### Better parenting through science

Owen's latest obsession is basketball. Scratch that, Owen's obsession has been basketball, for a while now. He practices his shot twice a day, once at school and again after school on the hoop we bought him for his birthday last year.

His practice routine is to shoot until he scores some predetermined number of points, usually 50 to 100. Like most young basketball players, he has been spending a lot of time shooting long-distance three-pointers. However, after missing several in a row he gets very frustrated, which starts a negative feedback loop that causes him to miss more shots (lack of concentration), which causes him to get more upset, etc.

Sometimes he's able to remind himself of what Kobe says: "I'll make the next one." But unfortunately, the more his shot improves, the more he's unsatisfied with anything less than perfection. I had been at a loss lately because, while I'd like to tell him that the likelihood of making a shot is just that, a mere probability, not a certainty. But this point is subtle enough to be missed by 90% of basketball players, based on my experience in pick-up games (and made-up percentages). I always shake my head when I play with people who yell at their teammates after they miss two shots in a row. "Com'mon, man!" Come on? As in, come on small-number binomial statistics?!

Anyway, this weekend when Owen was crying after missing too many shots in a row, I said "Owen, do you think we could---hmmmm, I don't know. Maybe you can't handle it..."

"Wait, what? Can't handle what?" he asked.

"Oh, nothing. I just had a cool idea about an experiment we could do. But I'm not sure you can do it if you're crying."

"What's an experiment?"

"It's something you can do to figure out how the world works."

"Oh...I want one."

"Okay, get a pen, paper and the measuring tape."

We began by marking off regular, 1-foot intervals on the "court."

Starting at 3 feet from the back of the rim...

Out to 16 feet, by the air conditioner.

I then had Owen take 10 shots at each position, keeping track of the number of made shots out of 10. Owen really liked the process of recording the distance and number of shots made after each round. However, note the "instrument failure" at 5 feet, when he nearly lost it after missing the first 3 shots. I reset the instrument ("Take a deep breath. Remember what Kobe says.") and he made 7 of 10.

Half way through, he was beginning to predict how many he'd make at the next step back. "I bet I'm going to make 3 shots at 13 feet." Then, at 16 feet, "Dad, it will be okay if I only make 0 shots or 1 shot from here!"

After we were done, I told him: "These numbers right here, these are (whispering) data." He asked, "Whoa...what are data?" I replied, "They're pieces of information that tell us about how the world works. We can plot them, model them and start understanding."
Owen typed the numbers into a text file, and I read them into IDL to make the plot above. I asked him a bunch of questions and we had a great discussion of topics including:
• What kind of shots are the easiest? "3 feet or 4 feet."
• Is it okay to miss longer shots? "Yeah, they're harder."
• "Dad, this mark means 3, and this mark means 5, and this is 7!"
• How many shots do you think you'll make at 10 feet? "Um...five!" We then checked the log sheet and high-fived.
Next weekend we'll go over how to fit a linear function of distance and compare it to an alternative model (logistic function) using Bayesian parameter estimation and evidence ratios.

Or maybe we'll just shoot around.

kelle said…
JohnJohn, I think you're gonna have to write a book. This is just *too* amazing.
Stephanie Casey said…
Wowzers. That is high level thinking! You should celebrate tonight with a Justin Beaver music party!
blissful_e said…
Awesome! What a great breakthrough in his thinking.

Love how you whispered "data." I do that, too, when I'm getting the kids intrigued with something. Soooo much fun to expand their minds!
Duane said…
This is amazing! I think the canonical numbers for scoring are 50% for 2pts and 33% for 3pts - that's to say that the best average around 1pt per shot. From the look of that curve, he may be close to those numbers already! Regardless, it's a marvelous way to give perspective on performance. I will be sure to remember this experiment for my kids. Thanks!
Natalie said…
I love this!

### On the Height of J.J. Barea

Dallas Mavericks point guard J.J. Barea standing between two very tall people (from: Picassa user photoasisphoto).

Congrats to the Dallas Mavericks, who beat the Miami Heat tonight in game six to win the NBA championship.

Okay, with that out of the way, just how tall is the busy-footed Maverick point guard J.J. Barea? He's listed as 6-foot on NBA.com, but no one, not even the sports casters, believes that he can possibly be that tall. He looks like a super-fast Hobbit out there. But could that just be relative scaling, with him standing next to a bunch of extremely tall people? People on Yahoo! Answers think so---I know because I've been Google searching "J.J. Barea Height" for the past 15 minutes.

So I decided to find a photo and settle the issue once and for all.

I then used the basketball as my metric. Wikipedia states that an NBA basketball is 29.5 inches in circumfe…

### Finding Blissful Clarity by Tuning Out

It's been a minute since I've posted here. My last post was back in April, so it has actually been something like 193,000 minutes, but I like how the kids say "it's been a minute," so I'll stick with that.
As I've said before, I use this space to work out the truths in my life. Writing is a valuable way of taking the non-linear jumble of thoughts in my head and linearizing them by putting them down on the page. In short, writing helps me figure things out. However, logical thinking is not the only way of knowing the world. Another way is to recognize, listen to, and trust one's emotions. Yes, emotions are important for figuring things out.
Back in April, when I last posted here, my emotions were largely characterized by fear, sadness, anger, frustration, confusion and despair. I say largely, because this is what I was feeling on large scales; the world outside of my immediate influence. On smaller scales, where my wife, children and friends reside, I…

### The Force is strong with this one...

Last night we were reviewing multiplication tables with Owen. The family fired off doublets of numbers and Owen confidently multiplied away. In the middle of the review Owen stopped and said, "I noticed something. 2 times 2 is 4. If you subtract 1 it's 3. That's equal to taking 2 and adding 1, and then taking 2 and subtracting 1, and multiplying. So 1 times 3 is 2 times 2 minus 1."

I have to admit, that I didn't quite get it at first. I asked him to repeat with another number and he did with six: "6 times 6 is 36. 36 minus 1 is 35. That's the same as 6-1 times 6+1, which is 35."

Ummmmm....wait. Huh? Lemme see...oh. OH! WOW! Owen figured out

x^2 - 1 = (x - 1) (x +1)

So $6 \times 8 = 7 \times 7 - 1 = (7-1) (7+1) = 48$. That's actually pretty handy!

You can see it in the image above. Look at the elements perpendicular to the diagonal. There's 48 bracketing 49, 35 bracketing 36, etc... After a bit more thought we…