Nylon Calculus: In pursuit of the divine stat line

There is a geometrical proportion that occurs throughout nature, which shapes the form of everything from the lowliest one-celled ameoboid to the most grandiose galaxy of the heavens. The spontaneous and widespread recurrence of this number has led mathematicians to describe it variously as: “The fundamental tool God used while creating the universe”, “The supreme epithet of God,” and “The Divine Proportion.” You might have also heard it referred to as: “The Golden Ratio” or “The Golden Section” or just plain “Phi”, for short. It’s a non-terminating, non-repeating number that begins 1.6180339887498948482045868…

Phi has a certain harmonious appeal, which has caused people to use the ratio again and again in art, architecture, and music, since antiquity. The basketball court is not exempt to the pervasiveness of Phi. From the logarithmic spirals that comprise the nets of the goals to the densely-packed grains of leather on the ball  — the Golden Ratio is everywhere you look in the NBA, including in the box score.

Larry Bird and Fibonacci’s Box Score

Phi is an irrational number, which means it cannot be expressed as the ratio of two integers — it’s incommensurable. But one can approximate the Golden Ratio using the string of numbers in Fibonacci’s Sequence: 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144,  233… You may have a vague memory of this quirky set of digits from your high school geometry class. The sum of any two consecutive numbers in the sequence is equal to the subsequent number on the list — for example, add 8 to 13 and you’ll find the next number in the series: 21. Weirdly, the ratio of any two adjacent Fibonacci Numbers is also roughly equal to Phi (e.g., 233/144 = 1.61806).

Visually, by arranging a series of nested Golden Rectangles and then connecting the dots between the points where the whirling squares divide the Golden Sections, one creates a so-called “logarithmic spiral” that loops inward towards a diminishing point referred to as “God’s Eye”. Astonishingly, if you overlay one of these equiangular spirals on top of a photo of Larry Bird’s face the path arcs perfectly around his majestic mullet, encircles his prodigious nose, and winds directly into the eye of Basketball Jesus.

“Hold on. You have to slow down. You’re losing it. You have to take a breath. Listen to yourself. You’re connecting the mullet Larry had with…some religious hogwash.”

– Sol Robeson, basically, in Darren Aronofsky’s film, “Pi” (1998)

Thanks, Sol. Before I get too sidetracked, let me return to Fibonacci and his numbers and explain what, exactly, I mean by a Divine Stat Line. Here’s the famous sequence again:

1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144,  233…

The Divine Stat Line or Fibonacci’s Box Score is defined by those five bold numbers in the middle, there. Although various stat combinations are theoretically possible, the most feasible arrangement is probably 21 points, 13 rebounds, 8 assists, 5 steals, and 3 blocks. It’s the ideal line and one that has never been recorded in NBA history; but, the man who came closest to achieving box-score perfection was the legendary Larry Bird.

“When I was a little kid my mother told me not to stare into the sun. So once when I was six I did. The doctors didn’t know if my eyes would ever heal. I was terrified, alone in that darkness. Slowly, daylight crept in through the bandages, and I could see. But something else had changed inside of me. That day I made my first 3-pointer.”

-Larry Bird as Maximillian Cohen, in “Pi” (1998)

Bill Walton, Cosmic Guide

It was August, 1985 in a sweltering locker room buried deep beneath the parquet floor of the Boston Garden: Celtics coach KC Jones had just introduced Bill Walton to his new teammates and the players we’re busying themselves with tube socks and shoelaces in preparation for the summer’s first practice. The 7-foot red-headed mystic-numerologist sauntered over to Bird’s locker and, with his characteristic self-assuredness, he began to explain what, exactly, the back-to-back league MVP had missing from his game: i.e., the Golden Number.

“The box score is just a long string of numbers, Larry. Some say that it’s a code sent to us from God. The Hebrew word for the Boston Garden? It’s numerical translation is 144. Now the code for the Clover of Knowledge…in the Garden, right? 233. If you divide 144 into 233, the result approaches the Golden Ratio. The Golden Spiral, Larry.”

– Bill Walton as Lenny Meyer, in “Pi” (1998)

Walton was clued-into the mysteries of the universe, he explained. He had peeked behind the veil in 1977 and he was standing there, ready to impart some real knowledge to his new teammate.

Walton’s obsession with the Fibonacci Sequence explains why, during the 1985-86 season with Boston, he decided to abandon what had been his customary uniform number. Throughout his career, he had worn No. 32, but with the Celtics he opted for jersey No. 5 instead. Walton reasoned that a 5 would help complete the Fibonacci Sequence initiated by teammates Dennis Johnson (No. 3), Scott Wedman (No. 8), and Rick Carlisle (No. 34).

Although initially skeptical of Walton’s cosmic basketball theories, Bird saw enough during the season to be convinced of their merit. By the time the Celtics faced off with the Rockets in the 1986 NBA Finals, Bird had fully embraced the inexorable power of the Golden Ratio. Some grainy videographic evidence of his ascension remains intact:

In the first game of the series, Bird came as close to achieving the Divine Stat Line as any other player in history, posting a 21-point, 13-assist, 8-rebound, 4-steal line. And check this out: do you recognize that hapless defender Bird is torturing in the clip? It’s none other than Mr. Phi Slamma Jama, himself, Hakeem Olajuwon. That’s right, a bonus Phi!

The series was the pinnacle for Bird — who was capping off his third straight MVP season — and, by extension, it was the culmination for his team, who were to win their second title in three consecutive trips to the Finals. Bird, sensing that he and the Celtics were peaking, joked that he should have just “quit right there.”

Candidates for a Divine Stat Line

Bird never did approach the Golden Ratio again after the 1986 Finals, but other players surely will. So, who’s the most likely candidate to accomplish the feat among the league’s current players?

Well, for a given stat line, one can characterize the deviation from Fibonacci’s ideal using the sum of squared errors. For example, a 20-10-10-0-0 line would yield the following:

SSE = (21 – 20)2 + (13 – 10)2 + (8 – 10)2 + (5 – 0)2 + (3 – 0)2 = 1 + 9 + 4 + 25 + 9 = 48

In the table below I list the six players who have approached the Divine Stat Line most frequently this season. As of Dec. 8, 2017, each of these six guys had produced 5+ games that each equated to a sum of squared errors of no more than 50.

Not surprisingly, triple-double monsters like Russell Westbrook and LeBron James are on the list, with five near misses each. The precocious Joel Embiid has matched these seasoned superstars with his Golden Ratio-ness so far this year. But nobody in the league has closed-in on the Golden Proportion more often than Embiid’s teammate, redshirt Rookie Ben Simmons. The Sixer point forward has a 19-13-9-2-0 game to his name, a 18-10-9-5-1 night, a 23-12-8-1-0 outing, and a 21-12-10-1-0 performance, too.

Next: Larry Bird is still talking trash after 25 years of retirement

In all, he’s responsible for ten of the league’s top-100 closest approximations to Fibonacci’s Box Score, this season. At various times during the year, Simmons has achieved all of the requisite individual components for the Divine Stat Line — posting a 21-point game, three 13-rebound games, three 8-assist games, two 5-steal games, and two 3-steal games.

Clearly, it’s only a matter of time before Simmons hits on a Divine Stat Line, the only question is when will it happen?