# A Slice of “Pi” To Go With Those Holiday Left-Overs

Guest Post by Abacus Reveals

Don’t you just love it when the in-game analysis of the legendary Tom Heinsohn– if Tommy-Gun hangs around long enough, he’ll be honored with a third plaque out there in Springfield – strays to the “trigonometry” of the game?

Like the magnificent oration he delivered at this summer’s Hall of Fame induction, the old coach’s words – entertainment value aside (I see you, Hank Finkel!!) – rarely fail to understandably de-compose the ten-man ballet that is the game we all so enjoy.

Strangely, there’s a little purely mathematical trigonometry in the Boston Celtics’ performance during the first eight weeks of the 2015-16 NBA calendar (which happens to be one-third of the regular season, if you’re counting). By one statistical measurement, Coach Stevens’s troops are exactly – or at least as “exact” as a non-terminating, non-repeating decimal is allowed to be – one “Pi” better than they graded out to be during last season’s surprise run to the playoffs.

Consider this data.

Last season in 82 games, Boston missed 4,018 field goal attempts and committed 1,133 turnovers; the C’s were credited with 911 offensive rebounds. If we were to add the misses and TO’s then subtract the OR’s, would we not be identifying the number of occasions last season when the Celtic offense came up empty? (Note that our “solution” would be slightly lower and a bit more accurate if we could also subtract any Team Offensive Rebounds. Access to such data, alas, continues to elude me.)

Since this calculation is derived from information easily obtainable from any box-score nowadays, let’s call these “Box-Stops.”

The Boys in Green accrued 4,240 such empty possessions while on the other end of the floor inducing 4,164 opponent foibles. For the season, then, the C’s were “stopped” 76 more times than they were able to “stop” the other guys, a nearly one (actually, 0.93) possession-per-game disadvantage – No. 23 in the league. (Through 28 games this season, the deficit has dropped to 0.54 possessions per game and the ranking to No. 17.)

In the pre-1980’s NBA, only some truly horrific opponent free throw shooting could have elevated such a team anywhere near playoff status. But the implementation of a rule whereby the value of certain field goals increases by 50 percent – not to mention a far more aggressive and savvy approach to the use of said rule in the past eight years or so – has created a way for a team to compensate for the point loss of empty possessions and “foul” foul shots.

That’s where our heroes make their surge – though the progress is grounded at the defensive end of the floor.

Time to go back to the numbers:

Last season, the Celts misfired on 412 fouls shots while tallying 660 successful treys. Simple arithmetic reveals a 248-point boost to team scoring. Opponent shooting – due in no small part to Boston’s No. 4 rating in 3-point defense – showed only a 140-point increase. The overall 108-point differential represents a swing of 1.32 points per game toward the Green corner, eighth best in the league.

Now remember, at the same time the opposition holds a 0.93 possession per game edge. Given that we’ve accounted for the specialty shooting separately, a possession may reasonably be defined as the opportunity to put two points on the scoreboard. Consequently, that 0.93 of a possession costs the team 1.86 points per game.

Therefore, by this “metric,” the 40-42 Celtics were outscored by just over half a point (1.86 – 1.32 = 0.54) a game last season, No. 18 in the Association.

(In point of fact, the C’s held an overall 13-point scoring advantage on the season, essentially one point for every six games).

Believe it or not, there were three NBA teams last season that accumulated more errant free throws than successful three-point shots. Do you think you can identify them? (Here’s a truthful but misleading hint – all three are Western Conference teams.)

 Would Parish have to stretch the floor today?

Here’s an even better head-scratcher for ya! It was fewer than ten years ago (2007-08) when, FOR THE VERY FIRST TIME EVER, the average NBA team racked up more three-pointers than misses from the charity stripe. (It took a full decade before the league’s most frequent heavers from the arc would regularly have as many three-point attempts as they did missed FT’s.)

OK, let’s get back to this season and one last visit to the box-score. The C’s have drained 265 three balls and bricked 133 FT’s (+132); their opponents 199, 170 and (+29) respectively, through 28 games. The 103-point differential converts to a per-game advantage of 3.68 points – nearly tripling their ’14-15 showing, and second in the league only to Golden State’s otherworldly 6.07 point a game edge due to this specialty shooting.

As noted earlier, the other guys are recording 0.54 more per-game box-stops so far, a cost of 1.08 points. But (since 3.68 – 1.08 = 2.60), our guys are – even fresh off the most fearsome fortnight of their young season – statistically out-achieving their foes by a little over two-and-a-half points a game. (In actuality, through 28 games the C’s outscore their opponents by 3.9 points a game.)

Consequently, after finishing last season 0.54 points per game worse than the opposition, the 2015-16 squad is 2.60 points better – an increase of 3.14, or pi.

The C’s surge on the “Box-Stop Scale” ranks No. 10 currently. The Knicks and KD’s Thunder, each with an improvement of better than nine points a game, sit atop these ratings; Phoenix and Milwaukee occupy the basement.

So … should we be anticipating a duck-boat parade through the streets of Boston come June?

Compared to the first six weeks (19 games) of 2014-15, this season’s play is essentially four (3.96) points better.

Compared to the final six weeks (23 games) of 2014-15, this season’s play is essentially two-and-a-half (2.66) points worse.

Maybe with good health, a roster tweak or two, and a similar collective second-half growth spurt in a young team’s maturity and confidence, there is a perfect storm a-brewin’.

Or maybe too much holiday “pi” has just made me giddy.

[Trivia Answer:  The three NBA teams with more errant free throws than successful three-point shots last season? Neither the Rockets nor Clippers qualified, though the Clips, Pistons and Heat are turning that dubious little trick this season. Last year’s Gang That Couldn’t Shoot Straight was comprised of Sacramento, Minnesota and the old-school stylings of the Memphis Grizzlies.]