## Times Fouled and Possessions

Expand Messages
• I have noticed that many people have used the following formula to estimate possessions: FGA + (FTA)(.4) + TO - OReb The times fouled shooting factor should be
Message 1 of 8 , Jun 22, 2003
I have noticed that many people have used the following formula to
estimate possessions:

FGA + (FTA)(.4) + TO - OReb

The times fouled shooting factor should be .457; not .4.

This figure is easily derived using the following 2001-02 NBA team
averages...

Free Throw Attempts (FTA) = 1953
Technical Foul Free Throw Attempts (TFTA) = 82
Good plus Foul Shooting Opportunities (GF) = 160

Adjusted Free Throw Attempts will be used since TFTA have no relation
to shooting fouls = 1953 - 82 = 1871

This formula gives Times Fouled Shooting (TFS) = (AFTA - GF / 2) + GF
= (1871 - 160 / 2) + 160 = (1711 / 2) + 160 = 855.5 + 160 = 1015.5

The factor used to estimate TFS = 1015.5 / 1871 = .543

Since when estimating possessions, GF possessions are included in
Field Goal Attempts, the formula is adjusted to exclude GF.

The new factor = 855.5 / 1871 = .457

Therefore, the correct formula to estimate possessions = FGA + (AFTA)
(.457) + TO - OReb

GF may be estimated by subtracting (TFS)(2) from AFTA.

Ben Ricks
• could you please run the numbers for say the 97-98 season for each team and list poss/48min game for each team (both off and def poss)? thanks... bob chaikin
Message 2 of 8 , Jun 22, 2003

could you please run the numbers for say the 97-98 season for each team and list poss/48min game for each team (both off and def poss)? thanks...

bob chaikin
bchaikin@...
• Bob I don t have each team s technical FTA. Here are possessions per 48 minutes without team rebounds using FGA + (AFTA)(.457) + TO - OReb. Team rebounds are
Message 3 of 8 , Jun 22, 2003
Bob

I don't have each team's technical FTA. Here are possessions per 48
minutes without team rebounds using FGA + (AFTA)(.457) + TO - OReb.
Team rebounds are normally close anyway:

1997-98 OFF DEF Diff
Chicago 91.5 91.2 +0.3
Indiana 89.5 90.0 -0.5
Miami 89.8 90.0 -0.2
Charlotte 91.6 91.6 0.0
Atlanta 89.6 89.9 -0.3
Cleveland 91.7 92.1 -0.4
New Jersey 93.5 93.4 +0.1
New York 89.9 90.4 -0.5
Washington 93.9 93.8 +0.1
Orlando 90.1 88.9 +1.2
Detroit 90.8 90.1 +0.7
Boston 95.7 94.9 +0.8
Milwaukee 92.1 92.4 -0.3
Toronto 94.7 95.0 -0.3

Utah 91.6 91.4 +0.2
Seattle 91.9 91.5 +0.4
Los Angeles-L 95.6 95.6 0.0
Phoenix 93.4 93.5 -0.1
San Antonio 89.8 90.6 -0.8
Portland 92.3 92.3 0.0
Minnesota 94.9 95.1 -0.2
Houston 93.3 93.1 +0.2
Sacramento 94.2 94.2 0.0
Dallas 91.8 91.7 +0.1
Vancouver 94.2 93.7 +0.5
Golden State 93.7 93.6 +0.1
Los Angeles-C 94.6 94.5 +0.1
Denver 91.6 91.7 -0.1

The biggest difference is +/- 0.8 possessions per 48 minutes.

Ben Ricks

--- In APBR_analysis@yahoogroups.com, bchaikin@a... wrote:
>
> could you please run the numbers for say the 97-98 season for each
team and
> list poss/48min game for each team (both off and def poss)?
thanks...
>
> bob chaikin
> bchaikin@b...
• ... From: bricks299 To: Sent: Sunday, June 22, 2003 1:45 PM Subject: [APBR_analysis] Re: Times
Message 4 of 8 , Jun 22, 2003
----- Original Message -----
From: "bricks299" <homecourtgames@...>
To: <APBR_analysis@yahoogroups.com>
Sent: Sunday, June 22, 2003 1:45 PM
Subject: [APBR_analysis] Re: Times Fouled and Possessions

> Bob
>
> I don't have each team's technical FTA. Here are possessions per 48
> minutes without team rebounds using FGA + (AFTA)(.457) + TO - OReb.
> Team rebounds are normally close anyway:
>

<snip>

The following is a comparison of the two FTA coefficients (.4 vs .457), as
shown by the differences between offensive possessions and defensive
possessions,by season. The smaller coefficient outperforms the larger
exactly half the time, although with a larger standard error. The difference
is small enough (to me) as to not warrant using the extra decimal places.
What is needed is some empirical data, counting actual possessions in a
game, and seeing how close we are.

TrimMean SEMean
.4 .457 .4 .457

1974 -.037 -.044 .180 .194
1975 +.055 +.043 .162 .151
1976 +.702 +.693 .381 .371
1977 -.006 -.008 .133 .117
1978 +.072 +.102 .164 .145
1979 -.031 -.015 .096 .084
1980 -.158 -.167 .171 .197
1981 +.045 +.025 .153 .153
1982 -.016 -.013 .128 .119
1983 -.016 -.007 .145 .122
1984 -.005 -.001 .118 .120
1985 -.005 -.005 .217 .208
1986 -.009 +.004 .089 .082
1987 +.012 +.015 .096 .084
1988 +.004 +.019 .158 .134
1989 +.011 -.005 .113 .095
1990 -.013 -.013 .118 .102
1991 -.057 -.025 .159 .152
1992 +.061 +.064 .181 .169
1993 -.032 -.040 .090 .069
1994 -.090 -.080 .316 .305
1995 -.006 -.012 .106 .103
1996 -.003 -.003 .086 .081
1997 +.012 +.021 .085 .081
1998 -.008 -.003 .097 .084
1999 +.017 +.013 .162 .167

ed
• ... vs .457), as ... larger ... difference ... places. ... in a ... I ve got some of these. I ll try to pass them on after I m done traveling (again). My
Message 5 of 8 , Jun 22, 2003
--- In APBR_analysis@yahoogroups.com, igor eduardo küpfer
<igorkupfer@r...> wrote:
> <snip>
>
> The following is a comparison of the two FTA coefficients (.4
vs .457), as
> shown by the differences between offensive possessions and defensive
> possessions,by season. The smaller coefficient outperforms the
larger
> exactly half the time, although with a larger standard error. The
difference
> is small enough (to me) as to not warrant using the extra decimal
places.
> What is needed is some empirical data, counting actual possessions
in a
> game, and seeing how close we are.

I've got some of these. I'll try to pass them on after I'm done
traveling (again).

My general comment to Ben when he first passed on his note to me was
that he may be right that 0.45 works better to account for FT
possessions. However, there are minor errors in the rest of the
possession formula associated with team ORs and other little things
that get lumped into that multiplier on FTA. Or you can get more
complex with your possession formula, something BobC has done.

I share the sentiment that it doesn't matter too much. Soon, we will
be able to just count possessions for each team and do the simple
division to get pts/poss. Still, the formula estimate will remain
useful (in historical work, in individual possession calcs), but the
difference between 0.4 and 0.45 won't make a huge difference in
estimates. Plus, the multiplier changes with rules and enforcement
of such. It was lower in the 3-to-make-2 era, for example, and is
higher in the 1-and-1 world of college hoops.

DeanO
• I have noticed that many people have used the following formula to estimate possessions: FGA + (FTA)(.4) + TO - OReb The times fouled shooting factor should be
Message 6 of 8 , Jun 22, 2003
I have noticed that many people have used the following formula to
estimate possessions:

FGA + (FTA)(.4) + TO - OReb

The times fouled shooting factor should be .457; not .4.

Or you can get more complex with your possession formula, something BobC has done.

the proper formula is:

FGA + FTA/2 + TO - oreb - techFTA - (AOSF FGM) - flagrants

(denominator 2 larger prior to 81-82 when 3 to make 2 bonus was in affect), but i add 0.33 to account for the techs and flagrants...

and not more complex, just more exact, simply because it works in a simulation, which does not take into account technicals and flagrants, but does account for AOSF FGM (act of shooting fouls FGM, i.e. traditional 3 pt plays)...

your average for 97-98 (the last year i updated the sim) was 92.4 poss/48 min/team. the sim uses 91.5 on average and the stats come out pretty much exact (i.e. avg pts/g/team right on the money, well within 1%)....

if you ever run the B-BALL sim for a full season (takes about 40 seconds on a pentium to run an 1189 game season) it lists each team's poss/g in the final stats file...

bob chaikin
bchaikin@...
• I agree with the general sentiment -- if 0.4 vs. 0.44 would only change the result between two players are teams with microscopic differences. Also, in the
Message 7 of 8 , Jun 22, 2003
I agree with the general sentiment -- if 0.4 vs. 0.44 would only
change the result between two players are teams with microscopic
differences.

Also, in the specific example that brought up this thread, there's a
couple things missing -- times fouled on 3-pointers, flagrant fouls
and breakaway fouls -- that would further adjust the coefficient.

--- In APBR_analysis@yahoogroups.com, "Dean Oliver" <deano@r...>
wrote:
> --- In APBR_analysis@yahoogroups.com, igor eduardo küpfer
> <igorkupfer@r...> wrote:
> > <snip>
> >
> > The following is a comparison of the two FTA coefficients (.4
> vs .457), as
> > shown by the differences between offensive possessions and
defensive
> > possessions,by season. The smaller coefficient outperforms the
> larger
> > exactly half the time, although with a larger standard error. The
> difference
> > is small enough (to me) as to not warrant using the extra decimal
> places.
> > What is needed is some empirical data, counting actual
possessions
> in a
> > game, and seeing how close we are.
>
> I've got some of these. I'll try to pass them on after I'm done
> traveling (again).
>
> My general comment to Ben when he first passed on his note to me
was
> that he may be right that 0.45 works better to account for FT
> possessions. However, there are minor errors in the rest of the
> possession formula associated with team ORs and other little things
> that get lumped into that multiplier on FTA. Or you can get more
> complex with your possession formula, something BobC has done.
>
> I share the sentiment that it doesn't matter too much. Soon, we
will
> be able to just count possessions for each team and do the simple
> division to get pts/poss. Still, the formula estimate will remain
> useful (in historical work, in individual possession calcs), but
the
> difference between 0.4 and 0.45 won't make a huge difference in
> estimates. Plus, the multiplier changes with rules and enforcement
> of such. It was lower in the 3-to-make-2 era, for example, and is
> higher in the 1-and-1 world of college hoops.
>
> DeanO
• ... affect), ... The problem is that your last 3 terms aren t available in most stat books so we end up estimating them. I just end up rolling them into the
Message 8 of 8 , Jun 23, 2003
--- In APBR_analysis@yahoogroups.com, bchaikin@a... wrote:
> the proper formula is:
>
> FGA + FTA/2 + TO - oreb - techFTA - (AOSF FGM) - flagrants
>
> (denominator 2 larger prior to 81-82 when 3 to make 2 bonus was in
affect),
> but i add 0.33 to account for the techs and flagrants...
>

The problem is that your last 3 terms aren't available in most stat
books so we end up estimating them. I just end up rolling them into
the multiplier on FTA, but there are other ways.

DeanO
Your message has been successfully submitted and would be delivered to recipients shortly.