Posts tagged ‘length’

Which is Closest?

Not too long ago, I published a blog post about end-to-end comparisons, those silly feats of computational gymnastics that try to reduce an overwhelming statistic to something more tangible. Something like this:

If each piece of candy corn sold in a year by Brach’s — the top manufacturer of the waxy confection — were laid end to end, they would circle the Earth 4.25 times.

In writing that post, I inadvertently formulated a statistic that rather surprised me:

If all the players on an NFL team were laid end to end, they’d stretch from the back of one end zone to the opposite goal line.

That the players would almost line the entire field struck me as an amazing coincidence. And it got me to thinking — might this be true for other sports?

Basketball Player Laid End to End

Not one to let sleeping dogs — or professional athletes — lie, I decided to investigate. Based on that research, here’s a simple, one-question quiz for you.

Which of the following comparisons is the most accurate?

  1. If all of the players on an NHL (hockey) roster were laid end to end, they would reach from one end of the rink to the other.
  2. If all of the players on an NBA (basketball) roster were laid end to end, they would reach from one end of the court to the other.
  3. If all of the players on an NFL (football) roster were laid end to end, they would reach from one end line to the other.
  4. If all of the players on an MLB (baseball) roster were laid end to end, they would reach from home plate to second base.
  5. If all of the players on an MLS (soccer) roster were laid end to end, they would reach from one end to the other.

As you begin to think about that question, some notes:

  • Every professional baseball stadium has different measurements. Fenway Park (Boston) is a mere 310′ from home plate to the right field wall, whereas Comerica Park (Chicago) extends 420′ from home plate to straightaway center. Consequently, the distance from second to home is used in the fourth answer choice, because it’s the same for every field.
  • To my surprise, MLS stadiums are not uniform in length and width. Who knew? The length of the field must be at least 100 meters, at most 110 meters, and anywhere in between is fine. Assume an average length of 105 meters for the fifth answer choice.

Before you read much further, let me say how much fun I’ve had discussing this question around the dinner table and at the local pub. In spite of hard facts, there is resolute disagreement about player height, roster size, and field dimensions. And the shocking (or should I say predictable?) results raise an eyebrow every time. I only mention that to persuade you to think about the question, alone or with some friends, before continuing.

Okay, you’ve cogitated? Then let’s roll.

In researching the answer to the question, I was struck by how close the total length of all players on the roster is to the length of the field, court, or rink. Coincidence? Of course, a larger field requires more players, so perhaps this is the evolution of roster size that one would expect.

To answer the question, you need to know the height of an average player, the number of players on a roster, and the dimensions of professional venues. All of that data can be found in a matter of minutes with an online search, but I’ll save you the trouble.

League Average Height (in.) Players on a Roster Combined Height, Laid End to End (ft.) Dimensions
NHL 73 23 140 200 feet (from end to end)
NFL 74 53 327 120 yards (360 feet, from end to end)
NBA 79 14 92 94 feet (from end to end)
MLB 73 23 140 127 feet (from home to second)
MLS 71 28 166 105 meters (345 feet, from end to end)

As it turns out, the MLS comparison is the least accurate. The combined heights of soccer players is only 48% of the length of their field. The NHL comparison is a little better, with players’ heights extending 70% of the length of the field. But the NFL and MLB are both very close, with the players’ heights equalling 91% of the field length and 110% of the distance from home to second, respectively. Astoundingly, if the players on an NBA team were laid end to end, they’d come just 22 inches short of covering the entire court, accounting for a miraculous 98% of the length!

So there you have it. D, final answer.

One last thought about this. I play ultimate frisbee, a sport with a field that measures 120 yards (360 feet). For tournaments, our rosters are capped at 29 players, and I suspect my amateur teammates are, on average, shorter than most professional athletes. If we assume a height of 5’10” for a typical frisbee player, then the combined height is 172 feet. That puts us in the realm of soccer, with our combined length covering just 48% of the field.

If, like me, you play a sport that isn’t one of the Big 5 in the U.S., I’d love to hear about your sport’s field and roster size, and how it ranks with the comparisons above.

August 24, 2018 at 6:47 am Leave a comment

The Be-All, End-All of End-to-End Comparisons

It’s become quite fashionable to use “end to end” comparisons to visually demonstrate just how large or long or vast something is.

  • If all the atoms in your body were laid end to end, they would be able to encircle the Earth over 41 billion times, a length of almost 56 light years. (Trove 42)
  • If you laid the Knicks’ top six big men from end to end, you would get 41 feet and 4 inches of pain, and enough sore necks, feet, knees and ankles to fill a modest orthopedic ward. (New York Times, April 11, 2013)
  • If all of the fiber optic cable in the world were laid end to end, it would encircle the Earth 25,000 times. (NPR)
  • If all the rolls of toilet paper used in the United Kingdom in a year were laid end to end, they would reach further than Mars. (@ThomasCrapperCo)
  • If you laid all the DNA from all your cells side by side, their combined length would be about twice the diameter of the Solar System. (Science Focus)
  • If your blood vessels were laid end to end, they would be over 100,000 miles long for an adult and 60,000 for a child. (Franklin Institute)
  • If you laid all the M&M’s produced in a year end to end, they would stretch for a million miles. (MF4MF)

Though ubiquitous, these comparisons are often unreliable:

I checked with Google to see just how long the [Aleppo] souk actually is, if all its streets were laid end to end, and found it to be, variously, seven, eight, ten, twelve, thirteen, sixteen, and “about 30” kilometres. (Jonathan Raban)

But accuracy be damned. The point of these comparisons is not to demonstrate precise computational ability. Instead, they are meant to provide a reference point for a statistic that would be otherwise difficult to interpret.

If all the players on an NFL team were laid end to end, they’d stretch from the back of one end zone to the opposite goal line.

(This reminds me, for no good reason, of an entry in the Washington Post Style Invitational from some years back, in which entrants were asked to submit bad similes and metaphors: “He was as tall as a 6‑foot, 3‑inch tree.”)

Such end-to-end comparisons are not new, however. According to the Quote Investigator, this type of comparison was used in 1885 to describe the Vanderbilt family’s $200,000,000 fortune:

Enough to buy 40,000,000 barrels of flour at $5 each. If these barrels were placed end to end, they would reach around the Earth on the parallel of Boston, or they would fence in every State in the Union.

Alexander Wolcott, in his 1934 bestseller While Rome Burns, quoted Dorothy Parker as saying:

If all the girls attending [the Yale prom] were laid end to end, I wouldn’t be at all surprised.

The most famous of these comparisons, however, is probably the following:

If all economists were laid end to end, they would not reach a conclusion.

Who said it? Who knows. It’s most often attributed to George Bernard Shaw, but it seems that the quip existed a full decade before Shaw was ever credited. It has also been attributed to Isaac Marcosson, Farmer Brown, Stephen Leacock, and William Baumol. Regardless of its originator, it has been reiterated and modified a thousand times:

  • If the nation’s economists were laid end to end, they would point in all directions. (Arthur H. Motley)
  • If all economists were laid end to end, there would be an orgy of mathematics.
  • If all the economists in the world were laid end to end, it would probably be a good thing.

My favorite end-to-end comparisons, like the one attributed to Shaw, are usually garden-path sentences. They begin with an astounding statistic, but just when you think some simpler comparison will be made, they smack you in the nose with a twist:

  • Just to be clear, if you carefully removed, and laid end to end, all the veins, arteries, and capillaries of your body, you will die. (Neil deGrasse Tyson)
  • If all the world’s managers were laid end to end, it would be an improvement.
  • If you laid all our laws end to end, there would be no end. (Arthur “Bugs” Bae)
  • If all the salmon caught in Canada in one year were laid end to end across the Sahara Desert, the smell would be absolutely awful.
  • If all 206 bones were removed from your body and laid end to end… you’d be dead.
  • If all the cars in the world were laid end to end, someone from California would be stupid enough to try to pass them.
  • If all the joggers were laid end to end, it would be easier to drive to work in the morning. (Milton Berle)
  • If all students who fell asleep in their seats during math class were laid end to end, they’d be a lot more comfortable.

Finally — and with absolutely no bias whatsoever (wink, wink) — I present my all-time favorite end-to-end comparison, gloriously penned by my friend and colleague Gail Englert, and which appears on the back cover of More Jokes 4 Mathy Folks:

If you took all the people who fell on the floor laughing when they read this book and laid them end-to-end, you’d have a very long line of people. It’d be a silly thing to do, but at least you’d know who to avoid at a cocktail party.

Do you have a favorite end-to-end comparison? Have at it in the comments.

August 15, 2018 at 7:35 am 1 comment

Look Before You Leap

Too predictable?

Why do frogs, kangaroos, lords and leopards like 2012?
Because it’s a leap year!
(Did you know that a group of leopards is called a “leap”?)

Speaking of leaps, a friend and I were recently discussing the following problem:

A flea can jump up to 350 times its own length. If the same were true of humans, how far would a person whose height is 5′ 6″ be able to jump?

Though the intent is clear, the problem assumes that the length of a flea is analogous to the height of a human. A would-be solver who overthinks this problem might reason that a flea’s length is approximately twice its height, in which case it could jump 350 × length = 350 × (2 × height) = 700 times its own height. Solving the proportion required by the problem, a 5′ 6″ human would be able to jump 3,850 feet, which is twice the intended answer.

Not that it matters. Even long jumper Mike Powell, who holds the world record with a jump of 29′ 4″, was not able to leap even five times his height.

But the problem reminded me of this joke…

A team of engineers was required to measure the height of a flag pole. They only had a measuring tape, and they were frustrated that they couldn’t slide the tape up the pole. After a while, a mathematician happens by, hears about their problem, removes the pole from the ground, and proceeds to measure it easily.

When he leaves, one engineer says, “That is just like a mathematician! We need to know the height, and he gives us the length!”

February 29, 2012 at 11:18 am Leave a comment

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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