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Re: Similarity Scores

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  • Mike Goodman
    ... choose ... Another ... probably ... I tried my hand at a variation of the Euclidian distance, since I can understand the formula (and pronounce it, too). I
    Message 1 of 16 , Sep 14, 2001
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      --- In APBR_analysis@y..., "Michael K. Tamada" <tamada@o...> wrote:
      >.... Euclidean distance,
      > sqrt( X^2 + Y^2 + Z^2 + ...) where X, Y, Z, etc. are the difference
      > between, say, Magic Johnson and Larry Bird in whatever variables we
      choose
      > to look at.
      >
      > But there are problems with Euclidean distance, specfically one that
      > Dean Oliver alludes to: some variables are redundant or
      > partially redundant with each other,
      > e.g. FG Made and Points Scored, or even Off Rebds and Def Rebds.
      Another
      > problem is that not all variables are equally important: some
      probably
      > should be given greater weight than others ...

      I tried my hand at a variation of the Euclidian distance, since I can
      understand the formula (and pronounce it, too).
      I took 5 stats: scoring, rebounding, assists, steals, blocks. I used
      my normalized (standardized) versions. Because points are much more
      abundant than, say, steals, I reduced this difference by taking the
      square root of each stat. I compared the top 31 players on my
      infamous "alltime" list to the other 514 in the list. (I actually
      ran out of columns in Excel, for the first time.)
      The formula is drudgery to type, but it starts like this:
      E = (sqrt(a1)-sqrt(b1))^2 + (sqrt(a2)-sqrt(b2))^2 +... and so on, up
      to a5 and b5, for players a and b, and variables 1-5.
      I did not take the square root of the whole thing, since everything
      was already square-rooted once.
      Not surprisingly, the best players only correspond to other great
      players, but some players have much more unique statistical profiles.
      In order of "greatest distance from the next-closest profile", we
      have:
      Sco Reb Ast Stl Blk E
      Michael Jordan 33.5 6.5 5.1 2.3 .9
      Jerry West 25.1 4.2 6.0 (2.7 .9) .945 (estimated)
      No real surprise that Jordan is the "most unique" statistically.
      Others scored more than West, but didn't have quality numbers beyond
      that.
      (Iverson is next, then Karl Malone(!), Kobe, Gervin, Erving, Bird,
      Wilkins, Dantley, Barry)

      Bill Russell 11.8 14.6 3.8 (1.5 4.0)
      Bill Walton 15.9 12.8 4.0 1.0 2.7 .743
      Really not very similar, but as close as anyone comes to Russell's
      combination of skills.
      (Thurmond is close 2nd, then Sam Lacey, Elmore Smith, Mutombo)

      Magic Johnson 20.6 7.5 10.4 1.9 .4
      Oscar Robertson 22.4 5.3 8.0 (1.5 .3) .644
      Magic was "the next Oscar", and then some.
      (Grant Hill, Payton, Penny, Strickland, Isiah, Drexler, KJ, Frazier)

      John Stockton 17.1 3.3 11.9 2.4 .2
      Isiah Thomas 18.0 3.7 8.8 2.0 .3 .543
      Stockton is just a giant in the assists category.
      (Tim Hardaway, KJ, Strickland, Cousy, Kenny Anderson, Brandon)

      Jerry West 25.1 4.2 6.0 (2.7 .9)
      Allen Iverson 25.1 3.9 5.5 2.1 .2 .517
      Now we have some real across-the-board similarity.
      (Barry, Penny, Kobe, Drexler, Maravich, Oscar, Westphal)

      Oscar Robertson 22.4 5.3 8.0 (1.5 .3)
      Penny Hardaway 20.2 5.1 6.2 1.9 .6 .486
      (KJ, Payton, Frazier, Cassell, Tim Hardaway, Price, Brandon, Magic)

      Moses Malone 21.6 13.2 1.3 .9 1.4
      Shawn Kemp 20.9 11.8 2.2 1.4 1.6 .470
      (Parish, Gilmore, Reed, McDyess, Ewing, Hayes, Haywood, McAdoo)

      Shaquille O'Neal 29.7 12.7 2.8 .7 2.6
      Tim Duncan 25.1 12.0 3.0 .8 2.3 .466
      (Kareem, Robinson, Mikan, Pettit, Ewing, Mourning, Wilt, Hakeem)

      Artis Gilmore 20.3 11.9 2.3 .6 2.3
      Patrick Ewing 23.5 11.1 2.0 1.0 2.6 .446
      (Hayes, Parish, Derrick Coleman, Sabonis, McDyess, Kemp, Gallatin)

      The remainder of the top 31 (and their closest match)

      Kareem AbdulJab. 25.9 10.6 3.4 1.0 2.7
      Tim Duncan 25.1 12.0 3.0 .8 2.3 .288
      (Robinson, Pettit, Mikan, Ewing, Neil Johnston, Shaq, Hakeem)

      Wilt Chamberlain 23.5 14.7 3.5 (1.5 3.0)
      George Mikan 24.8 13.1 2.9 (1.3 2.0) .432
      (Hakeem, Robinson, Duncan, Pettit, Kareem, Ewing)

      Karl Malone 28.1 11.2 3.4 1.4 .8
      Charles Barkley 24.2 12.4 3.8 1.6 .8 .444
      (Pettit, Johnston, Mikan, Baylor, Jeff Ruland, Bird, Duncan, McAdoo)

      Hakeem Olajuwon 23.7 11.7 2.6 1.8 3.2
      David Robinson 26.1 11.8 2.8 1.5 3.3 .275

      Julius Erving 23.0 7.8 4.0 1.9 1.7
      Elgin Baylor 22.5 9.6 3.9 (1.6 1.5) .347
      (Webber, Marques Johnson, Shareef, Johnston, Lanier, Ed Macauley,
      Schayes, Garnett, Bird, Drexler)

      Patrick Ewing 23.5 11.1 2.0 1.0 2.6
      Alonzo Mourning 24.5 10.9 1.6 .7 3.2 .332

      Bob Pettit 24.2 11.7 2.8 (1.3 1.8)
      George Mikan 24.8 13.1 2.9 (1.3 2.0) .231

      Elgin Baylor 22.5 9.6 3.9 (1.6 1.5)
      Chris Webber 21.1 10.1 4.2 1.5 1.8 .215
      (Lanier, Erving, Schayes, Johnston, Shareef, Garnett, Pettit, McAdoo)

      Scottie Pippen 18.4 7.5 5.4 2.1 .9
      Clyde Drexler 20.6 6.7 5.5 2.1 .7 .306
      (Alvan Adams, Connie Hawkins, Toni Kukoc, Billy C., Grant Hill,
      Antoine Walker, Marques Johnson, Penny, Cliff Hagan)

      Clyde-Scottie likewise

      Robert Parish 18.1 11.4 1.5 .9 1.8
      Elvin Hayes 17.8 10.9 1.7 1.0 2.6 .161
      (Gallatin, McDyess, Seikaly, Reed, Larry Foust, Dan Roundfield,
      Sampson, Haywood, Brian Grant)

      Bob Lanier 21.4 10.5 3.3 1.2 1.7
      Dolph Schayes 20.0 10.1 3.1 (1.4 1.6) .194

      (Elvin Hayes-Robert Parish match)

      Rick Barry 21.9 5.5 4.5 2.1 .5
      Kobe Bryant 23.0 5.2 4.2 1.4 .8 .345
      (Chris Mullin, Drexler, Hagan, Moncrief, Penny, Ray Allen)

      Kevin McHale 22.1 8.6 1.8 .4 2.0
      Rik Smits 19.9 8.3 1.8 .6 1.6 .306
      (Lovellete, Darryl Dawkins, Haywood, McAdoo, Yardley, McDyess)

      (George Mikan-Bob Pettit)

      Dan Issel 21.1 8.5 2.2 1.1 .6
      Terry Cummings 19.1 9.3 2.2 1.3 .7 .280
      (Chambers, Ceballos, Calvin Natt, Shareef, Yardley, Glenn Robinson)

      Clearly, as one goes down the list into more "ordinary" players,
      there is a proliferation of close profiles.


      Mike Goodman

      > >
      > >
    • harlanzo@yahoo.com
      It occurred to me that when comparing players through their statistics should we be weighting the comparisons so that some statistics are more important based
      Message 2 of 16 , Sep 15, 2001
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        It occurred to me that when comparing players through their
        statistics should we be weighting the comparisons so that some
        statistics are more important based on positions? For example, when
        comparing point guards the assist category might be more important
        for weighing similarity than rebound category. Conversely, do we
        really care whether two centers have similar assist numbers if their
        points, rebounds, and fg % are similar? I think this sounds somewhat
        right with some notable exceptions. The counter argument of course
        is that centers who pass well (a la Walton) or shoot 3s well
        (Laimbeer and Sikma) are unique and the similarity scores will help
        identify players with similar rare skill sets. (To digress, I wonder
        if Jason Kidd and some of the Darrell Walker early 90s seasons are
        comparable). I am beginning to babble but I think that the question
        I am asking is whether positional demands should change how we weight
        statistical categories when we try to apply similarity scores?


        --- In APBR_analysis@y..., "Mike Goodman" <msg_53@h...> wrote:
        > --- In APBR_analysis@y..., "Michael K. Tamada" <tamada@o...> wrote:
        > >.... Euclidean distance,
        > > sqrt( X^2 + Y^2 + Z^2 + ...) where X, Y, Z, etc. are the
        difference
        > > between, say, Magic Johnson and Larry Bird in whatever variables
        we
        > choose
        > > to look at.
        > >
        > > But there are problems with Euclidean distance, specfically one
        that
        > > Dean Oliver alludes to: some variables are redundant or
        > > partially redundant with each other,
        > > e.g. FG Made and Points Scored, or even Off Rebds and Def Rebds.
        > Another
        > > problem is that not all variables are equally important: some
        > probably
        > > should be given greater weight than others ...
        >
        > I tried my hand at a variation of the Euclidian distance, since I
        can
        > understand the formula (and pronounce it, too).
        > I took 5 stats: scoring, rebounding, assists, steals, blocks. I
        used
        > my normalized (standardized) versions. Because points are much
        more
        > abundant than, say, steals, I reduced this difference by taking the
        > square root of each stat. I compared the top 31 players on my
        > infamous "alltime" list to the other 514 in the list. (I actually
        > ran out of columns in Excel, for the first time.)
        > The formula is drudgery to type, but it starts like this:
        > E = (sqrt(a1)-sqrt(b1))^2 + (sqrt(a2)-sqrt(b2))^2 +... and so on,
        up
        > to a5 and b5, for players a and b, and variables 1-5.
        > I did not take the square root of the whole thing, since everything
        > was already square-rooted once.
        > Not surprisingly, the best players only correspond to other great
        > players, but some players have much more unique statistical
        profiles.
        > In order of "greatest distance from the next-closest profile", we
        > have:
        > Sco Reb Ast Stl Blk E
        > Michael Jordan 33.5 6.5 5.1 2.3 .9
        > Jerry West 25.1 4.2 6.0 (2.7 .9) .945 (estimated)
        > No real surprise that Jordan is the "most unique" statistically.
        > Others scored more than West, but didn't have quality numbers
        beyond
        > that.
        > (Iverson is next, then Karl Malone(!), Kobe, Gervin, Erving, Bird,
        > Wilkins, Dantley, Barry)
        >
        > Bill Russell 11.8 14.6 3.8 (1.5 4.0)
        > Bill Walton 15.9 12.8 4.0 1.0 2.7 .743
        > Really not very similar, but as close as anyone comes to Russell's
        > combination of skills.
        > (Thurmond is close 2nd, then Sam Lacey, Elmore Smith, Mutombo)
        >
        > Magic Johnson 20.6 7.5 10.4 1.9 .4
        > Oscar Robertson 22.4 5.3 8.0 (1.5 .3) .644
        > Magic was "the next Oscar", and then some.
        > (Grant Hill, Payton, Penny, Strickland, Isiah, Drexler, KJ, Frazier)
        >
        > John Stockton 17.1 3.3 11.9 2.4 .2
        > Isiah Thomas 18.0 3.7 8.8 2.0 .3 .543
        > Stockton is just a giant in the assists category.
        > (Tim Hardaway, KJ, Strickland, Cousy, Kenny Anderson, Brandon)
        >
        > Jerry West 25.1 4.2 6.0 (2.7 .9)
        > Allen Iverson 25.1 3.9 5.5 2.1 .2 .517
        > Now we have some real across-the-board similarity.
        > (Barry, Penny, Kobe, Drexler, Maravich, Oscar, Westphal)
        >
        > Oscar Robertson 22.4 5.3 8.0 (1.5 .3)
        > Penny Hardaway 20.2 5.1 6.2 1.9 .6 .486
        > (KJ, Payton, Frazier, Cassell, Tim Hardaway, Price, Brandon, Magic)
        >
        > Moses Malone 21.6 13.2 1.3 .9 1.4
        > Shawn Kemp 20.9 11.8 2.2 1.4 1.6 .470
        > (Parish, Gilmore, Reed, McDyess, Ewing, Hayes, Haywood, McAdoo)
        >
        > Shaquille O'Neal 29.7 12.7 2.8 .7 2.6
        > Tim Duncan 25.1 12.0 3.0 .8 2.3 .466
        > (Kareem, Robinson, Mikan, Pettit, Ewing, Mourning, Wilt, Hakeem)
        >
        > Artis Gilmore 20.3 11.9 2.3 .6 2.3
        > Patrick Ewing 23.5 11.1 2.0 1.0 2.6 .446
        > (Hayes, Parish, Derrick Coleman, Sabonis, McDyess, Kemp, Gallatin)
        >
        > The remainder of the top 31 (and their closest match)
        >
        > Kareem AbdulJab. 25.9 10.6 3.4 1.0 2.7
        > Tim Duncan 25.1 12.0 3.0 .8 2.3 .288
        > (Robinson, Pettit, Mikan, Ewing, Neil Johnston, Shaq, Hakeem)
        >
        > Wilt Chamberlain 23.5 14.7 3.5 (1.5 3.0)
        > George Mikan 24.8 13.1 2.9 (1.3 2.0) .432
        > (Hakeem, Robinson, Duncan, Pettit, Kareem, Ewing)
        >
        > Karl Malone 28.1 11.2 3.4 1.4 .8
        > Charles Barkley 24.2 12.4 3.8 1.6 .8 .444
        > (Pettit, Johnston, Mikan, Baylor, Jeff Ruland, Bird, Duncan, McAdoo)
        >
        > Hakeem Olajuwon 23.7 11.7 2.6 1.8 3.2
        > David Robinson 26.1 11.8 2.8 1.5 3.3 .275
        >
        > Julius Erving 23.0 7.8 4.0 1.9 1.7
        > Elgin Baylor 22.5 9.6 3.9 (1.6 1.5) .347
        > (Webber, Marques Johnson, Shareef, Johnston, Lanier, Ed Macauley,
        > Schayes, Garnett, Bird, Drexler)
        >
        > Patrick Ewing 23.5 11.1 2.0 1.0 2.6
        > Alonzo Mourning 24.5 10.9 1.6 .7 3.2 .332
        >
        > Bob Pettit 24.2 11.7 2.8 (1.3 1.8)
        > George Mikan 24.8 13.1 2.9 (1.3 2.0) .231
        >
        > Elgin Baylor 22.5 9.6 3.9 (1.6 1.5)
        > Chris Webber 21.1 10.1 4.2 1.5 1.8 .215
        > (Lanier, Erving, Schayes, Johnston, Shareef, Garnett, Pettit,
        McAdoo)
        >
        > Scottie Pippen 18.4 7.5 5.4 2.1 .9
        > Clyde Drexler 20.6 6.7 5.5 2.1 .7 .306
        > (Alvan Adams, Connie Hawkins, Toni Kukoc, Billy C., Grant Hill,
        > Antoine Walker, Marques Johnson, Penny, Cliff Hagan)
        >
        > Clyde-Scottie likewise
        >
        > Robert Parish 18.1 11.4 1.5 .9 1.8
        > Elvin Hayes 17.8 10.9 1.7 1.0 2.6 .161
        > (Gallatin, McDyess, Seikaly, Reed, Larry Foust, Dan Roundfield,
        > Sampson, Haywood, Brian Grant)
        >
        > Bob Lanier 21.4 10.5 3.3 1.2 1.7
        > Dolph Schayes 20.0 10.1 3.1 (1.4 1.6) .194
        >
        > (Elvin Hayes-Robert Parish match)
        >
        > Rick Barry 21.9 5.5 4.5 2.1 .5
        > Kobe Bryant 23.0 5.2 4.2 1.4 .8 .345
        > (Chris Mullin, Drexler, Hagan, Moncrief, Penny, Ray Allen)
        >
        > Kevin McHale 22.1 8.6 1.8 .4 2.0
        > Rik Smits 19.9 8.3 1.8 .6 1.6 .306
        > (Lovellete, Darryl Dawkins, Haywood, McAdoo, Yardley, McDyess)
        >
        > (George Mikan-Bob Pettit)
        >
        > Dan Issel 21.1 8.5 2.2 1.1 .6
        > Terry Cummings 19.1 9.3 2.2 1.3 .7 .280
        > (Chambers, Ceballos, Calvin Natt, Shareef, Yardley, Glenn Robinson)
        >
        > Clearly, as one goes down the list into more "ordinary" players,
        > there is a proliferation of close profiles.
        >
        >
        > Mike Goodman
        >
        > > >
        > > >
      • deano@tsoft.com
        ... Yes and No. What we re trying to come up with here is a general set of rules that can be applied at default (as a basis for studies, that can be
        Message 3 of 16 , Sep 16, 2001
        • 0 Attachment
          --- In APBR_analysis@y..., harlanzo@y... wrote:
          > It occurred to me that when comparing players through their
          > statistics should we be weighting the comparisons so that some
          > statistics are more important based on positions?

          Yes and No. What we're trying to come up with here is a general set
          of rules that can be applied at default (as a basis for studies,
          that can be modified). James always said that the method's blessing
          and curse was its flexibility. We SHOULD modify it for specific
          comparisons -- perhaps among point guards. There will always be a
          lot of different versions around, but we want one set for general
          comparisons, in part because, using your example, we can't
          necessarily identify who point guards are.

          I also thought of a reason not to use Euclidean distance -- it
          weights big differences too much. At least that is the subjective
          opinion a lot of times. It's the old argument between standard
          deviation and mean absolute difference -- the first weights big
          differences a lot but is mathematically easier, but the second seems
          to reflect more of what we want. The similarity scores, as James did
          them and as I modified them, fit into the mean absolute difference
          category. In Mike's categories, then, this implies that there is
          likely one very big difference between Jordan's numbers and everyone
          else (probably scoring average) -- that gets emphasized, making him
          the most unique player. I'd like to take a stab at career similarity
          scores using the approach I've outlined to see whether it id's Jordan
          as most unique, too.

          MikeG -- While I like the comparisons you did, there are 2 comments I
          would make:

          1. I'd like to see some non-standardized comparisons. I do like the
          standardized because they make some sense, but I think
          non-standardized will also tell a story.

          2. You really need some comparison of shooting percentages and
          turnovers. It really caught my eye with the Duncan-Kareem
          comparison. I see some similarity between these two, but there are
          big differences in offensive efficiency. Kareem was nearly
          unstoppable offensively - my floor%'s and offensive efficiencies
          reflect that. Duncan is very stoppable, his offensive rating and
          floor percentage blending in to be about average. Kareem fell to
          average offensively only in his last year. (I also don't think that
          Kareem was the defensive force that Duncan is, but my memories are
          biased by the Kareem post-'80, when he wasn't as good as he was when
          younger.)

          Dean Oliver
          Journal of Basketball Studies


          > For example,
          when
          > comparing point guards the assist category might be more important
          > for weighing similarity than rebound category. Conversely, do we
          > really care whether two centers have similar assist numbers if
          their
          > points, rebounds, and fg % are similar? I think this sounds
          somewhat
          > right with some notable exceptions. The counter argument of course
          > is that centers who pass well (a la Walton) or shoot 3s well
          > (Laimbeer and Sikma) are unique and the similarity scores will help
          > identify players with similar rare skill sets. (To digress, I
          wonder
          > if Jason Kidd and some of the Darrell Walker early 90s seasons are
          > comparable). I am beginning to babble but I think that the
          question
          > I am asking is whether positional demands should change how we
          weight
          > statistical categories when we try to apply similarity scores?
          >
          >
          > --- In APBR_analysis@y..., "Mike Goodman" <msg_53@h...> wrote:
          > > --- In APBR_analysis@y..., "Michael K. Tamada" <tamada@o...>
          wrote:
          > > >.... Euclidean distance,
          > > > sqrt( X^2 + Y^2 + Z^2 + ...) where X, Y, Z, etc. are the
          > difference
          > > > between, say, Magic Johnson and Larry Bird in whatever
          variables
          > we
          > > choose
          > > > to look at.
          > > >
          > > > But there are problems with Euclidean distance, specfically one
          > that
          > > > Dean Oliver alludes to: some variables are redundant or
          > > > partially redundant with each other,
          > > > e.g. FG Made and Points Scored, or even Off Rebds and Def
          Rebds.
          > > Another
          > > > problem is that not all variables are equally important: some
          > > probably
          > > > should be given greater weight than others ...
          > >
          > > I tried my hand at a variation of the Euclidian distance, since I
          > can
          > > understand the formula (and pronounce it, too).
          > > I took 5 stats: scoring, rebounding, assists, steals, blocks. I
          > used
          > > my normalized (standardized) versions. Because points are much
          > more
          > > abundant than, say, steals, I reduced this difference by taking
          the
          > > square root of each stat. I compared the top 31 players on my
          > > infamous "alltime" list to the other 514 in the list. (I
          actually
          > > ran out of columns in Excel, for the first time.)
          > > The formula is drudgery to type, but it starts like this:
          > > E = (sqrt(a1)-sqrt(b1))^2 + (sqrt(a2)-sqrt(b2))^2 +... and so on,
          > up
          > > to a5 and b5, for players a and b, and variables 1-5.
          > > I did not take the square root of the whole thing, since
          everything
          > > was already square-rooted once.
          > > Not surprisingly, the best players only correspond to other great
          > > players, but some players have much more unique statistical
          > profiles.
          > > In order of "greatest distance from the next-closest profile", we
          > > have:
          > > Sco Reb Ast Stl Blk E
          > > Michael Jordan 33.5 6.5 5.1 2.3 .9
          > > Jerry West 25.1 4.2 6.0 (2.7 .9) .945 (estimated)
          > > No real surprise that Jordan is the "most unique" statistically.

          > > Others scored more than West, but didn't have quality numbers
          > beyond
          > > that.
          > > (Iverson is next, then Karl Malone(!), Kobe, Gervin, Erving,
          Bird,
          > > Wilkins, Dantley, Barry)
          > >
          > > Bill Russell 11.8 14.6 3.8 (1.5 4.0)
          > > Bill Walton 15.9 12.8 4.0 1.0 2.7 .743
          > > Really not very similar, but as close as anyone comes to
          Russell's
          > > combination of skills.
          > > (Thurmond is close 2nd, then Sam Lacey, Elmore Smith, Mutombo)
          > >
          > > Magic Johnson 20.6 7.5 10.4 1.9 .4
          > > Oscar Robertson 22.4 5.3 8.0 (1.5 .3) .644
          > > Magic was "the next Oscar", and then some.
          > > (Grant Hill, Payton, Penny, Strickland, Isiah, Drexler, KJ,
          Frazier)
          > >
          > > John Stockton 17.1 3.3 11.9 2.4 .2
          > > Isiah Thomas 18.0 3.7 8.8 2.0 .3 .543
          > > Stockton is just a giant in the assists category.
          > > (Tim Hardaway, KJ, Strickland, Cousy, Kenny Anderson, Brandon)
          > >
          > > Jerry West 25.1 4.2 6.0 (2.7 .9)
          > > Allen Iverson 25.1 3.9 5.5 2.1 .2 .517
          > > Now we have some real across-the-board similarity.
          > > (Barry, Penny, Kobe, Drexler, Maravich, Oscar, Westphal)
          > >
          > > Oscar Robertson 22.4 5.3 8.0 (1.5 .3)
          > > Penny Hardaway 20.2 5.1 6.2 1.9 .6 .486
          > > (KJ, Payton, Frazier, Cassell, Tim Hardaway, Price, Brandon,
          Magic)
          > >
          > > Moses Malone 21.6 13.2 1.3 .9 1.4
          > > Shawn Kemp 20.9 11.8 2.2 1.4 1.6 .470
          > > (Parish, Gilmore, Reed, McDyess, Ewing, Hayes, Haywood, McAdoo)
          > >
          > > Shaquille O'Neal 29.7 12.7 2.8 .7 2.6
          > > Tim Duncan 25.1 12.0 3.0 .8 2.3 .466
          > > (Kareem, Robinson, Mikan, Pettit, Ewing, Mourning, Wilt, Hakeem)
          > >
          > > Artis Gilmore 20.3 11.9 2.3 .6 2.3
          > > Patrick Ewing 23.5 11.1 2.0 1.0 2.6 .446
          > > (Hayes, Parish, Derrick Coleman, Sabonis, McDyess, Kemp,
          Gallatin)
          > >
          > > The remainder of the top 31 (and their closest match)
          > >
          > > Kareem AbdulJab. 25.9 10.6 3.4 1.0 2.7
          > > Tim Duncan 25.1 12.0 3.0 .8 2.3 .288
          > > (Robinson, Pettit, Mikan, Ewing, Neil Johnston, Shaq, Hakeem)
          > >
          > > Wilt Chamberlain 23.5 14.7 3.5 (1.5 3.0)
          > > George Mikan 24.8 13.1 2.9 (1.3 2.0) .432
          > > (Hakeem, Robinson, Duncan, Pettit, Kareem, Ewing)
          > >
          > > Karl Malone 28.1 11.2 3.4 1.4 .8
          > > Charles Barkley 24.2 12.4 3.8 1.6 .8 .444
          > > (Pettit, Johnston, Mikan, Baylor, Jeff Ruland, Bird, Duncan,
          McAdoo)
          > >
          > > Hakeem Olajuwon 23.7 11.7 2.6 1.8 3.2
          > > David Robinson 26.1 11.8 2.8 1.5 3.3 .275
          > >
          > > Julius Erving 23.0 7.8 4.0 1.9 1.7
          > > Elgin Baylor 22.5 9.6 3.9 (1.6 1.5) .347
          > > (Webber, Marques Johnson, Shareef, Johnston, Lanier, Ed Macauley,
          > > Schayes, Garnett, Bird, Drexler)
          > >
          > > Patrick Ewing 23.5 11.1 2.0 1.0 2.6
          > > Alonzo Mourning 24.5 10.9 1.6 .7 3.2 .332
          > >
          > > Bob Pettit 24.2 11.7 2.8 (1.3 1.8)
          > > George Mikan 24.8 13.1 2.9 (1.3 2.0) .231
          > >
          > > Elgin Baylor 22.5 9.6 3.9 (1.6 1.5)
          > > Chris Webber 21.1 10.1 4.2 1.5 1.8 .215
          > > (Lanier, Erving, Schayes, Johnston, Shareef, Garnett, Pettit,
          > McAdoo)
          > >
          > > Scottie Pippen 18.4 7.5 5.4 2.1 .9
          > > Clyde Drexler 20.6 6.7 5.5 2.1 .7 .306
          > > (Alvan Adams, Connie Hawkins, Toni Kukoc, Billy C., Grant Hill,
          > > Antoine Walker, Marques Johnson, Penny, Cliff Hagan)
          > >
          > > Clyde-Scottie likewise
          > >
          > > Robert Parish 18.1 11.4 1.5 .9 1.8
          > > Elvin Hayes 17.8 10.9 1.7 1.0 2.6 .161
          > > (Gallatin, McDyess, Seikaly, Reed, Larry Foust, Dan Roundfield,
          > > Sampson, Haywood, Brian Grant)
          > >
          > > Bob Lanier 21.4 10.5 3.3 1.2 1.7
          > > Dolph Schayes 20.0 10.1 3.1 (1.4 1.6) .194
          > >
          > > (Elvin Hayes-Robert Parish match)
          > >
          > > Rick Barry 21.9 5.5 4.5 2.1 .5
          > > Kobe Bryant 23.0 5.2 4.2 1.4 .8 .345
          > > (Chris Mullin, Drexler, Hagan, Moncrief, Penny, Ray Allen)
          > >
          > > Kevin McHale 22.1 8.6 1.8 .4 2.0
          > > Rik Smits 19.9 8.3 1.8 .6 1.6 .306
          > > (Lovellete, Darryl Dawkins, Haywood, McAdoo, Yardley, McDyess)
          > >
          > > (George Mikan-Bob Pettit)
          > >
          > > Dan Issel 21.1 8.5 2.2 1.1 .6
          > > Terry Cummings 19.1 9.3 2.2 1.3 .7 .280
          > > (Chambers, Ceballos, Calvin Natt, Shareef, Yardley, Glenn
          Robinson)
          > >
          > > Clearly, as one goes down the list into more "ordinary" players,
          > > there is a proliferation of close profiles.
          > >
          > >
          > > Mike Goodman
          > >
          > > > >
          > > > >
        • msg_53@hotmail.com
          Personally, I don t ever consider position to be a quantifiable statistic. Many forwards have been forced to play center; many forwards are not clearly
          Message 4 of 16 , Sep 16, 2001
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            Personally, I don't ever consider 'position' to be a quantifiable
            statistic. Many forwards have been forced to play center; many
            forwards are not clearly 'power' or 'small' forwards; many players
            are not exclusively guards or forwards; many versatile guards do
            plenty of scoring and passing, and rebounding.
            The possible fragmenting of these lists is virtually infinite. An
            assist from a center is exactly as important as an assist from a
            guard. A rebounding guard, a center who gets steals as well as
            blocks, all these things make a player unique, or at least
            differentiate him from the norm.
            The issue of 3-point shooting might be worth looking into. How one
            goes about racking up one's scoring totals is of some interest. Then
            again, it might invite breaking down points into dunks, layups, etc.
            In the end, points are points. A player's scoring may come from
            inside moves when he is young, and from outside shots later. The
            contribution is still the same.
            One thing these similarity indexes do reveal, is that there are
            some 'classic' profiles by position. Wilt, Kareem, Hakeem, Shaq,
            Robinson, Ewing, Moses, Gilmore, all averaged 22-28 pts, 12-15 reb, 2-
            3 blocks. But the well-rounded centers seem to have enjoyed more
            success.
            The demands of one's position are somewhat situational. The best
            players can usually do whatever is most needed.

            --- In APBR_analysis@y..., harlanzo@y... wrote:
            > It occurred to me that when comparing players through their
            > statistics should we be weighting the comparisons so that some
            > statistics are more important based on positions? For example,
            when
            > comparing point guards the assist category might be more important
            > for weighing similarity than rebound category. Conversely, do we
            > really care whether two centers have similar assist numbers if
            their
            > points, rebounds, and fg % are similar? I think this sounds
            somewhat
            > right with some notable exceptions. The counter argument of course
            > is that centers who pass well (a la Walton) or shoot 3s well
            > (Laimbeer and Sikma) are unique and the similarity scores will help
            > identify players with similar rare skill sets. (To digress, I
            wonder
            > if Jason Kidd and some of the Darrell Walker early 90s seasons are
            > comparable). I am beginning to babble but I think that the
            question
            > I am asking is whether positional demands should change how we
            weight
            > statistical categories when we try to apply similarity scores?
            >
            >
          • msg_53@hotmail.com
            ... seems ... I operate under the assumption that points and rebounds are equally important as contributions; so are steals and blocks, but almost everyone
            Message 5 of 16 , Sep 16, 2001
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              --- In APBR_analysis@y..., deano@t... wrote:
              >..... a reason not to use Euclidean distance -- it
              > weights big differences too much. At least that is the subjective
              > opinion a lot of times. It's the old argument between standard
              > deviation and mean absolute difference -- the first weights big
              > differences a lot but is mathematically easier, but the second
              seems
              > to reflect more of what we want.

              I operate under the assumption that points and rebounds are equally
              important as contributions; so are steals and blocks, but almost
              everyone gets fewer than 2-3 of these, so it seems fair to weigh them
              less. Taking the standard deviation from the mean gives you the
              burden of assigning a weight to the statistical category. I avoid
              this by presuming that bigger numbers implies bigger weights. That
              is, scoring is and should be more important than, say, steals.
              (I did reduce the 'difference' factor by taking their square roots.)

              > The similarity scores, as James did
              > them and as I modified them, fit into the mean absolute difference
              > category. In Mike's categories, then, this implies that there is
              > likely one very big difference between Jordan's numbers and
              everyone
              > else (probably scoring average) -- that gets emphasized, making him
              > the most unique player. I'd like to take a stab at career
              similarity
              > scores using the approach I've outlined to see whether it id's
              Jordan
              > as most unique, too.
              >
              > MikeG -- While I like the comparisons you did, there are 2 comments
              I
              > would make:
              >
              > 1. I'd like to see some non-standardized comparisons. I do like
              the
              > standardized because they make some sense, but I think
              > non-standardized will also tell a story.

              Dean, you could do raw averages, but players from the 60s would only
              compare to players in the 60s. Actually, a great rebounder in the
              90s would seem to compare to an average rebounder in the 60s, for
              example.
              I don't have a ready database of raw averages.

              > 2. You really need some comparison of shooting percentages and
              > turnovers. It really caught my eye with the Duncan-Kareem
              > comparison. I see some similarity between these two, but there are
              > big differences in offensive efficiency. Kareem was nearly
              > unstoppable offensively - my floor%'s and offensive efficiencies
              > reflect that. Duncan is very stoppable, his offensive rating and
              > floor percentage blending in to be about average. Kareem fell to
              > average offensively only in his last year. (I also don't think
              that
              > Kareem was the defensive force that Duncan is, but my memories are
              > biased by the Kareem post-'80, when he wasn't as good as he was
              when
              > younger.)
              >
              > Dean Oliver
              > Journal of Basketball Studies

              Shooting percentages are part of what determines my standardized
              scoring rate, along with game pace (defined as points allowed). I
              only did career totals, so Kareem's incredibly long career has been
              smoothed over, and his very dominant early seasons are not truly
              reflected. Maybe Duncan has peaked, and his career averages really
              won't rank close to Kareem's.
              Further, Duncan's offensive numbers, in my system, get a big boost
              from his being on a great defensive team. You have to agree his
              offensive strength is way above average on his team. In other words,
              the go-to guy on the championship Spurs is going to rate favorably to
              the go-to guy on the champion Bucks from 30 years before, in my
              system.

              Mike Goodman
              >
              >
              > > > > >
            • Dean Oliver
              ... only ... I think this is what I was interested in. I was curious who from today would fit in the 60 s. Or, more interestingly, who from the 70 s might
              Message 6 of 16 , Sep 17, 2001
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                --- In APBR_analysis@y..., msg_53@h... wrote:
                > > 1. I'd like to see some non-standardized comparisons. I do like
                > the
                > > standardized because they make some sense, but I think
                > > non-standardized will also tell a story.
                >
                > Dean, you could do raw averages, but players from the 60s would
                only
                > compare to players in the 60s. Actually, a great rebounder in the
                > 90s would seem to compare to an average rebounder in the 60s, for
                > example.
                > I don't have a ready database of raw averages.
                >

                I think this is what I was interested in. I was curious who from
                today would fit in the '60's. Or, more interestingly, who from the
                '70's might fit in today's game. Are West's raw #'s similar to
                Iverson's or to Richmond's? What happens in baseball is that
                outstanding players tend to be dissimilar to other players in their
                era, but similar to outstanding players of other eras. I have doubt
                that this would happen in basketball, using raw #'s, because of the
                style change. You seem to be saying the same thing.

                (I didn't realize that you don't have a db of raw#'s.)

                > > 2. You really need some comparison of shooting percentages and
                > > turnovers. It really caught my eye with the Duncan-Kareem
                > > comparison. I see some similarity between these two, but there
                are
                > > big differences in offensive efficiency. Kareem was nearly
                > > unstoppable offensively - my floor%'s and offensive efficiencies
                > > reflect that. Duncan is very stoppable, his offensive rating and
                > > floor percentage blending in to be about average. Kareem fell to
                > > average offensively only in his last year. (I also don't think
                > that
                > > Kareem was the defensive force that Duncan is, but my memories
                are
                > > biased by the Kareem post-'80, when he wasn't as good as he was
                > when
                > > younger.)
                >
                > Shooting percentages are part of what determines my standardized
                > scoring rate, along with game pace (defined as points allowed). I
                > only did career totals, so Kareem's incredibly long career has been
                > smoothed over, and his very dominant early seasons are not truly
                > reflected.

                One of my personal quibbles with all the tendex-like rating systems
                out there is there is that they do combine offensive with defensive
                contributions. There is a big difference in my mind between Moses
                Malone, who was an offensive force, and Hakeem Olajuwon, who has been
                dominant defensively. Both were good in the other thing, but
                dominant in just one. Kareem was dominant offensively (and probably
                defensively) early on. Duncan has been dominant defensively, not
                offensively. (Duncan appears to have more of the competitive fight
                than Kareem, but, again, I missed the early Kareem.)

                > Maybe Duncan has peaked, and his career averages really
                > won't rank close to Kareem's.

                I don't think I'd say that Duncan's peaked. He's been pretty
                remarkably consistent since entering the league. Maybe it's only
                remarkable that he stayed in school long enough to actually be ready
                for the league when entering.

                > Further, Duncan's offensive numbers, in my system, get a big boost
                > from his being on a great defensive team. You have to agree his
                > offensive strength is way above average on his team.

                Depending on how you define "average", but, yeah, Duncan looks better
                offensively than he really is because he plays on a great defensive
                team. (He would make most teams better defensively, too.)

                > Personally, I don't ever consider 'position' to be a quantifiable
                > statistic.

                James defined numbers to positions for defensive purposes (a
                shortstop is much more valuable to a defense than a 1st baseman, for
                example). That might be necessary for some of the older guys because
                defensive stats really don't exist in the '60's and early '70's. But
                we can probably still assume that a center was the most important
                defensive player back then, as he is now. This gets adequately
                reflected in blocks, steals, and defensive boards, but you do need
                those #'s.

                > assist from a center is exactly as important as an assist from a
                > guard.

                Only a minor point here -- this is not precisely true (though
                probably true enough for government work). Assists from guards tend
                to be more valuable. This is because they often have to make the
                tougher pass than big men. The weight on an assist is proportional
                to the expected FG% of the guy he passes to. Historically, big men
                have had higher FG% than guards -- hence their assists are weighted
                less. (The assists of the best shooting player on a team are less
                valuable than the assists of the guys getting him the ball.) This
                has changed with the 3 pt shot, but it's a conversion from FG% to
                effective FG%...

                Dean Oliver
                Journal of Basketball Studies
              • Mike Goodman
                ... My raw totals and per-game averages are contained in my season files, along with team totals and averages for that season. My composite lists only have
                Message 7 of 16 , Sep 18, 2001
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                  --- In APBR_analysis@y..., "Dean Oliver" <deano@t...> wrote:
                  > (I didn't realize that you don't have a db of raw#'s.)
                  >
                  My raw totals and per-game averages are contained in my 'season'
                  files, along with team totals and averages for that season. My
                  composite lists only have the 'standardized' rates. From those
                  rates, I can generate 'equivalent totals'. For 'average'
                  scoring/rebounding teams, these would be equal to raw season totals.

                  >
                  > One of my personal quibbles with all the tendex-like rating systems
                  > out there is there is that they do combine offensive with defensive
                  > contributions. There is a big difference in my mind between Moses
                  > Malone, who was an offensive force, and Hakeem Olajuwon, who has
                  been
                  > dominant defensively. Both were good in the other thing, but
                  > dominant in just one. Kareem was dominant offensively (and
                  probably
                  > defensively) early on. Duncan has been dominant defensively, not
                  > offensively. (Duncan appears to have more of the competitive fight
                  > than Kareem, but, again, I missed the early Kareem.)

                  I get your point, Dean, but your examples don't seem the clearest.
                  Olajuwan is better than Malone because he has all the offense Malone
                  had PLUS defense. Never seen the Dream shake?
                  Duncan has virtually all the offense Kareem had, averaged over their
                  careers, according to my numbers. Kareem did maintain a great
                  shooting pct., but Duncan plays in an era of universally-tough D.

                  > I don't think I'd say that Duncan's peaked. He's been pretty
                  > remarkably consistent since entering the league. Maybe it's only
                  > remarkable that he stayed in school long enough to actually be
                  ready
                  > for the league when entering.

                  Some guys enter the league at full strength: Wilt, Oscar, Kareem,
                  Robinson, never improved beyond their first 3 years. Others start as
                  near- superstars, then several years along suddenly shift into true
                  superstar mode: Magic, Bird, Olajuwon, ...

                  >
                  > Depending on how you define "average", but, yeah, Duncan looks
                  better
                  > offensively than he really is because he plays on a great defensive
                  > team. (He would make most teams better defensively, too.)

                  Don't know how a guy 'looks better than he really is', DeanO.

                  >Assists from guards tend
                  > to be more valuable. This is because they often have to make the
                  > tougher pass than big men. The weight on an assist is proportional
                  > to the expected FG% of the guy he passes to. Historically, big men
                  > have had higher FG% than guards -- hence their assists are weighted
                  > less. (The assists of the best shooting player on a team are less
                  > valuable than the assists of the guys getting him the ball.) This
                  > has changed with the 3 pt shot, but it's a conversion from FG% to
                  > effective FG%...
                  >
                  > Dean Oliver
                  > Journal of Basketball Studies

                  This is fun, splitting hairs!
                  If your center kicks out 3 nice passes to guards, who only hit one of
                  the 3 shots, the center only gets one assist.
                  The guard can make 3 nice passes inside, 2 of which may be converted,
                  so he gets 2 assists.
                  So an equally valid argument is that assists from guards
                  are 'easier', and assists from centers are 'undercounted'.
                  I say they are equal.

                  Perhaps more to the issue, evaluate which players make those
                  practical passes which may or may not get them an assist, versus
                  those who will not give up the ball unless it gets them an assist. I
                  can't discern the 2 types from the statistics, but I know it when I
                  see it. (It might be partly discernible in that old assist/turnover
                  ratio.)


                  Mike Goodman
                • Dean Oliver
                  ... systems ... defensive ... fight ... Olajuwon was very solid offensively (not stellar, like Kareem) -- I didn t mean to imply otherwise. Malone was just
                  Message 8 of 16 , Sep 18, 2001
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                    --- In APBR_analysis@y..., "Mike Goodman" <msg_53@h...> wrote:
                    > > One of my personal quibbles with all the tendex-like rating
                    systems
                    > > out there is there is that they do combine offensive with
                    defensive
                    > > contributions. There is a big difference in my mind between Moses
                    > > Malone, who was an offensive force, and Hakeem Olajuwon, who has
                    > been
                    > > dominant defensively. Both were good in the other thing, but
                    > > dominant in just one. Kareem was dominant offensively (and
                    > probably
                    > > defensively) early on. Duncan has been dominant defensively, not
                    > > offensively. (Duncan appears to have more of the competitive
                    fight
                    > > than Kareem, but, again, I missed the early Kareem.)
                    >
                    > I get your point, Dean, but your examples don't seem the clearest.
                    > Olajuwan is better than Malone because he has all the offense Malone
                    > had PLUS defense. Never seen the Dream shake?
                    > Duncan has virtually all the offense Kareem had, averaged over their
                    > careers, according to my numbers. Kareem did maintain a great
                    > shooting pct., but Duncan plays in an era of universally-tough D.

                    Olajuwon was very solid offensively (not stellar, like Kareem) -- I
                    didn't mean to imply otherwise. Malone was just the epitome of a good
                    offensive center who wasn't that good defensively. Rik Smits is
                    another example of the poor defensive type who can score (not as well
                    as Olajuwon/Moses). Olajuwon is very DISSIMILAR to these guys because
                    he is much better defensively. Similarity is all I'm trying to
                    capture, not quality.

                    I looked at Duncan's offensive #'s last night and his offensive rating
                    has been between about 104 and 108 since entering the league, when
                    average offensive ratings have been between about 100 and 103. He's a
                    little more efficient than average. My recollection of Kareem's #'s
                    were about 115 in the early '80s, when average was about 106-108 --
                    relatively higher than Duncan's. Again, these two players just don't
                    seem very SIMILAR to me. I would think of David Robinson as more
                    similar to Kareem. Or possibly Olajuwon. Probably Wilt. Not
                    Russell.

                    > >
                    > > Depending on how you define "average", but, yeah, Duncan looks
                    > better
                    > > offensively than he really is because he plays on a great
                    defensive
                    > > team. (He would make most teams better defensively, too.)
                    >
                    > Don't know how a guy 'looks better than he really is', DeanO.
                    >

                    Another way of saying that the hype on Duncan has been a little
                    extreme. Put him on the Hawks last year and, while he's better than
                    Mutombo offensively, the team still wouldn't have scored much. They
                    would have been pretty close to as good defensively as they were with
                    Mutombo (or better), but they wouldn't be an offensive threat. I
                    don't think Kareem ever played on a weak offensive team.

                    > This is fun, splitting hairs!
                    > If your center kicks out 3 nice passes to guards, who only hit one
                    of
                    > the 3 shots, the center only gets one assist.
                    > The guard can make 3 nice passes inside, 2 of which may be
                    converted,
                    > so he gets 2 assists.
                    > So an equally valid argument is that assists from guards
                    > are 'easier', and assists from centers are 'undercounted'.
                    > I say they are equal.
                    >
                    > Perhaps more to the issue, evaluate which players make those
                    > practical passes which may or may not get them an assist, versus
                    > those who will not give up the ball unless it gets them an assist.

                    The goal is to identify when a good pass is made. Generally a better
                    pass is one made to a better shooter. That's all I try to capture. I
                    capture it in formulas with teammate FG%. For years, I didn't worry
                    about it and it really didn't matter much. Now I've got more
                    sophisticated calculation devices. I've actually found that this
                    adjustment makes the most difference when evaluating different levels
                    of basketball (high school, college, women's).

                    Dean Oliver
                    Journal of Basketball Studies
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