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Re: Assist tracking update

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  • Charlie Board
    ... Indeed - what jumped out at me from Ed s original post was the *huge* percentage of 3FGA that were assisted. If I m reading his numbers correctly only 36%
    Message 1 of 18 , Feb 2, 2004
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      --- In APBR_analysis@yahoogroups.com, "Michael Tamada" <tamada@o...>
      wrote:

      >
      > But before we say that the assists aren't helping the 3-point shooters,
      > we need to look at the "opportunity cost": the assist might still have
      > value because it gave the 3-point shooter the chance to put up the shot
      > in the first place.

      Indeed - what jumped out at me from Ed's original post
      was the *huge* percentage of 3FGA that were assisted.
      If I'm reading his numbers correctly only 36% of all
      2FGA were assisted, while **74%** of all 3FGA were
      assisted. That sounds to me like not only are assists
      helping the 3 point shooters - the assist is *THE* major
      factor in getting off a good 3.
    • Michael Tamada
      ... From: Charlie Board [mailto:cboard@telesyn.com] Sent: Monday, February 02, 2004 8:40 AM ... A good point, but now we re getting into things which are
      Message 2 of 18 , Feb 2, 2004
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        -----Original Message-----
        From: Charlie Board [mailto:cboard@...]
        Sent: Monday, February 02, 2004 8:40 AM


        --- In APBR_analysis@yahoogroups.com, "Michael Tamada" <tamada@o...>
        wrote:

        >> But before we say that the assists aren't helping the 3-point shooters,
        >> we need to look at the "opportunity cost": the assist might still have
        >> value because it gave the 3-point shooter the chance to put up the shot
        >> in the first place.
        >
        >Indeed - what jumped out at me from Ed's original post
        >was the *huge* percentage of 3FGA that were assisted.
        >If I'm reading his numbers correctly only 36% of all
        >2FGA were assisted, while **74%** of all 3FGA were
        >assisted. That sounds to me like not only are assists
        >helping the 3 point shooters - the assist is *THE* major
        >factor in getting off a good 3.

        A good point, but now we're getting into things which are really
        hard to measure. The major factor probably was indeed the pass
        to the (presumably open) 3-point shooter. But to accurately put
        a value on that, we need to know what would've happened in the
        absence of that nice pass, a very hard hypothetical situation to
        measure.

        It's somewhat analogous to the assisted/unassisted basket situation,
        except taken a step further: the question now isn't the impact of
        the pass on the shooter's FG%, the question is whether the shooter
        got a look at the basket and a potential shot in at all.

        While we can measure FG% on assisted and unassisted baskets, we
        don't have stats on what sort of shot would've been attempted in
        the absence of the nice pass to the 3-point shooter.

        I supposed we could use unassisted 2pt FG% as a rough guesstimate
        (with cripple layins subtracted first).


        --MKT








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      • nick_scholtz
        I think the differences in 3pt and FT% obdcure the basic question: What is the scoring efficiency on plays with potential assists and on plays with no
        Message 3 of 18 , Feb 2, 2004
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          I think the differences in 3pt and FT% obdcure the basic question:

          What is the scoring efficiency on plays with "potential" assists and
          on plays with no assists?

          For example, look at the data suplied:
          > 2m-2a 2% 3m-3a 3% ftm-fta ft%
          > Ast'd 143-263 54% 41-125 33% 39-54 72%
          > UnAst'd 200-462 43% 12-43 28% 87-113 77%

          This generated the following.

          Shot attempts Points Scored PSA
          Ast 287 366 1.28
          Un 512 499 0.98

          Difference in PSA = value of assist = .3

          This is a far lower value than what I would have expected (I
          hypothesized a value of 1, John Hollinger uses a value
          of .67 for the calculations in the Pro Basketball Prospectus)

          In addition to my suprise at how low the value is, I am suprised by
          how few FT's come out of potential assist situations. Perhaps it makes
          sense that many fouls come on drives to the basket (not an assist) but
          that is a large reason why the calculated value is so low.

          Nick Scholtz

          --- In APBR_analysis@yahoogroups.com, "Michael Tamada" <tamada@o...>
          wrote:
          > -----Original Message-----
          > From: Charlie Board [mailto:cboard@t...]
          > Sent: Monday, February 02, 2004 8:40 AM
          >
          >
          > --- In APBR_analysis@yahoogroups.com, "Michael Tamada" <tamada@o...>
          > wrote:
          >
          > >> But before we say that the assists aren't helping the 3-point
          shooters,
          > >> we need to look at the "opportunity cost": the assist might
          still have
          > >> value because it gave the 3-point shooter the chance to put up
          the shot
          > >> in the first place.
          > >
          > >Indeed - what jumped out at me from Ed's original post
          > >was the *huge* percentage of 3FGA that were assisted.
          > >If I'm reading his numbers correctly only 36% of all
          > >2FGA were assisted, while **74%** of all 3FGA were
          > >assisted. That sounds to me like not only are assists
          > >helping the 3 point shooters - the assist is *THE* major
          > >factor in getting off a good 3.
          >
          > A good point, but now we're getting into things which are really
          > hard to measure. The major factor probably was indeed the pass
          > to the (presumably open) 3-point shooter. But to accurately put
          > a value on that, we need to know what would've happened in the
          > absence of that nice pass, a very hard hypothetical situation to
          > measure.
          >
          > It's somewhat analogous to the assisted/unassisted basket situation,
          > except taken a step further: the question now isn't the impact of
          > the pass on the shooter's FG%, the question is whether the shooter
          > got a look at the basket and a potential shot in at all.
          >
          > While we can measure FG% on assisted and unassisted baskets, we
          > don't have stats on what sort of shot would've been attempted in
          > the absence of the nice pass to the 3-point shooter.
          >
          > I supposed we could use unassisted 2pt FG% as a rough guesstimate
          > (with cripple layins subtracted first).
          >
          >
          > --MKT
          >
          >
        • nick_scholtz
          uh . . . make that obscures I don t mean to suggest that other questions are uninteresting (I would, for example, suggest that the reason why FT% is lower in
          Message 4 of 18 , Feb 2, 2004
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            uh . . . make that "obscures"

            I don't mean to suggest that other questions are uninteresting (I
            would, for example, suggest that the reason why FT% is lower in
            assisted situations is because more of the FT's are being shot by big
            men and fewer by guards -- who have a higher FT%). I would also note
            that the observed 5% difference in assisted and unassisted 3 pointers
            would work out to a 7.5% difference in "true shooting %" which is
            closer to the 2 point percentage difference. It's still true that the
            true shooting % for assisted 3 point shots is lower than that for
            assisted 2 point shots which may or may not mean that teams should
            stop shooting 3 point attempts :)

            Also I think the table below is incorrect -- I didn't realize that 3
            pointers had already been separated out.

            Try this:

            Shot Attempts Points PSA
            AST 412 448 1.09
            UN 555 523 0.94

            Value of assist (by my calculations) 0.15

            Nick Scholtz


            --- In APBR_analysis@yahoogroups.com, "nick_scholtz" <nick@l...>
            wrote:
            > I think the differences in 3pt and FT% obdcure the basic question:
            >
            > What is the scoring efficiency on plays with "potential" assists and
            > on plays with no assists?
            >
            > For example, look at the data suplied:
            > > 2m-2a 2% 3m-3a 3% ftm-fta ft%
            > > Ast'd 143-263 54% 41-125 33% 39-54 72%
            > > UnAst'd 200-462 43% 12-43 28% 87-113 77%
            >
            > This generated the following.
            >
            > Shot attempts Points Scored PSA
            > Ast 287 366 1.28
            > Un 512 499 0.98
            >
            > Difference in PSA = value of assist = .3
            >
            > This is a far lower value than what I would have expected (I
            > hypothesized a value of 1, John Hollinger uses a value
            > of .67 for the calculations in the Pro Basketball Prospectus)
            >
            > In addition to my suprise at how low the value is, I am suprised by
            > how few FT's come out of potential assist situations. Perhaps it
            makes
            > sense that many fouls come on drives to the basket (not an assist)
            but
            > that is a large reason why the calculated value is so low.
            >
            > Nick Scholtz
          • Dean Oliver
            ... Still preliminary, but that s pretty close to the difference between points per possession and points per play, i.e., the value of an offensive rebound. I
            Message 5 of 18 , Feb 3, 2004
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              --- In APBR_analysis@yahoogroups.com, "nick_scholtz" <nick@l...> wrote:
              > Try this:
              >
              > Shot Attempts Points PSA
              > AST 412 448 1.09
              > UN 555 523 0.94
              >
              > Value of assist (by my calculations) 0.15

              Still preliminary, but that's pretty close to the difference between
              points per possession and points per play, i.e., the value of an
              offensive rebound.

              I have been continuing my conversations with David Berri, the sports
              econ professor from Bakersfield. Using an approach that evaluates
              whether wins come from numerous different stats, he keeps seeing that
              assists have almost no value. That approach is different than this
              one and I've been trying to make a point that probably can be
              clarified just by stats like these (which, as I mentioned before, I
              didn't see in the smaller study I did in the early '90's). I believe
              the above is statistically significant. I'll have to follow up
              sometime to find out what games you were doing, though. You don't
              want it to be just a couple teams.

              DeanO
              www.basketballonpaper.com

              >
              >
              > --- In APBR_analysis@yahoogroups.com, "nick_scholtz" <nick@l...>
              > wrote:
              > > I think the differences in 3pt and FT% obdcure the basic question:
              > >
              > > What is the scoring efficiency on plays with "potential" assists and
              > > on plays with no assists?
              > >
              > > For example, look at the data suplied:
              > > > 2m-2a 2% 3m-3a 3% ftm-fta ft%
              > > > Ast'd 143-263 54% 41-125 33% 39-54 72%
              > > > UnAst'd 200-462 43% 12-43 28% 87-113 77%
              > >
              > > This generated the following.
              > >
              > > Shot attempts Points Scored PSA
              > > Ast 287 366 1.28
              > > Un 512 499 0.98
              > >
              > > Difference in PSA = value of assist = .3
              > >
              > > This is a far lower value than what I would have expected (I
              > > hypothesized a value of 1, John Hollinger uses a value
              > > of .67 for the calculations in the Pro Basketball Prospectus)
              > >
              > > In addition to my suprise at how low the value is, I am suprised by
              > > how few FT's come out of potential assist situations. Perhaps it
              > makes
              > > sense that many fouls come on drives to the basket (not an assist)
              > but
              > > that is a large reason why the calculated value is so low.
              > >
              > > Nick Scholtz
            • bchaikin@aol.com
              ... Still preliminary, but that s pretty close to the difference between points per possession and points per play, i.e., the value of an offensive rebound. I
              Message 6 of 18 , Feb 3, 2004
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                > Try this:
                >
                >         Shot Attempts   Points  PSA
                > AST       412          448    1.09
                > UN        555          523    0.94 
                >
                > Value of assist (by my calculations) 0.15

                Still preliminary, but that's pretty close to the difference between
                points per possession and points per play, i.e., the value of an
                offensive rebound.

                I have been continuing my conversations with David Berri, the sports
                econ professor from Bakersfield.  Using an approach that evaluates
                whether wins come from numerous different stats, he keeps seeing that
                assists have almost no value.  That approach is different than this
                one and I've been trying to make a point that probably can be
                clarified just by stats like these (which, as I mentioned before, I
                didn't see in the smaller study I did in the early '90's).  I believe
                the above is statistically significant.  I'll have to follow up
                sometime to find out what games you were doing, though.  You don't
                want it to be just a couple teams.

                anyone know if dave berri has any basketball related thoughts/musings posted somewhere on the internet, or in print?...





              • schtevie2003
                In the how big is big category, here is how I would contextualize the calculated value. Consider the case of Sacramento, the best passing team in the NBA,
                Message 7 of 18 , Feb 3, 2004
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                  In the "how big is big" category, here is how I would contextualize the calculated
                  value. Consider the case of Sacramento, the best passing team in the NBA, defeating
                  its opponents by 7.4 ppg (also perhaps league leading). If we take an assist value of
                  0.15 and note that they accumulate about 5.5 more assists than the median team in
                  the league (which by observation appears close to the average) then a fair estimate is
                  that their exceptional passing ability explains only about one tenth of their
                  exceptional superiority (calculation: 5.5*0.15/7.4). Does this seem high or low? I
                  guess that my prior would have been that it would have been a slightly higher.

                  ***********

                  --- In APBR_analysis@yahoogroups.com, "Dean Oliver" <deano@r...> wrote:
                  > --- In APBR_analysis@yahoogroups.com, "nick_scholtz" <nick@l...> wrote:
                  > > Try this:
                  > >
                  > > Shot Attempts Points PSA
                  > > AST 412 448 1.09
                  > > UN 555 523 0.94
                  > >
                  > > Value of assist (by my calculations) 0.15
                  >
                  > Still preliminary, but that's pretty close to the difference between
                  > points per possession and points per play, i.e., the value of an
                  > offensive rebound.
                  >
                  > I have been continuing my conversations with David Berri, the sports
                  > econ professor from Bakersfield. Using an approach that evaluates
                  > whether wins come from numerous different stats, he keeps seeing that
                  > assists have almost no value. That approach is different than this
                  > one and I've been trying to make a point that probably can be
                  > clarified just by stats like these (which, as I mentioned before, I
                  > didn't see in the smaller study I did in the early '90's). I believe
                  > the above is statistically significant. I'll have to follow up
                  > sometime to find out what games you were doing, though. You don't
                  > want it to be just a couple teams.
                  >
                  > DeanO
                  > www.basketballonpaper.com
                  >
                  > >
                  > >
                  > > --- In APBR_analysis@yahoogroups.com, "nick_scholtz" <nick@l...>
                  > > wrote:
                  > > > I think the differences in 3pt and FT% obdcure the basic question:
                  > > >
                  > > > What is the scoring efficiency on plays with "potential" assists and
                  > > > on plays with no assists?
                  > > >
                  > > > For example, look at the data suplied:
                  > > > > 2m-2a 2% 3m-3a 3% ftm-fta ft%
                  > > > > Ast'd 143-263 54% 41-125 33% 39-54 72%
                  > > > > UnAst'd 200-462 43% 12-43 28% 87-113 77%
                  > > >
                  > > > This generated the following.
                  > > >
                  > > > Shot attempts Points Scored PSA
                  > > > Ast 287 366 1.28
                  > > > Un 512 499 0.98
                  > > >
                  > > > Difference in PSA = value of assist = .3
                  > > >
                  > > > This is a far lower value than what I would have expected (I
                  > > > hypothesized a value of 1, John Hollinger uses a value
                  > > > of .67 for the calculations in the Pro Basketball Prospectus)
                  > > >
                  > > > In addition to my suprise at how low the value is, I am suprised by
                  > > > how few FT's come out of potential assist situations. Perhaps it
                  > > makes
                  > > > sense that many fouls come on drives to the basket (not an assist)
                  > > but
                  > > > that is a large reason why the calculated value is so low.
                  > > >
                  > > > Nick Scholtz
                • Dean Oliver
                  Plenty of papers available through... http://www.csub.edu/~dberri/ Some abstracts and papers at http://www.csub.edu/%7Edberri/Research.html ...
                  Message 8 of 18 , Feb 3, 2004
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                    Plenty of papers available through...

                    http://www.csub.edu/~dberri/

                    Some abstracts and papers at

                    http://www.csub.edu/%7Edberri/Research.html

                    --- In APBR_analysis@yahoogroups.com, bchaikin@a... wrote:
                    > > Try this:
                    > >
                    > > Shot Attempts Points PSA
                    > > AST 412 448 1.09
                    > > UN 555 523 0.94
                    > >
                    > > Value of assist (by my calculations) 0.15
                    >
                    > Still preliminary, but that's pretty close to the difference between
                    > points per possession and points per play, i.e., the value of an
                    > offensive rebound.
                    >
                    > I have been continuing my conversations with David Berri, the sports
                    > econ professor from Bakersfield. Using an approach that evaluates
                    > whether wins come from numerous different stats, he keeps seeing that
                    > assists have almost no value. That approach is different than this
                    > one and I've been trying to make a point that probably can be
                    > clarified just by stats like these (which, as I mentioned before, I
                    > didn't see in the smaller study I did in the early '90's). I believe
                    > the above is statistically significant. I'll have to follow up
                    > sometime to find out what games you were doing, though. You don't
                    > want it to be just a couple teams.
                    >
                    > anyone know if dave berri has any basketball related
                    thoughts/musings posted
                    > somewhere on the internet, or in print?...
                  • schtevie2003
                    ... defeating ... of ... is ... Perhaps I should also have added the calculation for New Jersey, the second best passing team in the league, as measured by
                    Message 9 of 18 , Feb 3, 2004
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                      --- In APBR_analysis@yahoogroups.com, "schtevie2003" <schtevie@h...> wrote:
                      > In the "how big is big" category, here is how I would contextualize the calculated
                      > value. Consider the case of Sacramento, the best passing team in the NBA,
                      defeating
                      > its opponents by 7.4 ppg (also perhaps league leading). If we take an assist value
                      of
                      > 0.15 and note that they accumulate about 5.5 more assists than the median team in
                      > the league (which by observation appears close to the average) then a fair estimate
                      is
                      > that their exceptional passing ability explains only about one tenth of their
                      > exceptional superiority (calculation: 5.5*0.15/7.4). Does this seem high or low? I
                      > guess that my prior would have been that it would have been a slightly higher.
                      >
                      > ***********
                      >
                      Perhaps I should also have added the calculation for New Jersey, the second best
                      passing team in the league, as measured by assists. For the Nets, assists explain
                      about 20% of their victory margin (=3.3*0.15/2.4).

                      The interest in this particular stat is this tentative interpretation: for a rather ordinary
                      (this year) above-average team, passing, at best (Kidd is the best, no?) can account for
                      "at most" 20% of success.

                      *************

                      > --- In APBR_analysis@yahoogroups.com, "Dean Oliver" <deano@r...> wrote:
                      > > --- In APBR_analysis@yahoogroups.com, "nick_scholtz" <nick@l...> wrote:
                      > > > Try this:
                      > > >
                      > > > Shot Attempts Points PSA
                      > > > AST 412 448 1.09
                      > > > UN 555 523 0.94
                      > > >
                      > > > Value of assist (by my calculations) 0.15
                      > >
                      > > Still preliminary, but that's pretty close to the difference between
                      > > points per possession and points per play, i.e., the value of an
                      > > offensive rebound.
                      > >
                      > > I have been continuing my conversations with David Berri, the sports
                      > > econ professor from Bakersfield. Using an approach that evaluates
                      > > whether wins come from numerous different stats, he keeps seeing that
                      > > assists have almost no value. That approach is different than this
                      > > one and I've been trying to make a point that probably can be
                      > > clarified just by stats like these (which, as I mentioned before, I
                      > > didn't see in the smaller study I did in the early '90's). I believe
                      > > the above is statistically significant. I'll have to follow up
                      > > sometime to find out what games you were doing, though. You don't
                      > > want it to be just a couple teams.
                      > >
                      > > DeanO
                      > > www.basketballonpaper.com
                      > >
                      > > >
                      > > >
                      > > > --- In APBR_analysis@yahoogroups.com, "nick_scholtz" <nick@l...>
                      > > > wrote:
                      > > > > I think the differences in 3pt and FT% obdcure the basic question:
                      > > > >
                      > > > > What is the scoring efficiency on plays with "potential" assists and
                      > > > > on plays with no assists?
                      > > > >
                      > > > > For example, look at the data suplied:
                      > > > > > 2m-2a 2% 3m-3a 3% ftm-fta ft%
                      > > > > > Ast'd 143-263 54% 41-125 33% 39-54 72%
                      > > > > > UnAst'd 200-462 43% 12-43 28% 87-113 77%
                      > > > >
                      > > > > This generated the following.
                      > > > >
                      > > > > Shot attempts Points Scored PSA
                      > > > > Ast 287 366 1.28
                      > > > > Un 512 499 0.98
                      > > > >
                      > > > > Difference in PSA = value of assist = .3
                      > > > >
                      > > > > This is a far lower value than what I would have expected (I
                      > > > > hypothesized a value of 1, John Hollinger uses a value
                      > > > > of .67 for the calculations in the Pro Basketball Prospectus)
                      > > > >
                      > > > > In addition to my suprise at how low the value is, I am suprised by
                      > > > > how few FT's come out of potential assist situations. Perhaps it
                      > > > makes
                      > > > > sense that many fouls come on drives to the basket (not an assist)
                      > > > but
                      > > > > that is a large reason why the calculated value is so low.
                      > > > >
                      > > > > Nick Scholtz
                    • nick_scholtz
                      So I get to be the first person to correct it :) Talking about calculating the value of assists I offered the ... This was computed from the following data ...
                      Message 10 of 18 , Feb 5, 2004
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                        So I get to be the first person to correct it :)

                        Talking about calculating the value of assists I offered the
                        following calculation:

                        > Shot Attempts Points PSA
                        > AST 412 448 1.09
                        > UN 555 523 0.94
                        >
                        > Value of assist (by my calculations) 0.15

                        This was computed from the following data

                        > > 2m-2a 2% 3m-3a 3% ftm-fta ft%
                        > > Ast'd 143-263 54% 41-125 33% 39-54 72%
                        > > UnAst'd 200-462 43% 12-43 28% 87-113 77%

                        The calculation was correct in saying that comparing the assisted
                        shot attempts non Unassisted the increase in PSA was 0.15 (which
                        seemed low). This is correct as far as it goes, but I forgot the
                        final step of distributing the value of the extra points to the
                        assists. In this case the 412 shot attempts with potential assists
                        generated 61 more points than if the same shots hadn't had potential
                        assists. They also were responsible for 184 assists (143 on 2 pt
                        basktes, 41 on 3 point shots).

                        This leads to a value of an assists of 61/184 or just under 1/3
                        point. This is still much lower than I expected but, at least,
                        should be the correct calculation.

                        I would be very interested if anyone else has collected similar data
                        for other teams to see how consistant that number is.

                        Nick
                      • igor eduardo küpfer
                        After 26 games, here s what it looks like: 2m 2a 2% 3m - 3a 3% ftm - fta ft% AST 311 - 570 55% 97 - 252 38% 97 - 142 68% UNAST
                        Message 11 of 18 , Feb 12, 2004
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                          After 26 games, here's what it looks like:

                          2m 2a 2% 3m - 3a 3% ftm - fta ft%
                          AST 311 - 570 55% 97 - 252 38% 97 - 142 68%
                          UNAST 441 - 1037 43% 20 - 95 21% 239 - 318 75%

                          DIFF 12% 17% -7%
                          p <.001 <.01 ns

                          Over the last dozen games I've started tracking shot attempts in the paint
                          separate from those outside the paint.

                          In2m - In2a In2% Out2m - Out2a Out2%
                          AST 89 - 137 65% 69 - 153 45%
                          UNAST 129 - 275 47% 66 - 192 34%

                          DIFF 18% 11%
                          p <.05 ns

                          We should be able to combine this with the data from the 82games site which
                          shows shot attempt distance for each player in order to begin to credit
                          assists properly -- more credit for inside attempts should go to the
                          assister. By the end of this season, I'll have enough games scored from a
                          wide variety of teams to know how much of the credit should go to the
                          passer.

                          ed
                        • Kevin Pelton
                          I ve scored about five Sonics games now ... I need to translate them to HTML. Hopefully the weekend. Are you doing road games as well as home games?
                          Message 12 of 18 , Feb 13, 2004
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                            I've scored about five Sonics games now ... I need to translate them
                            to HTML. Hopefully the weekend.

                            Are you doing road games as well as home games?
                          • Mike G
                            ... Trying to figure out what to make of these numbers. I ve reduced this chart to one that represents an average game in the sample: .category. 3pt. 2 pt.
                            Message 13 of 18 , Feb 13, 2004
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                              --- In APBR_analysis@yahoogroups.com, igor eduardo küpfer
                              <edkupfer@r...> wrote:
                              > After 26 games, here's what it looks like:
                              >
                              > 2m 2a 2% 3m - 3a 3% ftm - fta ft%
                              > AST 311 - 570 55% 97 - 252 38% 97 - 142 68%
                              > UNAST 441 - 1037 43% 20 - 95 21% 239 - 318 75%
                              >
                              > DIFF 12% 17% -7%
                              > p <.001 <.01 ns

                              Trying to figure out what to make of these numbers.

                              I've reduced this chart to one that represents an "average" game in
                              the sample:

                              .category. 3pt. 2 pt. FT

                              "assisted" 4-10 12-22 4-6
                              unassisted 1-5_ 17-40 9-12

                              Counting 2 FTA as one 'play':

                              On 35 "assisted" plays, 40 pts are scored, or 1.143 pts per play

                              On 51 unassisted plays, 46 pts are scored, at .902 ppp

                              The difference is .216 ppp

                              But: In reality, only 16 assists are counted. So, from 16 actual,
                              counted assists, 40 pts are produced.

                              Therefore, each assist produces 2.5 points; and the difference is
                              now 1.585 as the value of each assist.

                              (The actual difference, from Ed's 2184 plays, is 1.561)


                              We probably all know that a counted assist is only the 'tip of the
                              iceberg' which represents all 'good passes' a player executes.
                              While there have been players (Kevin Porter? Ray Williams?) who have
                              ONLY passed when an assist was to be had, many players get few
                              assists, yet are credible passers.

                              So the assist represents an "estimate" of the number of
                              good, "assist-worthy" passes a player throws.
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