The Algebra of the Game: C’s spelunk their way past Raptors, streak hits 12

Back in the day, Rebounding was exemplified by a Bill Russell or Dave Cowens snatching a ball well above the rim and the crowd. Wily workers of the offensive backboard like a Silas or Rodman would grind their way to optimal position for follow-ups. The “work” took place in and around what we now call the “restricted area” (not to be confused with Hubie Brown’s “painted area”).

Nowadays, when about one in three FG attempts is being launched from what they then called the “hinterlands,” a missed shot is just as likely to initiate a scramble rather than a scrum … and this team that Danny re-built is proving to be rather proficient at that little component of play.

Sunday afternoon against Toronto, the C’s generated second-chance opportunities at a rate of almost three-to-one (20-7) and more than doubled the Raptors in “follow-up” points (21-10). Six different Celtics – three off the bench – grabbed at least five rebounds.


Summative Equation:
Bos – 43 Conversions + [6 “Stripes”] {10 treys “minus” 4 missed FT’s “equals” 6 stripes}
Tor – 42 Conversions + [7 “Stripes”] {10 treys “minus” 3 missed FT’s “equals” 7 stripes}
Expected Outcome -- +1 Conversion + [-1 Stripes] = C’s win by 1 point
Actual Score: Boston 95, Toronto 94 


Through 36 minutes of play, Boston had misfired on 42 FGA’s, compared to just 24 errant Raptor attempts. Toronto hadn’t been overly active on the O-glass, but had been amazingly proficient when they were. In the first half, they converted four of their five OR’s for all of their “follow-up” tallies. In Q3, Toronto was shut out on OR’s – they only missed five shots (and still squandered a five-point lead???). The Raptors were off-target on their two Q4 second chances.


Summative Equation (Season-to-date):
Bos – 653 Conversions + [+76 “Stripes”] {152 treys “minus” 76 missed FT’s “equals” 76 stripes}
Opp – 611 Conversions + [+39 “Stripes”] {112 treys “minus” 73 missed FT’s “equals” 39 stripes}
Expected Outcome -- +42 Conversions + [+37 Stripes] = C’s win by (84 + 37) 121 points
Actual Score: Boston 1431, Opponents 1316 


In this most improbable of victories, the Stevens Gang nursed a one-point lead through a Fourth Quarter in which they made no three-point shots and attempted no FT’s.

Go figure, huh?


The Algebra of the Game

1st Quarter
FG: C’s – 10-25, .400 / Tor – 7-17, .412
3FG: C’s – 1-4, .250 / Tor – 4-9, .444
FT: C’s – 3-5, .600 [2] / Tor – 6-7, .857 [3]
TO: C’s – 5 / Tor – 7
OR: C’s – 7 + 0 (team) / Tor – 2 + 0 (team)
Poss: C’s – 25 / Tor – 25
CV%: C’s – 12 / 25, .480 / Tor – 10 / 25, .400

2nd Quarter
FG: C’s – 6-23, .261 / Tor – 11-20, .550
3FG: C’s – 3-9, .000 / Tor – 2-6, .333
FT: C’s – 5-6, .833 [2] / Tor – 1-2, .500 [0]
TO: C’s – 4 / Tor – 4
OR: C’s – 4 + 3 (team) / Tor – 3 + 0 (team)
Poss: C’s – 22 / Tor – 21
CV%: C’s – 8 / 22, .364 / Tor – 11 / 21, .524

"You see that leprechaun, man?"
3rd Quarter
FG: C’s – 10-20, .500 / Tor – 9-14, .643
3FG: C’s – 6-9, .667 / Tor – 4-5, .800
FT: C’s – 7-8, .875 [4] / Tor – 5-6, .833 [3]
TO: C’s – 2 / Tor – 4
OR: C’s – 3 + 1 (team) / Tor – 0 + 0 (team)
Poss: C’s – 22 / Tor – 21
CV%: C’s – 14 / 22, .636 / Tor – 12 / 21, .571

4th Quarter
FG: C’s – 9-19, .474 / Tor – 5-18, .278
3FG: C’s – 0-4, .000 / Tor – 0-4, .000
FT: C’s – 0-0, .000 [0] / Tor – 8-8, 1.000 [4]
TO: C’s – 4 / Tor – 2
OR: C’s – 1 + 1 (team) / Tor – 1 + 1 (team)
Poss: C’s – 21 / Tor – 22
CV%: C’s – 9 / 21, .429 / Tor – 9 / 22, .409

Full Game
FG: C’s – 35-87, .402 / Tor – 32-69, .464
3FG: C’s – 10-26, .385 / Tor – 10-24, .417
FT: C’s – 15-19, .789 [8] / Tor – 20-23, .870 [10]
TO: C’s – 15 / Tor – 17
OR: C’s – 15 + 5 (team) / Tor – 6 + 1 (team)
Poss: C’s – 90 / Tor – 89
CV%: C’s – 43 / 90, .478 / Tor – 42 / 89, .472

Note re Calculations:
The number of “possessions” is an accurate count, not a formula-based estimated value.

For purposes of clarity, the bracketed digit following the FT% is the exact count of “conversions” represented by those FTA’s.

“Possessions” calculation: FGA’s + FT conversions + TO’s – OR’s (including Team OR’s)
“Conversions” calculation: FG’s + FT conversions


Abacus Revelation for the Road

Team Rebounds – the ones not awarded to a particular player, like when a missed shot goes out of bounds or when there’s a Loose Ball Foul – were originally created by statisticians as a bookkeeping tool.

Any missed shot – FG or FT, live ball or dead ball – got tallied as a Team Rebound if it could not be awarded to a player. That’s why the shooter’s team gets a TR any time he misses the first of two FT’s, for example.

Consequently, the total of missed shots had to equal the total of rebounds (individual plus team).

In pre-computer times, the stat man always had to double-check his arithmetic. Philadelphia 76er legend Harvey Pollack said he was never so nervous as when he was re-adding Chamberlain’s point total one famous night in a town more renowned for its chocolate.

Technology has made the original need for Team Rebounds obsolete – it’s time for basketball records to track only “significant” team rebounds, the ones that extend a possession or create a new one. (Something of that sort must be in place in order to calculate possessions exactly, rather than to compute formula-based estimates that never really seem to match up with an actual count.)