## Archive for May, 2015

### Jon Lester, Eugenio Vélez, and Hitlessness

I was reminded of my second-favorite joke, which is only mildly mathy, while watching the Cubs-Nationals game last night…

What do you do with an elephant who has three balls?

Walk him, and pitch to the rhino.

(If you’re wondering what my favorite joke is, read all about it in Make Your Own (Math) Joke.)

When it comes to pitching and hitting, Jon Lester is clearly better at one than the other. His ERA is an impressive 3.30, but his batting average is .000. That’s right, he’s never gotten a hit in 9 Major League seasons. With two more outs last night — the first, a deep fly ball that was caught by Denard Span, which you can watch on Yahoo sports; the latter, a strikeout — he “improved” to an incredible 0-for-59, a Major League record for futility with the longest hitless streak to start a career.

Lester’s hitless streak is the longest ever by a pitcher. But pitchers aren’t paid to hit. The dubious distinction of the longest hitless streak for a position (non-pitching) player in the Major Leagues is held by Eugenio Vélez, who didn’t get a hit in 46 consecutive at-bats during the 2010-2011 seasons.

A starting player averages 3.3 at‑bats per game, so Velez’s record is equivalent to 14 games without a hit. Assuming that a player is actually *trying* to hit the ball, a 14-game hitless streak is an impressive accomplishment; and probabilistically, it’s damn near impossible. Not withstanding the likelihood that very few sane general managers would let such a player continue to bat, it also defies the odds that the sun wouldn’t shine at least once on this slumping hitter’s behind.

A while back, I created an **Excel file (XLS) to analyze hit streaks**. But you could also use it to analyze hitless streaks by changing a couple formulas.

Using Eugenio Velez’s career batting average of .241 (which is deflated, because it *includes* his record-breaking streak), a hitless streak of 14 games didn’t occur even once in 500,000 games using the Excel sheet model. With 162 games per season, that’s more than 3,000 seasons. Only the very best pro baseball players have a career that spans 20 seasons; those players who hit only .241 have careers that are far shorter, so 46 consecutive at-bats without a hit is impressive, indeed.

Have fun playing with the spreadsheet. Now for a trivia question…

Who is the only Major League player to have 7 hits in one 9-inning game?

Rennie Stennett, Pittsburgh Pirates, September 16, 1975. The Pirates won the game 22‑0 against the Cubs. (Johnny Burnett had 9 hits in an 18-inning game in 1932; three other players have had 7 hits in a game, but all of them required extra innings.)

And a joke…

Why was the calculus teacher bad at baseball?

He was better at fitting curves than hitting them.

And a quote…

Slowest pitch in baseball to reach the catcher? 30 mph, thrown at a 45° angle. Any slower at any other angle hits ground.

— Neil deGrasse Tyson

### Let Me Pencil You In

Pencils are infintely useful yet ridiculously simple — just a cylindrical piece of graphite surrounded by a hexagonal wooden sheath.

Well, typically.

Pencils come in all shapes and sizes, actually. They often have hexagonal cross sections, though some are octagonal, rectangular, circular, and oval.

Heck, there are even pentagonal pencils…

Which has to make you wonder, do we really need pencils in such a wide variety of shapes?

The answer may be no, but there is a practical reason for the multitude of cross sections. Can you think of any possible benefits that a rectangular pencil would have over a circular one, or vice versa?

The following problem about a pencil comes from Peter Winkler’s *Mathematical Mind-Benders*:

A pencil with pentagonal cross-section has a maker’s logo imprinted on one of its five faces. If the pencil is rolled on the table, what is the probability that it stops with the logo facing up?

And here’s a good Fermi question:

How many pencils are there in the world?

I have no idea what the answer is, but one respondent to this question on www.answers.com said, “42,462,013,000,000,000 pencils about.” The amazing part is that **17 people found this useful**!

Slightly less ambiguous is this question:

How many pencils were used to make this sculpture by George Hart?

Or maybe you prefer selected-response items…

Which of the following is the best estimate for the length of a continuous line that could be drawn using a standard pencil?

- 0.35 mile
- 3.50 miles
- 35.0 miles
- 350 miles

Or maybe you’re tired of all these questions. You didn’t come here for a quiz. You came here for some jokes. Fine.

Did you hear about the constipated mathematician?

He worked it out with a pencil.What kind of pencil?

A #2 pencil, of course!What’s the largest pencil in the world?

Pennsylvania.

If you’d like to learn more about pencils and their history — and, let’s be honest, who wouldn’t — you can **download a free copy** of Every Pencil is a Sandwich. In return, you’ll be asked to sign up for the pencils.com newsletter. If you love pencils and use them as much as I do, receiving the newsletter will be a treat, not a burden!

### Sock Probability

I don’t know if problems like the following are famous, but there sure are a lot of them online — Cut the Knot, Stack Exchange, and Braingle, for example — and they’re typical for a high school classroom or middle school math competition:

There are 14 red, 6 orange, 10 yellow, 8 green, 4 blue, 12 indigo, and 2 violet socks in my sock drawer. How many socks must I randomly remove from the drawer to guarantee that I have two socks of the same color?

You may or may not know the answer, but the problem itself leads to a follow-up question:

Why the hell do I own socks in every color of the rainbow?

That’s just weird. But if you can get past that, here is a related problem:

If I randomly remove two socks from the drawer, what is the probability that they form a matching pair?

As it turns out, I’m something of a sock aficionado. (Yeah, it’s weird, but surely not surprising. I mean, I write a math jokes blog. You didn’t think I was normal, did you?) Although the context above is fictitious, I am indeed the owner of three pairs of identical socks that look like those shown in the picture. And yes, those are *my* feet and ankles. My mathematical sexy runs all the way down to my toes.

Here’s a close-up of one of them, in case you can’t see it in the larger picture:

That’s a letter **R**, because these socks are specially designed for each foot. The other sock has a letter **L**. (Duh.)

This leads to another mathematical question, more real-world than those above:

I just finished washing these three pairs of socks. While folding them, I selected two socks at random and rolled them together. What’s the probability that there’s one R and one L?

The answer, of course, is **zero**.

Yes, I know that *theoretically* the answer should be **3/5**. But theory doesn’t match practice in this case. When I do my laundry, I sometimes forget to pay attention to the R and the L, and my sock drawer invariably results in one pair of two R’s, one pair of two L’s, and one correctly matched pair. And then when I wake up at 5:30 a.m. and put on my socks in the dark (so as not to rouse my wife from slumber), my feet feel all weird. The one with the wrong sock starts tingling, so I have to remove the socks and choose another pair entirely.

Similarly, here’s another real-world problem, based on my sock experience:

If there are 10 socks in a load of laundry that I place in the washer and then transfer to the dryer, how many socks will remain when the load is finished drying?

**Nine.** Yes, I *know* it’s a cliche. Everyone makes jokes about losing socks. It’s so overdone that the National Comedian’s Guild has declared a moratorium against them. But, *I’m not joking*. I can’t remember the last time I did a load of laundry and wasn’t missing a sock. I now have a drawer filled with unmatched socks, each like Tiger Woods longing for the return of its Lindsey Vonn.

Sadly, this post is going public just a little too late. **Lost Socks Memorial Day** was **May 9**, so we just missed that one. Likewise, we missed **No Socks Day** on **May 8**. But there are other holidays in the coming months when you can celebrate the amazing undergarments that protect our feet from our shoes:

- July (exact date TBD):
**Red Socks Day**(commemorating Sir Peter Blake) - October 4:
**Odd Socks Day**(Australia) - January (every Friday):
**Snow Sock Day**

And though not an official holiday, there are unlimited **Crazy Sock Days** happening at elementary, middle, and high schools near you.

99% of socks are single, and you don’t see them crying about it.

How do engineers make a bold fashion statement?

They wear their dark grey socks instead of the light grey ones.Somewhere, all of my socks, Tupperware lids, and ball point pens are hanging out together, just laughing at me.

—

Because I know you won’t be able to sleep tonight…

- I need to remove
**8 socks**from my sock drawer to guarantee a color match. - I don’t actually own socks in
**every color**of the rainbow. Just most colors. - The probability of selecting two socks from my drawer and getting a matching pair is
**23/140**.

### Math and Prolific Writers in the 21st Century

The FAQ at the Folger Shakespeare Library, referencing Martin Spevack, claims that Shakespeare’s complete works consist of 884,647 words. Open Source Shakespeare claims that his complete works consist of 884,421 words. Whatever. I’m not going to split hairs over one-twentieth of a percent.

What do you get if you add 1 rabbit + ½ rabbit + ¼ rabbit + … ?

Two rabbits, but that’s just splitting hares.

Those numbers got me thinking. Shakespeare — or whichever “secret author(s)” actually wrote all that stuff — is often considered to be one of the most prolific authors of all time.

Yet here’s my typical annual output over the last 5 years.

Category |
Number |
Approximate Word Length |

Email – Short | 500 | 10 |

Email – Medium | 1,500 | 100 |

Email – Long | 50 | 1,000 |

Facebook Post | 50 | 50 |

Blog Post | 70 | 600 |

Journal Article | 1 | 2,000 |

Math Joke Book | 1/5 | 12,000 |

That translates to over 250,000 words a year, which means that I write the equivalent of Shakespeare’s 37 plays and 154 sonnets in about 42 months.

I mean, sure, Shakespeare’s typical lines are something like

For as the sun is daily new and old,

So is my love still telling what is told

whereas a line from my typical email is more like

I’d like to see the storyboard for the Featherless Birds interactive by the end of the week

but I’m not talking about quality here. I’m only referring to quantity.

And in that regard, Will, you got nothing.

Of course, he does deserve props for his occasional reference to math:

There is divinity in odd numbers, either in nativity, chance or death.

— The Merry Wives of Windsor, Act V, Scene 1

And whether deliberate or not, he had a penchant for 2 × 7:

So, sure, maybe William Shakespeare was not as prolific as I am. Or, for that matter, as prolific as most 21st century office workers who sit in a cubicle, stare at a screen, and bang on a keyboard all day. But he was pretty cool.

Better three hours too soon than a minute too late.