## Nationals Win Probability, and Other Meaningless Statistics

The first pitch of last night’s Nationals-Phillies game was 8:08 p.m. That’s pretty late for me on a school night, and when a 38-minute rain delay interrupted the 4th inning, well, that made a late night even later.

The Phillies scored 4 runs in the top of the 5th to take a 6‑2 lead. When the Nationals failed to score in the bottom of the 5th, I asked my friends, “What are the chances that the Nationals come back?” With only grunts in response and 10:43 glowing from the scoreboard, we decided to leave.

On the drive home, we listened as the Nationals scored 3 runs to bring it to 6‑5. That’s where the score stood in the middle of the 8th inning when I arrived home, and with the Nats only down by 1, I thought it might be worth tuning in.

The Nats then scored 3 runs in the bottom of the 8th to take an 8-6 lead. And that’s when an awesome stat flashed on the television screen:

Nats Win Probability

• Down 6-2 in the 6th: 6%
• Up 8-6 in the 8th: 93%

Seeing that statistic reminded me of a Dilbert cartoon from a quarter-century ago:

I often share Dogbert’s reaction to statistics that I read in the newspaper or hear on TV or — egad! — are sent to me via email.

I had this kind of reaction to the stat about the Nationals win probability.

For a weather forecast, a 20% chance of rain means it will rain on 20% of the days with exactly the same atmospheric conditions. Does the Nats 6% win probability mean that any team has a 6% chance of winning when they trail 6-2 in the 6th inning?

Or does it more specifically mean that the Nationals trailing 6-2 in the 6th inning to the Phillies would only win 1 out of 17 times?

Or is it far more specific still, meaning that this particular lineup of Nationals players playing against this particular lineup of Phillies players, late on a Sunday night at Nationals Stadium, during the last week of June, with 29,314 fans in attendance, with a 38-minute rain delay in the 4th inning during which I consumed a soft pretzel and a beer… are those the right “atmospheric conditions” such that the Nats have a 6% chance of winning?

As it turns out, the win probability actually includes lots of factors: whether a team is home or away, inning, number of outs, which bases are occupied, and the score difference. It does not, however, take into account the cost or caloric content of my mid-game snack.

A few other stupid statistics I’ve heard:

• Fifty percent of all people are below average.
• Everyone who has ever died has breathed oxygen.
• Of all car accidents in Canada, 0.3% involve a moose.
• Any time Detroit scores more than 100 points and holds the other team below 100 points, they almost always win.

Have you heard a dumb stat recently? Let us know in the comments.

## How Would You Answer These Questions?

The following is one of my all-time favorite assessment items:

 Which of the following is the best approximation for the volume of an ordinary chicken egg? 0.7 cm3 7 cm3 70 cm3 700 cm3

The reason it’s one of my favorites is simple: it made me think. Upon first look, I didn’t immediately know the answer, nor did I even know what problem-solving strategy I should use to attack it.

I used estimation, first assuming that the egg was spherical — and, no, that is not the start of a math joke — and then by attempting to inscribe the egg in a rectangular prism. Both of those methods gave different answers, though, and not just numerically; each led to a different letter choice from above.

Not satisfied, I then borrowed a method from Thomas Edison — I filled a measuring cup with 200 mL of water, retrieved an ordinary egg from my refrigerator, and dropped it into the cup. The water level rose by 36 mL. This proved unsatisfying, however, because although choice B is numerically closer to this estimate than choice C — only 29 mL less, compared to 34 mL more — it was five times as much as B but only half as much as C. For determining which is closer, should I use the difference or the ratio?

It was at this point that I decided the answer doesn’t matter. I had been doing some really fun math and employing lots of grey matter. I was thinking outside the box, except when I attempted to inscribed the egg in a rectangular prism and was literally thinking inside the box. And, I was having fun. What more could a boy ask for?

On a different note, here’s one of the worst assessment questions I’ve ever seen:

What is the value of x?

3 : 27 :: 4 : x

I can’t remember if it was a selected-response (nee, multiple-choice) item, or if was a constructed-response question. Either way, it has issues, because there are multiple possible values of x that could be justified.

On the other hand, it’s a great question for the classroom, because students can select a variety of correct responses, as long as they can justify their answer.

The intended answer, I’m fairly certain, is x = 36. The analogy is meant as a proportion, and 3/27 = 4/36. (Wolfram Alpha agrees with this solution.)

But given the format, it could be read as “3 is to 27 as 4 is to x,” which leaves room for interpretation. Because 27 = 33, then perhaps the correct answer is 64 = 43.

Or perhaps the answer is x = 28, because 3 + 24 = 27, and 4 + 24 = 28.

Don’t like those alternate answers? Consider the following from Math Analogies, Level 1, a software package from The Critical Thinking Company that was reviewed at One Mama’s Journey.

If this analogy represents a proportion, then the correct answer is $10.50, but that’s not one of the choices. Instead, the analogy represents the rule “add$1,” and the intended answer choice is \$10.00.

What amazing assessment items have you seen, of either the good or bad variety?

## What Do They Think of RCV in Bah Hahba?

The Society of Actuaries does it.

Seventy-five percent of Great Britain — Scotland, Northern Ireland, and the United Kingdom — does it. (Fucking Wales.)

The Academy of Motion Picture Arts and Sciences does it.

And now Maine, the first state to implement a one-to-one laptop program for all students, does it, too.

The “it” is ranked-choice voting, a method that allows voters to rank the candidates in their order of preference. When used to elect a single candidate, ranked-choice voting helps to select a winner that reflects the support of a majority of voters.

Many cities and towns already use ranked-choice voting to elect mayors and members of council. But Maine is the first state to use it for state and federal elections.

Many people, including Jennifer Lawrence, support ranked-choice voting. (That should mean something, right? After all, she’s the only person born in the 1990’s who’s won as Oscar. So far, anyway. Maybe she supports ranked-choice voting because the Academy used ranked-choice voting to award her an Oscar? Who knows.)

This video gives a very simple example of how ranked-choice voting works.

But maybe there’s a better example. Imagine that a book club is trying to decide which book they should read next, and rather than just voting for their top choice, the group instead ranks each of three books:

• Math Jokes 4 Mathy Folks (MJ4MF)
• The Grapes of Math (GM)
• Riot at the Calc Exam, and Other Mathematically Bent Stories (RCE)

The voting proceeds as follows:

 Order Number of Votes MJ4MF / Grapes / Riot 4 MJ4MF / Riot / Grapes 5 Grapes / MJ4MF / Riot 6 Grapes / Riot / MJ4MF 2 Riot / MJ4MF / Grapes 2 Riot / Grapes / MJ4MF 1

Since no one won, the candidate with the fewest first-place votes is eliminated. Sorry, Colin Adams; we’ll have to say good-bye to Riot at the Calc Exam.

Now, the voters who had their first choice eliminated will have their votes counted for their second choice instead. So, 2 additional votes go to MJ4MF, while 1 vote goes to Grapes.

This means that MJ4MF, with 9 + 2 = 11 votes, is the winner, since Grapes received only 8 + 1 = 9 votes in the second round. Sorry, Greg Tang; you should’ve chosen a less worthy adversary.

C’mon, now… you didn’t really think MJ4MF was gonna lose, did ya?

On Tuesday, voters in Maine used ranked-choice voting to decide several political races, but they also got to vote on whether to use ranked-choice voting in future elections. Because ranked-choice voting takes time to tabulate, two of Tuesday’s contests were still undecided as of Thursday morning. So, voters literally were asked to decide if they should keep or reject a system that they had never seen used in an election. Doesn’t that seem just a bit odd?

You know what else is odd? Numbers that aren’t divisible by 2.

## Fortune Bank Teller

One of the radio commercials in the GEICO “Surprising” campaign features a fortune bank teller who dispenses both greenbacks and prognostications. The commercial ends with the teller saying,

I see a yellow light serpent… and a low APR.

What you may also find surprising is that this commercial reminds me of my father-in-law, Julian Block, a nationally known tax expert. Julian used to work for a company that connected advisors to people seeking help. An operator would ask a few questions of each caller and then connect the advisee with an appropriate consultant. Sometimes, however, the advisee would be connected to the wrong expert. And the problem? The company specialized in dispensing two types of advice: tax and psychic.

You may now see why the GEICO commercial reminds me of my father-in-law. When calls were incorrectly routed to him, he would become a de facto psychic tax advisor. I imagine conversations like the following:

Young Woman: My boyfriend just proposed. Should I marry him?

Julian: That depends. What’s his tax bracket?

These combinations — fortune teller and bank teller; psychic advisor and tax advisor — yield rather whimsical new professions. It made me wonder if there were others. Sadly, an hour of brainstorming yielded only a handful of satisfactory results:

Super Hero Intendent, who still has time to fight crime after 8 hours of dealing with stopped-up toilets

Dog Street Walker, who thinks the oldest profession is picking up Spot’s poo

Antique Debt Collector, who will accept payment in Ming vases and pocket watches

Switchboard Lottery Operator, who has a 1-in-500 chance of connecting you to the right person

Social Construction Worker, who can strike up a conversation with anyone while shingling a roof

Foreign Language Flight Instructor, who will teach you how to land safely after you give her the declension for agricola

Got any others you’d add to the list? Post them in the comments.

## Stick Figure Math

I’ll never forget the first time I saw the pattern

1, 2, 4, 8, 16, __

and was dumbfounded to learn that the missing value was 31, not 32, because the pattern was not meant to represent the powers of 2, but rather, the number of pieces into which a circle is divided if n points on its circumference are joined by chords. Known as Moser’s circle problem, it represents the inherent danger in making assumptions from a limited set of data.

Last night, my sons told me about the following problem, which they encountered on a recent math competition:

What number should replace the question mark?

Well, what say you? What number do you think should appear in the middle stick figure’s head?

Hold on, let me give you a hint. This problem appeared on a multiple-choice test, and these were the answer choices:

1. 3
2. 6
3. 9
4. 12

Now that you know one of those four numbers is supposed to be correct, does that change your answer? If you thought about it in the same way that the test designers intended it, then seeing the choices probably didn’t change your answer. But if you didn’t think about it that way and you put a little more effort into it, and you came up with something a bit more complicated — like I did — well, then, the answer choices may have thrown you for a loop, too, and made you slap your head and say, “WTF?”

For me, it was Moser’s circle problem all over again.

So, here’s where I need your help: I’d like to identify various patterns that could make any of those answers seem reasonable.

In addition, I’d also love to find a few other patterns that could make some answers other than the four given choices seem reasonable.

For instance, if the numbers in the limbs are a, b, c, and d, like this…

then the formula 8a – 4d gives 8 for the first and third figures’ heads and yields 8 × 6 – 4 × 9 = 12 as the answer, which happens to be one of the four answer choices.

Oh, wait… you’d don’t like that I didn’t use all four variables? Okay, that’s fair. So how about this instead: ‑3a + b + c – 2d, which also gives ‑3 × 6 + 7 + 5 + 2 × 9 = 12.

[UPDATE (3/9/18): I sent a note to the contest organizers about this problem, and I got the following response this afternoon: “Thanks for your overall evaluation comments on [our] problems, and specifically for your input on the Stick Figure Problem. After careful consideration, we decided to give credit to every student for this question. Therefore, scores will be adjusted automatically.”]

## Six Degrees of Titillation

It was 75° today. If you live in Honolulu, Karachi, Gaberone, or Rio de Janeiro, that might not strike you as unusual. But let me assure you that during late February in Crofton, MD, a temperature that high is rather unexpected.

But no complaints. It was nice to wear only a t-shirt and no jacket, and it allowed me to use this joke at the start of my presentation:

What a beautiful day! When I was invited to this event, I suspected it’d be close to 20° outside. I just didn’t realize it’d be Celsius.

Horrible, ain’t it? But don’t worry… I’ve got more:

• If it’s 0° today, and it’s supposed to be twice as cold tomorrow, how cold is it going to be? (Stephen Wright)
• Are you a 45° angle? Because you’re acute-y.
• Why did the obtuse angle go to the beach? Because it was more than 90°.
• Are you cold? Go sit in a corner. It’s 90° over there.
• Why didn’t the circle go to college? It already had 360 degrees.
• I asked the trigonometer what the weather was like, and he said it was 15π/16 outside.
• The number you dialed is imaginary. Please rotate your phone 90° and try again.
• What brand of deodorant did the angle use? Degree.

## A Mathematical Thank-You Note

I recently sent a copy of More Jokes 4 Mathy Folks to a friend of an acquaintance, and today I received a thank-you letter from the recipient. I think the letter is worth sharing, so here you go:

Patrick —

Thanks so much for sending me More Jokes… I’ve already annoyed my entire family, and I’m only 46/111 through the book. (I think your work here is done.)

I can’t provide a formal proof, but empirically speaking, this is the best collection of math jokes known to exist. Honestly, I enjoy the blend of quips and jokes; almost everything I read translates well into a groaner I can splice into my physics classroom repertoire!

Hoping you don’t object to the informality of my “stationery” — thought you’d appreciate the utility of engineering paper.1

Thanks again! Best,
Rob

P.S. I noticed — when I looked up your address (ed. note: STALKER!) — that we only live about seven root two2 minutes apart. How would you feel about raising a pint some evening? I’d love to hear about your work and exchange a few quips!

This is one of the nicer letters I’ve received, and it was fun to be reminded that not all mail needs to be electronic. And you can bet that some of those compliments will be used on a promotional flyer soon!

1 Quarter-inch quadrille paper, if you must know.

2 He had correctly written the irrational number as

$7\sqrt{2}$

but since LaTeX looks like shit as inline text, I converted it to straight English.

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.