- Sep 16, 2001--- In APBR_analysis@y..., harlanzo@y... wrote:
> It occurred to me that when comparing players through their

Yes and No. What we're trying to come up with here is a general set

> statistics should we be weighting the comparisons so that some

> statistics are more important based on positions?

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

their

> for weighing similarity than rebound category. Conversely, do we

> really care whether two centers have similar assist numbers if

> points, rebounds, and fg % are similar? I think this sounds

somewhat

> right with some notable exceptions. The counter argument of course

wonder

> 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

> if Jason Kidd and some of the Darrell Walker early 90s seasons are

question

> comparable). I am beginning to babble but I think that the

> I am asking is whether positional demands should change how we

weight

> statistical categories when we try to apply similarity scores?

wrote:

>

>

> --- In APBR_analysis@y..., "Mike Goodman" <msg_53@h...> wrote:

> > --- In APBR_analysis@y..., "Michael K. Tamada" <tamada@o...>

> > >.... Euclidean distance,

variables

> > > sqrt( X^2 + Y^2 + Z^2 + ...) where X, Y, Z, etc. are the

> difference

> > > between, say, Magic Johnson and Larry Bird in whatever

> we

Rebds.

> > 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

> > Another

the

> > > 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

> > square root of each stat. I compared the top 31 players on my

actually

> > infamous "alltime" list to the other 514 in the list. (I

> > ran out of columns in Excel, for the first time.)

everything

> > 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

> > was already square-rooted once.

Bird,

> > 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,

> > Wilkins, Dantley, Barry)

Russell's

> >

> > 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

> > combination of skills.

Frazier)

> > (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,

> >

Magic)

> > 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,

> >

Gallatin)

> > 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,

> >

McAdoo)

> > 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,

> >

Robinson)

> > 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

> >

> > Clearly, as one goes down the list into more "ordinary" players,

> > there is a proliferation of close profiles.

> >

> >

> > Mike Goodman

> >

> > > >

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