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240Re: Similarity Scores

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  • harlanzo@yahoo.com
    Sep 15 9:49 PM
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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
      >
      > > >
      > > >
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