A bat and a ball cost $1.10 in total
There's a problem, if you can call it that – because its function is not to be solved, but missolved – which runs as follows:
A bat and a ball cost $1.10 in total. The bat costs $1.00 more than the ball. How much does the ball cost?
This question is often used to prove why people are incapable of critical thinking, and it often comes in the first chapter of a book designed to reveal the one true secret to thinking correctly.
The trouble is that this is the only question that ever comes up.
This makes me believe that the bat-and-ball problem is in fact the only example of the bat-and-ball problem.
If there were twelve questions that we regularly misunderstood the same way we misunderstand bat-and-ball, the other eleven would make at least one appearance in one or another of these books.
But they never do, and all of these researchers continue to cite the same old bat-and-ball problem over and over and over, to the point at which Larry has seen me bring home a book on cognition from the library, turn its first few pages, and say "it's just another bat-and-ball book!"
I don't know how many of these authors ever try the bat-and-ball problem on another human.
Here's what happened when I tried it on Larry.
"A bat and a ball cost $1.10 in total. The bat costs $1.00 more than the ball. How much does the ball cost?"
"Wait," Larry said. "Say that again."
"A bat and a ball cost $1.10 in total. The bat costs $1.00 more than the ball. How much does the ball cost?"
"Bat plus ball equals $1.10," Larry said. "The bat costs $1.00, so the ball costs –"
He paused and looked at me. "Say it again slowly."
"A bat and a ball cost $1.10 in total. The bat costs $1.00 more than the ball –"
"So the bat costs whatever the ball costs plus a dollar?"
"Right," I said. "If the ball cost 25 cents, the bat would cost a dollar and 25 cents."
"Got it," Larry said. "And the total's $1.10? Then the ball costs $0.05 and the bat costs $1.05."
The original point of the bat-and-ball problem was to trick people into providing the wrong answer, not only by encouraging round-number thinking but also by including the phrase "the bat costs $1.00" right in the middle of the riddle.
(It's worth noting that the only other riddle I can think of that works this way is "How many of each animal did Moses take on the ark?" which doesn't often get mentioned in these cognitive fallacy books unless you're reading Kahneman, and you should.)
But the current function of the bat-and-ball problem is to serve as a substitute for original research. If bat-and-ball thinking was really an issue, in terms of how real humans solved real problems, anyone who wrote a book on cognition might be able to come up with similar types of questions on their own and test them on real people.
But why do that when you can cite one question developed specifically by one person (Shane Frederick, the Richard Ely Professor of Marketing at Yale) to prompt a specific kind of cognitive error, and use the results of his study in lieu of your own?
All of this is to say that the internet has become an enormous bat-and-ball problem.
Not only is it trying to manipulate you into providing the responses it wants you to provide (even if those responses include cognitive errors), but it's also generating these manipulations by recycling an unvetted collection of inputs.
If you haven't yet gotten a chance to read Gisele Navarro and Danny Ashton's "How to find helpful content in a sea of made-for-Google BS," recently published on HouseFresh, you should.
I will admit that I was a little nervous, halfway through the article, that they would post a slightly blurry screenshot of my face along with the admonishment that there wasn't any way I could publish a new personal finance article every day and still produce quality work, especially because I also run this blog where I write about theater and education and how can I do all of that while also being a personal finance expert????
First of all, you may read my most recent feature on Vox, "What to know before you start investing," and let me know how you think my personal finance expertise holds up.
Second of all, I do take my work extremely seriously, and that doesn't prevent me from working extremely quickly. The other day I was updating an article about top business credit cards, and when I checked the recommendations I did in fact do the math. If Card X offers Y points per dollar and each point has Z value, how does that compare to Card X1 that offers Y1 points per dollar with Z1 value? What if Card X2 offers Y2 points per dollar but there's a quarterly cap? (I've been doing this math for over a decade and I've gotten a lot faster at it than I used to be.)
Third of all, I'm not getting the assignments I used to. Not by half.
This is, I suspect, because of the bat-and-ball problem. I wouldn't have written 1,000 words explaining the problem if I didn't believe it to be the single best analogy for what's happening online right now.
Fortunately, there's a solution to the bat-and-ball problem.
(OH MY BLOG NICOLE ARE YOU GOING TO SAY IT'S ONE-TO-ONE EDUCATION)
(DID I REALLY READ THIS ENTIRE THING FOR YOU JUST TO TELL ME THAT TALKING THROUGH A PROBLEM WITH SOMEONE HELPS YOU TO SOLVE IT)
(IS THAT WHY YOU INCLUDED THE EXAMPLE WHERE YOU TALKED THROUGH THE PROBLEM WITH LARRY)
The solution is to write better problems.
Give us something we can solve without feeling tricked.
Make the rest of the internet as dull as that slimy coupon insert that used to come with the evening paper.
And yes, I am still available for personal finance freelance writing assignments – but I'm also here, writing this, for you, and tomorrow morning I will go back to writing my musical. ❤️
(p.s. yes I am aware that Frederick wrote two other cognitive riddles in addition to bat-and-ball, you may look them up on your own.)