## Posts tagged ‘Ravens’

### P (NFL ∪ Math) > 0

John Urschel is an offensive lineman for the Baltimore Ravens and admits, “I love hitting people.” As it turns out, he loves hitting the books, too. He earned a masters degree in mathematics from Penn State, and he recently published a paper with the impressive title A Cascadic Multigrid Algorithm for Computing the Fiedler Vector of Graph Laplacians in the *Journal for Computational Mathematics*.

Note that Urschel was the *lead author*, even though his three co-authors were an associate math professor from Tufts and two math professors from Penn State.

I have to wonder if the paper was fairly refereed. I mean, honestly, who in the math community is gonna tell a 6’3″, 308‑pound football player that he made an error?

A la Paul Erdös, Urschel doesn’t need much to be happy. In an essay published March 18, he wrote:

I drive a used hatchback Nissan Versa and live on less than $25k a year. It’s not because I’m frugal or trying to save for some big purchase, it’s because the things I love the most in this world (reading math, doing research, playing chess) are very, very inexpensive.

I was thinking about how Urschel has superior talent in two fields, when I saw this comment on an article on Deadspin:

Here’s the thing.

There are 1,596 players in the National Football League at any given time (32 teams with 53 players each). Throw in a few more who serve on practice squads and occasionally get a chance when someone else gets hurt, so maybe that number climbs to 2,000. Still, the chance of making it to the NFL is unbelievably remote. Recruit 757 claims that only 0.008% of all high school athletes get drafted by the NFL.

And if you can believe Wolfram Alpha, there are 2,770 mathematicians in the United States, or approximately 1/47,165 of the U.S. workforce.

Point is, the probability of becoming **either** a professional football player **or** a mathematician is ridiculously small. Becoming both is smaller still. Though John Urschel proved it’s greater than 0. The saving grace is that he seems like a down-to-earth guy who realizes how lucky he is.

To read a math article written by John Urschel, check out 1 in 600 Billion.

### One Joke Per Cent

So, I understand what Baltimore Ravens coach John Harbaugh meant when he said:

I never thought you could feel 100% elation and 100% devastation at the same time. But I learned tonight you can.

But it sure sounds to me like he has twice as much capacity for emotion as the rest of us. It reminds me of Yogi Berra’s famous quote:

Baseball is 90% mental, and the other half is physical.

Or the anonymous quote about our favorite subject:

Mathematics is 50% formulas, 50% proofs, and 50% imagination.

Dare to guess what percent of Americans wouldn’t be able to identify the math errors in those statements?

Here’s a good old-fashioned math joke involving percents:

What’s a proof?

One-half percent of alcohol.

And a slightly longer one:

“Statistics is wonderful!” said a statistician.

“How so?” asked his friend.

“Well, according to statistics, there are 42 million alligator eggs laid every year. Of those, only about 50% hatch. Of those that hatch, 75% are eaten by predators in the first 36 days. And of the rest, only 5% get to be one year old for one reason or another.”

“What’s so wonderful about that?”

“If it weren’t for statistics, we’d be up to our asses in alligators!”

### Results of a Wonderlic-SAT Comparison

Eli Manning and Tom Brady are arguably the smartest pair of quarterbacks to face each other in a Super Bowl. That’s not just hyperbole; there’s data to support it. Manning scored a 39 on the Wonderlic test, and Brady scored a 33, giving them an average score of 36. That’s the highest average ever for the starting quarterbacks in a Super Bowl.

The two starting quarterbacks for Super Bowl XLVII, Colin Kaepernick and Joe Flacco, are no intellectual slouches, either. Flacco scored a respectable 27 on the Wonderlic, and Kaepernick rocked the test with a 37, placing him *two* standard deviations above the norm. That puts him in the 97th percentile. If he wins the Super Bowl this Sunday, he’ll be the second-smartest quarterback to do so.

Last week, I asked readers to supply me with data for a research project. The Wonderlic test is used by the National Football League to measure the problem-solving abilities of prospective players. The SAT (and the ACT) have long been used as college entrance exams, and both claim to predict college success. My hypothesis is that the Wonderlic — a 12-minute, 50-question test — would be equally good at predicting college success.

The following presents the (I) results, (II) limitations of the research, and (III) some notes about the methodology. (Sorry, I don’t mean to be pretentious or to imply false erudition by using Roman numerals. I just know that some folks are interested in (I) but could give a rat’s butt about (II) or (III), so I thought dividing this post into sections might be helpful. Hopefully by using the phrase “rat’s butt,” I’ve removed all sense of pretense.)

**I. Results**

Neither the SAT nor the Wonderlic are good at predicting college success, but to my surprise, the SAT is better than the Wonderlic.

The following correlation coefficients resulted when three pair-wise correlations were performed:

- Wonderlic and GPA:
*r*= 0.0086 - SAT and GPA:
*r*= 0.0506 - Wonderlic and SAT:
*r*= 0.2897

When comparing the Wonderlic and college GPA (*n* = 46), the correlation coefficient was *r* = 0.0086, meaning that roughly 9% of the variance of college GPAs can be explained by Wonderlic scores.

When comparing the SAT and college GPA (*n* = 41), the correlation coefficient was *r* = 0.0506, meaning that roughly 22% of the variance of college GPAs can be explained by SAT scores.

When comparing the Wonderlic and SAT (*n* = 44), the correlation coefficient was *r* = 0.2897, meaning that roughly 54% of the variance of college GPAs can be explained by Wonderlic scores.

Though not quite as strongly, these results corroborate my previous findings that neither the SAT nor the Wonderlic is a very good predictor of college success, but both are pretty good predictors of scores on other standardized tests.

**II. Limitations**

A number of factors discredit the validity of this research, among them:

**Voluntary Response Bias.**The majority of respondents were above average in all categories. Additional data is needed from individuals who scored poorly on the SAT/ACT or Wonderlic or who had below-average college GPAs.**Sample Size.**It is difficult to draw conclusions from a sample of just 54 individuals.**Timing.**Those who responded often took the Wonderlic many years after taking the SAT. This is an issue with data from NFL prospects, too; they take the SAT prior to entering college, but they take the Wonderlic at least three years later. Certainly, those years of experience would influence the results.**Consistency.**College GPA is not transferrable. Without a doubt, earning a 3.1 GPA at Harvard University is more impressive than holding a 3.9 at the Univerity of the District of Columbia. Even within the same university, there can be discrepancies; it’s likely more difficult to hold a high GPA if your major is electrical engineering than, say, parks and recreation. Unfortunately, it’s one of the only means of comparing two students from different schools, apart from reputation of the issuing institution.

Consequently, this research should be taken in the spirit it was intended. It it not academic research. It was merely a tongue-in-cheek attempt to show that neither the SAT/ACT nor the Wonderlic test are terribly good at predicting college success.

That said, this analysis could serve as the impetus for an academic research project. By gathering Wonderlic scores from high school students at the same time that they take the SAT, and then tracking them to determine their success in college, the viability of the Wonderlic test as a college entrance exam could be determined. (It should be noted that the Wonderlic Personality Test (WPT) is used by the NFL when evaluating prospective players, but scores on the Wonderlic Basic Skills Test (WBST) are already accepted by some colleges.)

**III. Notes About the Method**

For consistent comparison, all college exam scores were converted to a scale based on the old SAT (out of 1600). ACT scores were converted using results of a concordance study conducted by the ACT and the College Board. Converting scores from the new SAT to the old SAT used the method described below.

Because the maximum score on the new SAT is 2400 and the maximum score on the old SAT was 1600, the following conversion formula might seem reasonable:

2/3 × new SAT = old SAT

However, there are two reasons that won’t work. First, in addition to covering the same math topics as the old SAT, the new SAT also covers Algebra II. Second, the writing section has proven to be the hardest part of the new test; the average score on the writing section is 493, since its inception in 2005; by comparison, the average scores for math and reading are 516 and 501, respectively, during the same time period.

Using scores from 2000-11, it seems that approximately 67.3% of a student’s score on the new SAT comes from the math and reading sections; the writing section only accounts for about 32.7% of the student’s total score. Second, the average score on the old SAT from 2000-05 was 1024, whereas the average combined score for the math and reading sections on the new SAT from 2005-11 was 1017, which means that the average score on the old SAT was about 0.7% higher than the average combined score on the math and reading sections of the new SAT.

Consequently, for any respondent who listed a new SAT score, I multiplied their score by 0.673 to find their score on just the math and reading sections, and then I multiplied by 1.007 to account for the higher average score on the old SAT. This is obviously an imperfect system. That said, one of the respondents told me that his combined math/reading score on the new SAT was 1390, and this formula yielded an old SAT estimate of 1410. Since the old SAT score should be slightly higher, it seems that the formula is reasonable. I therefore used this formula for all respondents who listed a new SAT score, of which there were only two.

No changes were made to the college GPAs, despite the inherent flaws described above.

Once the data was in comporable form, my good friend Excel was used to perform a linear regression and determine the correlation coefficient.