Posts tagged ‘NBA’

Russell, Robertson, and Ratios

In the NBA, a triple-double happens when a player has a double-digit total in three of the five categories (points, assists, rebounds, steals, and blocks) in a game. Triple-doubles are very rare; on average, one has been recorded only once every 27 games since 2003. So far this season, there have been 111 triple-doubles throughout the entire NBA — and Russell Westbrook has 41 of them.

Russell Westbrook

In 1961-62, Oscar Robertson set a record that Westbrook is about to break. That year, Robertson recorded 41 triple-doubles in 80 games. Westbrook recorded his 41st triple-double of the current season in just 78 games. When two fractions have the same numerator, the one with the smaller denominator is larger. Consequently, 41/78 > 41/80, so Westbrook’s accomplishment exceeds Robertson.

Oscar Robertson

But ratios can be used to make the point even more dramatically. In the early 1960’s, pro basketball games were played at a faster pace than they are today. In 1961‑62, the average game featured 126.2 possessions, meaning that Robertson typically had more than 60 tries to grab a rebound, make an assist, or score some points. By comparison, there have been an average of just 96.4 possessions per game during the current NBA season, meaning that Westbrook generally has fewer than 50 attempts per game to improve his stat line. So another ratio — the comparison of points, rebounds, and assists to number of possessions — also leans in Westbrook’s favor.

Who knew that either of these guys were such fans of math?

At Discovery Education, we’ve been having a lot of fun writing basketball problems based on real NBA data. Check out a few problems at http://www.discoveryeducation.com/nbamath, and get a glimpse of the NBA Analysis Tool within Math TechbookTM by signing up for a free 60-day trial at http://www.discoveryeducation.com/math.

#mathslamdunk

Math and the NBA All-Star Game

How awesome was Anthony Davis last night? In a word: very. He set a new All-Star Game scoring record with 52 points, adding 10 rebounds and 2 steals.

(Disclosure: I’ve liked A.D. since he was one-and-done at Kentucky. But it wasn’t until last night that I bought an Anthony Davis jersey:

Band. Wagon.)

But as much as I like A.D., I couldn’t help thinking that there needs to be an asterisk next to this new All-Star scoring record. If you only look at points, sure, 52 > 42, so Davis scored more points last night than Wilt Chamberlain scored in the 1962 All-Star Game. But that’s only a part of the mathematical story.

First, let’s talk scoring percentage. In 1962, the final score of the game was 150‑130, meaning that Chamberlain accounted for 15.0% of all scoring. The final score of last night’s game was 192‑182, meaning that Davis accounted for 13.9% of all scoring. Chamberlain gets the nod, but only slightly, and I’ll admit it’s not insignificant that Davis only played 31 minutes last night, while Chamberlain played 37 minutes in 1962. So, maybe this is a push.

But let’s consider shooting percentage. Last night, both teams combined for 55.5% shooting, whereas in 1962, they managed just 43.8% shooting. Perhaps the all-stars from 50 years ago just didn’t shoot as well as players today? Actually, that’s somewhat true: The league FG% for 1961‑62 was 42.6%, the league FG% for 2016‑17 (so far) is 45.6%. But the all-stars last night were 9.9% above the league average, whereas the all-stars in 1962 were just 1.2% above their league average, suggesting that the defense in New Orleans was negligible at best. Which brings me to my next point…

Let’s talk defense. Maybe the combined 374 points that were scored last night doesn’t convince you that defense was nonexistent. Then how about this: In the 1962 game, there were 62 personal fouls. Last night, there were only 16. Even more stark, though: In 1962, all-stars shot 95 free throws during the game; last night, they only shot 8. That’s not a typo, and it’s a pretty clear indication that no one was making much effort to contest shots.

Davis played a great game, but it doesn’t feel right that he unseats Chamberlain, given the circumstances. Not to mention, Chamberlain played a more complete game — shooting  73% from the field, grabbing 24 rebounds, and adding 1 assist.

This brings me to my final point, proportions. The teams last night scored 1/3 more points than their 1962 counterparts, and if you take away that extra third from Davis, he’d have ended the night with 39 points. So if an asterisk is good enough for Maris’s 61 and Flo-Jo’s 10.49, then it ought to be just fine for Davis’s 52, too.

But it is what it is. Congratulations, Anthony Davis.

Looking at the math of basketball is something I get to do quite a bit these days. Discovery Education has formed a partnership with the NBA, and we’re creating a collection of “problems worth solving” using NBA stats and highlight videos. Wanna see some of what we’ve done? Check out www.discoveryeducation.com/NBAMath.

NBA, Discovery, and the Math of Basketball

Last week, Discovery Education and the National Basketball Association (NBA) announced a partnership in which real-time data from stats.nba.com will flow into Math Techbook, and students will use that data to solve problems.

How cool is that?

Eighty students from John Hayden Johnson Middle School in Washington, DC, participated in the event, which was emceed by Hall-of-Famer “Big” Bob Lanier and made silly by Washington Wizards mascot G-Wiz.

G-Wiz and students at John Hayden Johnson Middle School in Washington, DC, at a joint event of the NBA and Discovery Education.

The event received a lot of press coverage, and as you may have heard, there’s no such thing as bad publicity. But one of the articles quoted me as saying:

It’s not like a beautiful, traditional math problem.

That is not what I said. I am absolutely certain that I have never used the words beautiful and traditional in the same sentence. Well, perhaps when referring to a wedding dress or an Irish cottage, maybe, but certainly not when referring to a math problem.

I was also quoted as saying:

It’s going to be messy, for sure.

That is, in fact, one of the things I did say. Because by definition, good math problems are messy. For this project, our writing team created problems that don’t have one right answer. For instance, one problem asks students to generate a formula to predict which players should be on the All‑NBA 1st Team. Should they use points and rebounds as part of their formula? If so, how much weight should they give to each? And should there be a deduction for the number of turnovers a player has? All of that is up to the student, and it’s certainly possible that more than one formula would give reasonable results. (If you don’t believe me, do a search for NBA Efficiency, TENDEX, Thibodeau, VORP, or New SPM to get a sense of some formulas currently used by professional statisticians.)

A microsite with a four sample problems is available at www.discoveryeducation.com/nbamath. To see all 16 problems and to experience the NBA Math Tool, you’ll need to login to Math Techbook; sign up for a 60‑day trial at www.discoveryeducation.com/mathtechbook.

I’m ecstatic about the problems that our writing team — which includes folks who love both math and basketball, like Brenan Bardige, Ellen Clay, Chris Shore, Shauna Hedgepeth, Katie Rhee, Jen Silverman, and Jason Slowbe — has created. One of the simpler problems they’ve written, meant for middle school students, is to determine which player should take a technical free throw. It’s not a hard problem, but students get to choose which team(s) to examine and how to use free-throw data to make their choice. With the NBA Math Tool that we’ve created, which includes FTM and FTA but not FT%, one possible formula is =ROUND(100*FTM/FTA,1), which will display the free-throw percentage to one decimal place of accuracy — though there are certainly less sophisticated formulas that will get the job done, too, and students could bypass formulas entirely by using equivalent fractions.

But a different article said that the “questions may look something like” this:

Andrew Wiggins is making 49.1% of his two-point shots and 52.3% of his threes. Which shot is he more likely to make?

Actually, we would never ask a question like this in Math Techbook, either as part of this NBA project or otherwise. By the time students start working with percentages in middle school (6.RPA.3.C), we expect that they already understand how to compare decimals (4.NF.C.7). Though basic exercises are included in the service, most problems — and especially those based on NBA data — exist at a greater depth of knowledge.

But what we might do is ask students to use proportions to make a prediction.

As you know, basketball announcers and sportswriters make predictions all the time. They talk about players being “on pace” to score some number of points or to grab a certain number of rebounds. In fact, the Washington Post recently prophesied that Steph Curry will hold the NBA’s all-time three-point record before the next presidential election.

During the first part of the event at Johnson Middle School, the students set out to make a prediction:

How many assists will John Wall finish the season with?

John Wall recently set the Wizards franchise record for assists, so the context was timely.

To solve this problem, students explored the NBA Math Tool, which now resides inside Math Techbook. This tool allows students to analyze both NBA and WNBA stats. Students considered data for the Washington Wizards:

Row 6 shows that John Wall had 98 assists through 11 games. Good information, to be sure, but it led to more questions from students than answers:

• Some players on the Wizards have played 13 games. How many games have the Wizards played so far this year?
• How many games will John Wall play this year?
• How many games are in an NBA season?

Looking at team data in the NBA Math Tool, students learned that the Wizards have played 13 games so far this year. And one student knew that every NBA team plays 82 games in a season. Good info… but now what?

One approach is to set up a proportion with the equation

$\frac{11}{13} = \frac{g}{82}$

which yields the number of games (g) that we can expect John to play this year (69), and then the equation

$\frac{11}{69} = \frac{98}{a}$

can be used to find the number of assists (a) that we can expect John to record (602).

But the eighty students in the gym were sixth- and seventh-graders, and they weren’t ready for algebraic equations. Instead, they attacked the problem by noting that Wall had 98 assists through the first 13 games, so they estimated:

• He should have about 200 assists through 25 games.
• He’d have about 400 assists through 50 games.
• He’d have about 600 assists through 75 games.
• That’s 7 games shy of a full 82‑game season, and Wall should have about 50 assists in 7 games.
• So, we can expect him to finish the season with about 650 assists.

My role at the event was to lead students through the solution as a group-problem solving activity; and then, to work with them in the media center on the free-throw problem described above. It was an incredible day! I got to co-teach with Ivory Latta, point guard for the Washington Mystics:

I got to meet some incredible people, including current players, former players, and NBA executives:

(L to R) Etan Thomas; Felipe Lopez; Patrick Vennebush, MJ4MF and Discovery Education; Bill Goodwyn, President and CEO of Discovery Education; Ivory Latta, Washington Mystics point guard; Elizabeth Lipscomb, Discovery Education; Todd Jacobson, Sr. VP of Social Responsibility, NBA; and “Big” Bob Lanier, Hall-of-Fame player for the Detroit Pistons and Milwaukee Bucks.

But most importantly, I was finally able to let the world know about this amazing project, which my team has been working on for a year.

The NBA slogan is, This is why we play. But today I say, this is why we work: to develop rich curriculum resources that are fun, relevant, and powerful in teaching kids math.

#mathslamdunk

I’m Playing Baaas-Ket-Baaall

Lego NBA Player

I recently had a meeting at the National Basketball Association (NBA) offices in New York City. I had gotten very excited about this meeting, thinking maybe I’d bump into Lebron or Kobe or Shaq or Dr. J or Jerry West or David Stern. (It could happen, ya know. Not so long ago, I bumped into Brooke Shields while attending a meeting for MoMath. All things are possible in NYC.)

But irony of ironies… when I arrived, I met no one famous; rather, one of the NBA staffers wanted to meet me because Math Jokes 4 Mathy Folks is his mom’s coffee table book. She’s a retired chemical-cum-mechanical engineer, so geeky jokes are her ilk.

Three engineers are arguing about God’s profession.

The first says, “God has to be a mechanical engineer. Look at the design of the joints and muscles.”

“No, no,” said the second. “Look at the central nervous system. All that wiring? Surely, God is an electrical engineer.”

“I think you’re both wrong,” said the third. “He’s got to be a civil engineer. Who else would put a waste management facility in the middle of a recreation area?”

Now, I know that this story likely sounds like an elaborate set-up.

Yo momma is so dorky, she reads Math Jokes 4 Mathy Folks.

Well, it’s not. All of this is true.

The wonderful young man who wanted to meet me was Daniel Feinberg. I asked about his mother’s favorite joke from Math Jokes 4 Mathy Folks, and he told me it was this one (which is sometimes known as the Pizza Theorem):

originally from Jay Fallon at Posterous Spaces,

Via email, Daniel told me:

It’s funny, because she [Daniel’s mom] hadn’t taken a look at the book in some time, and when I asked her for her favorite joke, she got sucked into reading the entire thing — again.

Now that’s a nice compliment.

Daniel isn’t an engineer or even a math guy. He loves golf, though, and his favorite joke from Math Jokes 4 Mathy Folks is:

A pastor, a doctor, and a mathematician were stuck behind a slow foursome while playing golf. The greenskeeper noticed their frustration and explained to them, “The slow group ahead of you is a bunch of blind firemen. They lost their sight saving our clubhouse from a fire last year, so we always let them play for free.”

The pastor responded, “That’s terrible! I’ll say a prayer for them.”

The doctor said, “I’ll contact my ophthalmologist friends and see if there isn’t something that can be done.”

And the mathematician asked, “Why can’t these guys play at night?”

Incidentally, Joshua Ferris included this same joke in his book To Rise Again at a Decent Hour, though the main character tells it with a priest, a minister, and a rabbi. Go figure.

I’d like to thank Daniel and his mom for their continued support. Hearing that MJ4MF made even one person smile is enough to think that it was worth writing.

Before you go, here are some basketball-related math jokes. Or maybe they’re math-related basketball jokes. Whatever. Enjoy.

What do basketball players call the last occurrence of the function that gives the greatest integer less than or equal to x?
The Final Floor.

What do athletes playing basketball and students taking a math test have in common?
They both dribble.

What’s the difference between the Knicks and a dollar bill?
You can get four quarters from a dollar bill.

Okay, maybe that last one isn’t very mathy, so here’s a mathy quote from basketball commentator and former coach Doug Collins:

Any time Detroit scores more than 100 points and holds the other team below 100 points, they almost always win.

Almost?

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.