louisiana-Lafayette (32)

Super Bowl XXXVIX – 2/6/05
Tom Brady, New England Patriots – Michigan (33)
Donovan McNabb, Philadelphia – Syracuse (14)

Super Bowl XL – 2/5/06
Ben Roethlisberger, Pittsburgh Steelers – Miami, Ohio (25)
Matt Hasselbeck, Seattle – Boston College (29)

Super Bowl XLI – 2/4/07
Peyton Manning, Indianapolis Colts – Tennessee (28)
Rex Grossman, Chicago Bears – Florida (29)

Super Bowl XLII – 2/3/08
Eli Manning, New York Giants – Ole Miss (39)
Tom Brady, New England Patriots – Michigan (33)

Super Bowl XLIII – 2/1/09
Ben Roethlisberger, Pittsburgh Steelers – Miami, Ohio (25)
Kurt Warner, Arizona Cardinals – Northern Iowa (29)

Super Bowl XLIV – 2/7/10
Drew Brees, New Orleans Saints – Purdue (28)
Peyton Manning, Indianapolis Colts – Tennessee (28)

As it turns out, the average Wonderlic score of an NFL player is 20, while the average score of an NFL quarterback is 24. Only one Super Bowl quarterback in the past ten years had a Wonderlic score below the league average. That was Donovan McNabb (14) in 2005. So while a higher Wonderlic score may not imply Super Bowl success, it does seem that quarterbacks who make it to the Super Bowl have above average scores.

Of course, a football team has more than just one player, so it might be more informative to look at the Wonderlic scores for every player on a team. Sadly, I don’t have that kind of time, but such an analysis was done at least once. The Denver Broncos defeated the Green Bay Packers in Super Bowl XXXII; the average Wonderlic score for the Broncos was 20.4, while the average score for the Packers was 19.6.

The Wonderlic test fascinates me. While it may not be the best predictor of success in the NFL, many companies use it to assess prospective employees’ problem-solving abilities. And it got me to thinking — if the Wonderlic test is adequate to predict job success, could it also be used to predict college success?

Consequently, I sought to answer the following question: Could the Wonderlic test be as good a predictor of college success as the SAT?

Unfortunately, acquiring data to analyze this question is no small task. Wonderlic scores of many NFL players are readily available online, but other companies aren’t willing to release the scores of their employees. (Truth be known, the NFL isn’t really willing to release its employees’ scores, either, but players’ scores are interesting trivia for the public, so sports reporters find ways to uncover them.) In a quick search, I was able to locate the Wonderlic scores of scads of NFL players. However, unearthing the college GPA and SAT scores of those players was exorbitantly difficult. I found all three numbers for just six players online (see table below). I tried to acquire the numbers for other players over the phone, but I met with limited success. A typical conversation went something like this:

Woman in Registrar’s Office at University of Virginia: Hello.
Me: Uh, good afternoon, ma’am. I’m trying to locate the GPA and SAT scores of one of your former students.
Woman: Whose information are you looking for, sir?
Me: Matt Schaub.
Woman: And you are?
Me:
 Patrick Vennebush.
Woman:
Are you related to Mr. Schaub?
Me: Um, no, ma’am.
Woman: Are you a prospective employer?
Me: No, ma’am.
Woman: So… why do you need Mr. Schaub’s information?
Me: Well, see, I’m comparing professional football players’ scores on the Wonderlic test…
Woman: The what?
Me: The Wonderlic test. It’s a test they give to professional football players to determine their problem‑solving ability.
Woman: Hold on — Mr. Schaub is a professional football player?
Me: Yes, ma’am. He played quarterback for the University of Virginia from 1999 to 2003, and now he plays for the Houston Texans.
Woman: So, why do you need Mr. Schaub’s GPA and SAT scores?
Me: Well, I’m trying to determine if the Wonderlic test could be used as a predictor of college success. I need Mr. Schaub’s GPA and SAT scores to see if the Wonderlic test was as accurate as the SAT in predicting how well he did in college.
Woman: Well, I can’t just go around giving out information about former students to total strangers.
Me: Yes, I understand, ma’am, but I’m not going to publicize the information. I just want to analyze it.
Woman: And what will you do with your analysis?
Me: Well, I was planning to post the results on my blog.
Woman: So, you write a sports blog?
Me: Well, no, ma’am. It’s actually a math blog.
Woman: A math blog that focuses on sports?
Me: Um, well, no.
Woman: Then what kind of math blog is it?
Me: Well, actually, it’s a blog about math jokes.
Woman: About what?
Me: Math jokes.
Woman: [click]

Several other calls met a similar fate. Consequently, I only have Wonderlic, GPA and SAT scores for six players. But, whatever. Let’s roll with it and see what happens. The three numbers for each player are shown below.

Player College Wonderlic GPA SAT
Tim Tebow Florida 22 3.66 890
Brady Quinn Notre Dame 29 3.00 1030
Peyton Manning Tennessee 28 3.61 1030
Aaron Rodgers California 35 3.60 1300
Myron Rolle Florida State 33 3.75 1340
Ryan Fitzpatrick Harvard 48 3.20 1580

From this limited sample, three pair-wise correlations were calculated:

  • SAT and GPA: r = ‑0.14
  • Wonderlic and GPA: r = ‑0.36
  • Wonderlic and SAT: 0.95

There’s not a very strong correlation between SAT and GPA. But here’s the thing: the correlation between SAT and GPA for this set of six football players isn’t that much worse than the correlation between SAT and GPA reported in Validity of the SAT for Predicting First-year College Grade Point Average, a study of 151,316 students at 726 four‑year institutions undertaken by the College Board; in that study, r = 0.29.

There’s not a very strong correlation between Wonderlic and GPA, either, but it’s stronger than the correlation between SAT and GPA for the six football players above and for the 151,316 students in the College Board study.

There is, however, a very strong correlation between Wonderlic and SAT, which is perhaps just another way of saying that both tests are equally lousy at predicting college success.

Of course, there are all kinds of reasons that this analysis might be invalid:

  • the sample is too small;
  • it is difficult to compare GPA from school to school, since it might be more difficult to earn a 3.20 at an Ivy League college than at a public university;
  • it is difficult to compare GPA between students within a school, since it might be more difficult to earn a 3.20 in electrical engineering than, say, in parks and recreation;
  • and, the grades of college football players may be artificially inflated.

Still, I think I’m onto something here. Wouldn’t it be great if we could replace the four‑hour SAT with the 12‑minute Wonderlic test? The marketing of it would be easy. For school administrators, simply tout a stronger correlation to college success than the SAT, and mention significantly lower costs. For students, simply state, “You can finish the Wonderlic in 5% of the time it takes to complete the SAT! You won’t have to give up your entire Saturday!” Now, wouldn’t that be grand?

January 31, 2011 at 3:01 am 14 comments

I Wanna Be Tangent to Your Curves, and Other Math Pick-Up Lines

Need help with chicks at the next math department mixer? Try a few of these…

I wish I were your derivative, so I could lie tangent to your curves.

I memorized the first 300 digits of π. If you gimme a chance, I bet I could memorize the first 7 digits of your phone number, too.

I wish I were your second derivative so I could investigate your concavities.

Hey baby, what’s your sine?

You’re a palindromic set of perfect squares: 36‑25‑36.

You are more fascinating than the Fundamental Theorem of Calculus.

I = { } when you’re not around.

I don’t like my current girlfriend. Mind if I do a you‑substitution?

Hey, baby… nice asymptote.

You may be out of my range, but I’d love to show you my domain.

I’ll take you to your limit if you show me your end behavior.

My love for you is a monotonically increasing.

I can take you to the limit as x → ∞.

No way! Your name is really Leslie? Look, I can spell your name on my calculator!

Your beauty cannot be spanned by a finite basis of vectors.

You’ve got more curves than a triple integral.

Warning: The following pick-up lines contain material that may be unsuitable for minors.

I need a little help with my calculus… can you integrate my natural log?

I wish I were a problem set, because then I’d be really hard, and you’d be doing me on the desk.

January 31, 2011 at 12:40 am Leave a comment

10s, anyone?

After a period of unprecedented dominance, Roger Federer has now gone an entire year without reaching the finals in a Grand Slam tournament. On Thursday, he was ousted from the Australian Open in straight sets by Novak Djokovic. The tennis pundits are sounding his death knell, saying he is no longer able to compete with younger players.

What if his career really is over? He has only earned $61,237,358. How will he survive?

Rumor has it that he may enroll in a doctoral program upon retirement from tennis. He’ll study string theory, of course.

Why aren’t geometricians good at tennis?
They continually try to fold the net into a cube.

(Those last two jokes are MJ4MF originals. Not that it’s worth bragging about.)

Several years ago, Penn had an ad implying that all Penn tennis balls are identical. It stated:

Penn tennis balls.
You’ve seen one.
You’ve seen them all.

I appreciate Jim Loy’s alternative commercial, which would open with the statement: 

Penn tennis balls. 
You’ve seen n.
You’ve seen n + 1.

The ad then shows one Penn tennis ball. Therefore, by mathematical induction, you’ve seen them all.

January 29, 2011 at 9:14 am Leave a comment

Tall Tail, and Other Funny Phrases

Tonight, I used the phrase “a tall tale” while talking to my sons, and I realized immediately that I had confused them. I spent the next several minutes trying to explain the difference between tale and tail. “There’s T‑A‑L‑E,” I said, “which is a type of story. A tall tale is a story that isn’t true.”

“And T‑A‑I‑L is a short tail,” Eli offered.

That made me laugh. Eli wasn’t really trying to offer a distinction between tale and tail. Rather, I think he was positing that since tall is associated with tale, then short must be associated with the other tail.

This got me to thinking — there are a lot of English idioms that would be a whole lot funnier, if one of the words were to be replaced by a synonym. (A synonym, according to Burt Bacharach, is a word you use when you can’t spell the word you first thought of.) For instance, based on Eli’s suggestion:

A short tale about a tall tail could be, perhaps, a children’s book about the posterior part of a giraffe.

Okay, so that one’s not really that funny. But I generated a list of others (below), and I think some of them are pretty damned hysterical.

Before I present the list, though, an apology. This is a math jokes blog, and this post isn’t about math jokes. But I’ve often contended that mathy folks are good at grammar because we like rules and systems, whereas literary folks are good at writing because they like words. So perhaps the implicit joke in this post is a pot‑shot at literary folks — if only their love of words followed more rules, then such linguistic silliness wouldn’t be possible.

If you’re greatly distressed about this, here’s a math pun involving a synonym. How do you tell one bathroom full of statisticians from another? Check the p-value.

Anyway, the disclaimer above reminds me of a brainteaser:

The five-letter sequence eight occurs at the end of many words and is responsible for at least two different sounds: in weight it sounds like “ate,” but in height it sounds like “ite.” What four-letter sequence, which occurs at the end of 26 words (according to More Words), is responsible for at least six different sounds? (I’ll post the answer in the comments later this week, unless someone beats me to the punch.)

Okay, on with the list…

The belle of the bawl continued to sob as the bell of the ball struck midnight.

Scientists were able to breed a pigeon with a zero (a true cross product). Two days later, this creature was bested by Mother Teresa in a race. The headline in a local newspaper read:

Newspaper Headline

It took him over an hour to strap Mickey to the roof of his station wagon. As he hummed along with the car tune playing on the radio, he thought to himself, “Gee, I sure can carry a toon.”

I ate an Easter sundae on an ice cream Sunday

Easter Sundae

She won two, and I won one, too.

He ate a clock at eight o’clock.

The farmer’s wife said to the fruit-growing sheep, “The two of ewe make quite a pear!” (Yes, this violates the format since it only uses each synonym once, but I thought it was just too funny not to include.)

On the supermarket isles of the South Pacific, you’ll find olives in the Greek aisles.

The guiding principals rarely made mature decisions, so the teachers held on to their middle school principles.

When two members of opposite sects — one Presbyterian, the other Episcopalian — have religious sex, do they scream, “Oh, God! Oh, God! Oh… my… God…”?

The florist’s flowers were worth fifty scents, and her change purse contained the cent of a woman.

Good knight,” said Batman in the dark night.

January 27, 2011 at 8:16 am 4 comments

Was Darrell Huff at the State of the Union Address?

Perhaps my all-time favorite joke:

How many school administrators does it take to change a light bulb?
Cha-a-a-a-a-a-a-a-ange?

Or, if you prefer:

How many school administrators does it take to change a light bulb?
What was wrong with the old light bulb?

These jokes seem particularly relevant after listening to last night’s State of the Union address. Here’s why.

President Obama made a bold statement about his plans for the future of education. “Over the next ten years, with so many Baby Boomers retiring from our classrooms, we want to prepare 100,000 new teachers in the fields of science, technology, engineering and math.”

Oh, please. I’m a Steel Town Democrat and generally an Obama supporter, but this is another instance of using a big number to sound impressive. Bill Clinton employed a similar tactic in his 1998 State of the Union address, when he announced funding for the training of 100,000 additional teachers to help reduce class size. Truth is, adding 100,000 teachers to the current pool of 3,000,000 teachers would only reduce class size by about 3% — which translates to 1 pupil fewer in a 25‑student classroom.

The problem is, 100,000 just isn’t enough. In 2007, Barbara Pytel claimed that hundreds of thousands will leave the teaching profession in the next few years as the baby boomer generation enters retirement. Her prediction for math and science was particularly dire. “It is estimated that the US will have a shortage of 280,000 math and science teachers by 2015” (Baby Boomer Teachers Retiring: Study Predicts Major Problem by 2015).

So what good will only 100,000 new teachers do? That’ll still leave a shortfall of 180,000.

In March 2009, Richard Ingersoll and David Perda of the University of Pennsylvania calculated that colleges and universities actually produce 150% more math and science teachers than schools require to replace those who are retiring. That’s right. Annually, the number of new teachers is 2.5 times the number that leave due to retirement.

The problem isn’t the number of new teachers or the number who retire. It’s the number of teachers who leave the profession for a better job. Statistics vary wildly, but some estimates say that 1/3 of new teachers leave the profession within 3 years, and up to 1/2 leave within 5 years.

Why do teachers leave? We all know the answers, and we have data to prove it. In the study by Ingersoll and Perda, they found that 59.9% of teachers said they leave the math classroom because of poor salary and benefits, and 67.5% said they leave because there was inadequate time to plan and prepare. Really? You mean teachers want time to do a good job, and they want to be adequately compensated for their efforts? Go figure.

Last night President Obama said, “In South Korea, teachers are known as ‘nation builders.’ Here in America, it’s time we treat the people who educate our children with the same kind of respect.” Yeah, no kidding. If you really believe that teachers deserve more respect, then please stop trying to deceive us with large numbers, Mr. President. Instead, how about some effort toward improving the salary and working conditions for our nation builders?

In his defense, I believe Obama is willing to take the steps necessary to resuscitate a broken system. Last night, I just kept wishing that he would have talked about his plans for reform that might actually fix the problem.

BONUS: Speaking of using large numbers to deceive, here’s a math problem for you. A radio commercial several years ago attempted to promote the selectivity of Dunkin Donuts. The commercial stated, “We reject more than 1,000,000 pounds of coffee beans a year.” Are they really that picky? Do a quick, back-of-the-envelope calculation to determine the percent that they reject. You can find information online about the number of Dunkin Donuts stores in the world, the amount of beans needed to make a cup of coffee, how many cups are sold, and so on. And even if you can’t, make some conservative estimates. You’ll still be surprised by the answer your calculation reveals.

January 26, 2011 at 6:13 am Leave a comment

My Perfect Sunday

WordPress is doing this thing called the Post A Week Challenge, where they challenge bloggers to publish at least one post a week for the entire year. One of the requirements to sign up is to post a message that announces you’re participating in the challenge. So, consider yourself warned — let this message serve as notice that I’ll be posting drivel at least once every seven days. (FYI, WordPress is also running a Post A Day Challenge, but I have too many commitment issues for that. I also have twin toddlers, so it’s unrealistic to think that I could actually post something every day.)

To help folks who have trouble finding something to write about every day, they are also running The Daily Post, a collection of suggestions for what to blog about. Many of these topics strike me as silly; more importantly, they aren’t relevant for a math jokes blog. For example:

  • What is your favorite sound?
  • Do you prefer to talk or text?
  • How do you define a friend?
  • Describe the sound of your laugh.

However, yesterday’s suggestion — What is your perfect Sunday? — may have been relevant for a math jokes blog. For instance, I could have written a witty post about how my perfect Sunday would involve a long walk on the beach while doing double integrals in my head. Or in the sand. While watching the sunset and thinking, “Gee, look at the majestic sky. I bet it contains all 216 web‑safe colors.”

But instead, I’d like to pretend this isn’t a math jokes blog and tell you about my truly perfect Sunday.

It would start with my twin sons sleeping till at least 7:30 a.m. (Oh, glory be!)

Following a breakfast of challah French toast prepared by my wonderful wife, we wouldn’t do much for the rest of the morning. Maybe read a good book, and then walk to the local bowling alley for a game.

Lunch at our favorite place, Pizzeria Orso.

An afternoon at a friends’ house. Our kids would enjoy their son’s toys, and the adults would enjoy watching a football game unencumbered by emotions, because no one really cared if the Bears or Packers won.

A fine dinner, maybe grilled salmon or crab cakes — or both.

Then, after the kids are asleep, retreating to the basement with a slice of chocolate cake, a scoop of chocolate ice cream, and a pint of Three Philosophers Quadrupel, poised to watch a recorded version of the Steelers beating the Jets 24‑19 in the AFC Championship to advance to Super Bowl XLV.

And finally, as I lay down to sleep, to realize exactly why all nontrivial zeros of the Riemann zeta function have a real part of ½.

(In fact, all of those great things did happen yesterday, except for that last one. Alas, no Fields Medal for me this year, either. But another Steelers trip to the Super Bowl is almost as good.)

January 25, 2011 at 8:18 am Leave a comment

More Math One-Liners

As we were dressing to play in the snow, I asked my son Eli if I could wear his hat. His response was an emphatic, “No!” When I asked why, his one-liner response made me chuckle:

Because your chin is too far from your head.

Here are some other one-liners that I’ve always enjoyed.

Pure mathematicians are like lighthouses in the middle of a swamp — brilliant, but completely useless.

If God wanted us to use the metric system, why did Jesus have 12 apostles?

I’m not worried about losing my job to a computer. They’ve yet to invent a machine that does absolutely nothing.

For every complex mathematical problem, there is a simple and elegant solution that is completely wrong.

For every complex mathematical problem, there is a solution. The difficulty lies in finding it.

A mathematics lecture is a process for transferring the notes of the teacher to the notes of the student without passing through the minds of either.

In a graph, the thickness of the curve is inversely proportional to the reliability of the data.

Statistics are like a bikini — what they reveal is suggestive, but what they conceal is vital.

January 24, 2011 at 12:27 am Leave a comment

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About MJ4MF

The Math Jokes 4 Mathy Folks blog is an online extension to the book Math Jokes 4 Mathy Folks. The blog contains jokes submitted by readers, new jokes discovered by the author, details about speaking appearances and workshops, and other random bits of information that might be interesting to the strange folks who like math jokes.

MJ4MF (offline version)

Math Jokes 4 Mathy Folks is available from Amazon, Borders, Barnes & Noble, NCTM, Robert D. Reed Publishers, and other purveyors of exceptional literature.

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