The Algebra of the Game: A power ranking without speculation? Uncivilized!

The proliferation of broadcast media and emergence of the opinion forum has certainly “bloviated” our poor English language and its usage … “sports lingo,” obviously, can dominate such conversation.

Maybe the most abused piece of terminology in “ball talk” is the word unique. Not only is this adjective grossly over-used, it’s generally mis-used. The latest-and-greatest whatever always gets dubbed very unique – and then is immediately compared to someone or something else.

An NBA icon who was truly “one-of-a-kind” was legendary Philadelphia publicist and innovative stat-man Harvey Pollack. It is said that when a young Mr. Pollack was taken to his first lacrosse match, he invented some new statistic that would soon become commonplace in the sport – at least Bob Ryan said so when eulogizing his friend on ESPN’s Around the Horn upon his passing a couple of years ago.

Power Ratings devoid of any Subjectivity

In recent seasons, I seem to have been channeling my inner-Harvey Pollack, seeking relatively simple but non-traditional statistical combinations by which to “grade” team performance and thus rank teams.

For instance, an enlightening perspective (maybe on a team’s “grit”) can be gained simply by subtracting its home losses from its road victories. The 2016-17 Celtics’ ride to No. 1 seeding was fueled by 23 away wins against just 11 defeats on their parquet – their grade of +12 was fourth best in the class.

Scoring the Game’s Flow

At its essence, basketball is a simple game comprised of three components: Ball Movement, Shooting and Rebounding – and of course the prevention thereof through legal defensive play. With a reliable and equitable standard to measure each of these elements of play, we should be able to devise an easy equation to evaluate overall play up and down the court.

Maybe we can take overall Field Goal Percentage, add in Offensive Rebounding Percentage, then subtract Turnover Percentage (FG% + OR% - TO%) – Shooting Plus Offensive Rebounding minus Turnovers.

During this season’s first six weeks, Boston shot .441 (No. 25) from the floor, posted an OR% of .223 (No. 14) and “earned” a .132 (No. 4) on the TO scale. That computes to a SPOR-t score of 532, which ranks them behind 18 other teams.

But on the flip-side, the opposition sports a paltry score of 491 by this standard – which positions Boston at the very top of that heap.

The Celtics’ differential of +41 places them in a three-way tie at No. 7 – not bad at all for a unit that finished last season with a score of -26 (No. 23) according to this Aba-metric.


While I’m sold on the SPOR-t notion philosophically, I’ve found that the current method for calculation tends to over-reward the more proficient rebounding teams and diminish excessively those with weaker board work. [There’s a need for more tinkering … I’m open to suggestions.]

Specialty Shooting, from the free-throw and three-point stripes, grows increasingly significant by the season in the NBA. The usage of the three-ball, as measured by 3PAr, continues to rise – up to 34% from 32% last season.

Last year’s Celtics made 985 treys while missing 367 FT’s, a gain of 7.54 points per game (second only to Houston’s crazy data). Boston’s per-game differential in this “Striping” – 4.32 ppg – topped the Association and drove their unexpected success even more than their road prowess.

This season’s differential, at the six-week juncture, has slipped to +2.04 but still ranks No. 6.

Conversion Efficiency

Striping, SPOR-t and Road-Home differential provide evaluation from a diversity of angles. To this ranking smorgasbord, I’d like to add a measurement and ranking for the simple matter of converting possessions.

Ideally, I’d prefer the straight ratio of converted possessions to total possessions, but alas such data seems unavailable (I’ve been generating my own for the C’s season so far).

Last season, I computed a team’s “Empty Possessions” (i.e. the other guys’ “stops”) by adding missed FG’s (FGA’s minus FG’s) to Total Turnovers, then subtracting the team’s Offensive Rebounds. In 82 regular-season games, the East’s best team was out-played by 28 possessions – one faux-pas every three games. That relatively even play ranked Boston No. 20 by this criterion.

In winning 18 of their first 22 games, this season’s iteration of Coach Stevens’s squad has 30 fewer EP’s, a +1.36 per-game edge on the opposition, and an 11-position jump in this hierarchy.

Here’s the Celtics’ Six-week Progress Report:

Flow (EP’s): +1.36 (No. 9)
Striping: +2.04 (No. 6)
SPOR-t: +41 (No. 7-t)
Road Swag: +8 (No. 1)

Here’s the Six-week Top Ten, according to the Abacus System:

Golden State (10) – [No. 1 Flow]
Houston (15) – [No. 1 Striping]
Toronto (23) – [No. 3 Flow, Road]
Boston (24) – [No. 1 Road]
San Antonio (32) – [No. 1 SPOR-t]
Portland (35.5) – [No. 4-t SPOR-t]
Detroit (40) – [No. 4 Road]
Philadelphia (45.5) – [No. 7-t SPOR-t, Road]
Oklahoma City (48.5) – [No. 6 Flow, SPOR-t]
Indiana (51) – [No. 5 Flow]

Note: The number in parenthesis represents the sum of a team’s ranking in the four sub-categories, with its best performance noted in the brackets.

Abacus Revelation for the Road

Despite all this data-based diatribe, I’m still inclined to think that there’s a component to this beautiful game that defies measurement. Take, for example, the first quarter of the Celtics’ loss in San Antonio Friday night.

After losing the opening tap, the C’s held Pop’s gang scoreless through seven possessions, easing their way to an 11-0 lead. But the Spurs – who’d battled for an offensive rebound on each of the sixth and seventh of those Empty Possessions – made good on 13 of their next 15 chances and ended the quarter down by only five points.

Back in the day, Bird’s Celtics could create the aura that they’d taken control of play – and the outcome was no longer in doubt – even when the scoreboard suggested otherwise.

A Gregg Popovich team is cut from that same cloth – following that Q1 close, it felt as if the Spurs were destined to win that game, no matter how hard the C’s fought.

If you were listening real closely as Kyrie’s final shot rimmed out, you just might have heard a voice whispering, “Ball don’t lie!”

Now if I could only find a way to put a numerical value to Momentum …

Boston at San Antonio, Friday Dec. 8

The Algebra of a Decisive Quarter

1st Quarter
FG: C’s – 13-22, .591 / SA – 10-22, .455
3FG: C’s – 4-9, .444 / SA – 0-3, .000
FT: C’s – 1-1, 1.000 [0] / SA – 6-6, 1.000 [3]
TO: C’s – 3 / SA – 1
OR: C’s – 3 + 0 (team) / SA – 4 + 0 (team)
Poss: C’s – 22 / SA – 22
CV%: C’s – 13 / 22, .591 / SA – 13 / 22, .591

Summative Equation:
Bos – 45 Conversions + [9 “Stripes”] {11 treys “minus” 2 missed FT’s “equals” 9 stripes}
SA – 50 Conversions + [5 “Stripes”] {8 treys “minus” 3 missed FT’s “equals” 5 stripes}
Expected Outcome -- -5 Conversions + [+4 Stripes] = C’s lose by 6 points
Actual Score: Boston 102, San Antonio 105

Conversions and [Stripes} by Quarter
Bos – 13 [4] + 10 [3] + 14 [-1] + 8 [3] = 45 + [9]
SA – 13 [0] + 13 [4] + 10 [1] + 14 [0] = 50 + [5]

Summative Equation (Season-to-date):
Bos – 1278 Conversions + [+168 Stripes] {308 treys minus 140 missed FT’s equals 168 stripes}
Opp – 1219 Conversions + [+112 Stripes] {238 treys minus 126 missed FT’s equals 112 stripes}
Expected Outcome -- +59 Conversions + [+56 Stripes] = C’s win by (118 + 56) 174 points
Actual Score: Boston 2818, Opponents 2633

Conversions and [Stripes} by Quarter [Season-to-date]
Bos – 314 [46] + 298 [42] + 333 [43] + 326 [38] + 7 [-1] = 1278 + [168]
Opp – 314 [27] + 311 [38] + 284 [21] + 307 [26] + 3 [0] = 1219 + [112]