## Shot Effect on Shooting Accuracy

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• Roland s site (http://www.82games.com/index.htm) provides some very cool data, lots of stuff to chew on. My first bite is to test DeanO s hypothesis on the
Message 1 of 3 , Oct 12, 2003
Roland's site (http://www.82games.com/index.htm) provides some very cool
data, lots of stuff to chew on. My first bite is to test DeanO's hypothesis
on the relationship between shot clock and offensive effectiveness. The site
breaks down the amount of clock into four discrete states:

Elapsed shot clock time
0-10 seconds
11-15
16-20
21-24

The leaguewide averages for Effective FG% by shot clock state:

0-10 11-15 16-20 21-24

51.8% 46.0% 44.7% 40.8%

These differences are statistically significant. Here, I'll paste the ANOVA
results from the Minitab output:

Analysis of Variance for Eff%%
Source DF SS MS F P
state 3 0.181590 0.060530 115.42 0.000
Error 112 0.058738 0.000524
Total 115 0.240329
Individual 95% CIs For Mean
Based on Pooled StDev
Level N Mean StDev ------+---------+---------+---------+
0-10 29 0.51786 0.01880 (-*-)
11-15 29 0.46021 0.02815 (-*--)
16-20 29 0.44652 0.02102 (--*-)
21-24 29 0.40759 0.02259 (-*--)
------+---------+---------+---------+
Pooled StDev = 0.02290 0.420 0.455 0.490 0.525

Here's the breakdown of each team's EFF% relative to their total EFF% within
each shot clock state (EFF%_state - EFF%_season)

TEAM 0-10 11-15 16-20 21-24

ATL 4.1% -1.5% -2.3% -7.7%
BOS 2.5% 0.2% -0.7% -8.2%
CHI 5.9% -4.7% -4.0% -3.8%
CLE 4.4% -2.4% -2.4% -7.2%
DAL 4.2% 0.6% -2.7% -11.2%**
DEN 4.1% -1.1% -3.2% -5.9%
DET 5.7% -0.3% -2.6% -9.2%
GS 4.7% -3.9% -3.1% -6.5%
HOU 4.4% -2.0% -1.4% -5.3%
IND 4.2% 0.5% -4.1% -6.8%
LAC 7.3%** -4.2% -3.3% -8.2%
LAK 4.7% -2.9% -2.3% -5.9%
MEM 4.6% -1.9% -3.4% -7.0%
MIA 4.5% -4.5% 1.1%** -5.1%
MIL 3.5% -0.1% -2.4% -6.3%
MIN 5.9% -1.6% -5.6%* -8.0%
NJ 4.8% -3.7% -3.1% -4.9%
NO 4.7% 0.5% -3.4% -8.4%
NY 2.6% -0.1% -2.2% -3.7%
ORL 2.7% -0.4% -3.3% -5.4%
PHI 5.2% -2.8% -4.0% -3.8%
PHX 3.1% 0.7% -3.7% -7.7%
POR 4.2% -1.1% 0.0%* -9.1%
SAC 2.7% -1.2% -3.0% -4.9%
SAN 4.0% -0.7% -1.9% -7.0%
SEA 5.4% -0.2% -4.7% -5.1%
TRN 5.1% -2.9% -3.5% -3.1%
UTA 5.1% 0.5% -2.1% -9.2%
WAZ 3.6% 1.9% -1.7% -7.3%

* Significant at 5%
** significant at 1%

It's pretty clear from this that teams consistently shoot _much_ worse at
the tail end of shot clocks.

ed
• ... very cool ... My own first reaction to 82games is to wonder if it isn t too good to be true. But I ll put my skepticism aside for the moment. ...
Message 2 of 3 , Oct 14, 2003
--- In APBR_analysis@yahoogroups.com, igor eduardo küpfer
<igorkupfer@r...> wrote:
> Roland's site (http://www.82games.com/index.htm) provides some
very cool
> data, lots of stuff to chew on.

My own first reaction to 82games is to wonder if it isn't too good
to be true. But I'll put my skepticism aside for the moment.

>My first bite is to test DeanO's hypothesis
> on the relationship between shot clock and offensive
effectiveness. The site
> breaks down the amount of clock into four discrete states:

> The leaguewide averages for Effective FG% by shot clock state:
>
> 0-10 11-15 16-20 21-24
>
> 51.8% 46.0% 44.7% 40.8%
>
> These differences are statistically significant...

Presumably, the 0-10 sec 'state' includes offensive putbacks, as
well as fast-breaks and the occasional backcourt steal.

I've averaged the teams' rates into a league-wide rate table,
summarized thus:

range Att. eFG% Pts FGA 24sec
00-10 .397 .518 33.2 32.0 5
11;15 .250 .460 18.6 20.2 13
16-20 .230 .447 16.6 18.6 18
21-24 .124 .408 08.1 10.0 22.2
total 1.00 .473 76.5 80.8 12.1
35.6 .680

'range' is what Ed was calling shot clock 'state'.

The 'Att.' column is the % of shots taken in the various ranges of
the shot clock.

eFG% does not, apparently, include points from FT.

'Pts' thus is a measure of points from FG.

FGA is a number I've calculated as ( FGA = Pts x 2 / eFG% ).

Under '24sec' is an estimated average time of shot-release within
the associated range. Thus, shots taken at 11-15 sec are considered
to all be taken at 13 sec, for purposes of calculation.

The average time on the clock when a shot is attempted is here
estimated at 12.1 (from the parameters in the chart).

The number 35.6 is 2880 seconds ( = 48 x 60 ) divided by total FGA.
Thus a team attempts a FG every 35.6 seconds.

The factor .680 is ( 2 x 12.1 / 35.6 ), or the percent of time that
ultimately leads to a FG attempt. Presumably the other 32% leads to
FT and turnovers.

Now, if we assume this .68 number is constant, and plug in
alternative parameters, we can estimate how scoring and shooting %
might change with other shot-clock states.

Suppose a team manages to get their shots off more quickly, without
hurting their shooting percentages:

range Att. eFG% Pts FGA 24sec
0-10 .420 .518 37.1 35.8 5
11;15 .270 .460 21.2 23.0 13
16-20 .240 .447 18.3 20.5 18
21-24 .070 .408 04.9 06.0 22.2
total 1.000 .477 81.4 85.2 11.5
33.8 .680

Reducing last-seconds shots by almost half has boosted eFG% by a
mere .004; but the decreased time-per-possession has upped scoring
by 5 PPG.

What about increasing the shot-clock to 30 seconds? While this
introduces a number of unknowns, we can play around with some
possibilities.

Suppose eFG% remain the same for early, late, and middle parts of
the shot clock. Further, let's assume the .68 is constant. And for
starters, assume (optimistically) that teams continue to shoot
within 12.5 seconds, on average:

range Att. eFG% Pts FGA 30sec
0-10 .400 .518 32.4 31.3 5
11;18 .360 .460 26.0 28.2 14
19-26 .210 .447 14.7 16.4 22
27-30 .030 .408 1.9 2.3 28
total 1.000 .479 75.0 78.3 12.5
36.8 .680

Here, I've merely tweaked the Att. column to add up to 1.00. Now,
last-second shots are only a quarter of the frequency they really
are. But amazingly (to me), eFG% is only up .006

Meanwhile, scoring has actually dropped by 1.5 PPG; and this is
perhaps unrealistically optimistic.

Another possibility in the 30-seconds-to-shoot fantasy is that teams
might still let the clock run out at the same frequency:

range Att. eFG% Pts FGA 30sec
0-10 .400 .518 29.1 28.1 5
11;18 .250 .460 16.2 17.6 14
19-26 .230 .447 14.4 16.2 22
27-30 .120 .408 6.9 8.4 28
total 1.000 .474 66.6 70.3 13.9
41.0 .680

This is the pessimistic end. While eFG% is effectively unchanged,
total points have plummeted by 10 PPG, due to the increase of 1.8
sec/possession.

While I've made assumptions within these scenarios, the numerical
evidence supports the idea that lengthening the shot clock could
only reduce scoring in the NBA.

But I'm not 100% convinced. What we can't prove beforehand is that
players would perform identically under the changed conditions.
Specifically, would aggressive defenders maintain their stamina for
the extra 6 seconds?

Mike G
• ... I would agree with this because of the simple principle that a smaller shot clock means more possessions. Lengthening the shot clock would require less
Message 3 of 3 , Oct 15, 2003
>While I've made assumptions within these scenarios, the numerical
>evidence supports the idea that lengthening the shot clock could
>only reduce scoring in the NBA.

I would agree with this because of the simple principle that a smaller shot
clock means more possessions. Lengthening the shot clock would require
less shots, especially from teams like the Miami Heat who already run
agonizingly slow. Lowering the shot clock ensures that quicker (and thus
more) shots are taken. I'm sure that there's a point of diminished returns
though, where the extra shots gained are cancelled out by the lower
accuracy rating.

>But I'm not 100% convinced. What we can't prove beforehand is that
>players would perform identically under the changed conditions.
>Specifically, would aggressive defenders maintain their stamina for
>the extra 6 seconds?

That would make for a very interesting study. Does defensive intensity and
aggressiveness change at the shot clock diminishes? You could check it out
by seeing if there's an increased rate of steals and blocks during the last
five or ten seconds of the shot clock. I would imagine that the rate would
be higher, because teams usually try to put more pressure on the ball as
the shot clock winds down, and the offense is more often then not forced to
take a low percentage shot.

Along the same lines as the defenders maintaining stamina for an extra six
seconds - Would it be possible to chart defensive effectiveness based on
per possession based on shot clock left? Even more interestingly, how
about defensive effectiveness for individual players as game time
accumulates? i.e. How less effective is Bruce Bowen after 15 minutes then
at the start of a game? This would be vital information for coaches for
rely on defensive stoppers like Bowen and Michael Curry, and I can't say
that I've ever run across it. The only way I would know of to determine
such information would be to study individual game box scores and
videotape, which is impossible since I'm in college right now ;)
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