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1870Re: [APBR_analysis] Re: Consistency Score

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  • igorkupfer@rogers.com
    Feb 26, 2003
    • 0 Attachment
      ----- Original Message -----
      From: "Michael Tamada" <tamada@...>
      To: <APBR_analysis@yahoogroups.com>
      Sent: Wednesday, February 26, 2003 5:45 PM
      Subject: RE: [APBR_analysis] Re: Consistency Score
      <snip>
      >
      > I guess this is what causes the nagging doubt that I still have; although the inverse
      > coefficient of variation idea is a good one, I wonder to what extent it really is
      > measuring what we would call "consistency" as opposed to measuring who's got
      > a large mean.
      >

      Looking back on what I wrote, it seems I left that part largely undefined. The
      inspiration for Consistency Scores was the frequent characterization of some players as
      inconsistent, seemingly without regards to what that meant -- the type of stuff you
      hear regularly from colour commentators. CS was an attempt to lend some objective basis
      to the notion of consistency.

      But the more I think about it, the whole area lies uncharted. What does it mean for a
      player do be "consistent"? And if we agree on a definition, would that mean that
      consistency is a valuable trait in a player? Is this even measurable?

      In order to not get bogged down with these legitimate questions, I'll just ignore them
      for now, and focus on a better measure (see below). Perhaps after I get something good,
      I can test it to see if consistency is indeed an important asset.

      > Igor is correct that simply looking at standard deviation penalizes the Duncans and
      > Malones who'll tend to have larger standard deviations than the bench scrubs of the
      > league, who simply don't accumulate enough points or Manley credits (do we have
      > to (TM) them like Tendex?) to have large standard deviations.
      >

      Heh. Does anyone else use the credits? I often use them because I love the simplicity.
      But most of the measures I devise are completely neutral with regards to the rating
      being used -- credits works fine, but TENDEX and Individual Wins works as well.

      > But I wonder if the Consistency Score goes too far in the other direction, in terms
      of
      > rewarding the Duncans and Shaqs with their large means.
      >

      This is an important point, one I overlooked earlier. You are right: means are weighted
      too highly. I forgot what it was that Consistency Scores was supposed to be
      measuring -- consistency, not overall performance. There are plenty of other ratings to
      measure that, no need to duplicate those efforts.

      So the problem then becomes: how do you "isolate" consistency, without rewarding
      players who contribute too little to vary much from their average performances? This is
      my second pass at a solution:

      CS = 1 / (variance / mean) * 100

      By using the square of the standard deviation, less weight is placed on the mean, and
      the CS is concentrated more on the actual variation. To show how Consistency Scores
      attempts to capture the variation, I'll use the hypothetical example of 3 players, each
      playing 5 games:


      Games #
      Plyr 1 2 3 4 5 mean sdv var CS
      ------------------------------------------------------
      1 | 30 12 6 36 6 18 14.1 198.0 9.1
      |
      2 | 14 15 16 20 25 18 4.5 20.5 87.8
      |
      3 | 9 10 11 15 20 13 4.5 20.5 63.4
      |
      4 | 4 5 6 10 15 8 4.5 20.5 39.0


      Players 1 and 2 have identical means, but the first is clearly less consistent -- and
      the CS reflects that. Players 2 and 3 have identical variances, but different means.
      Under my formula, player 2 is rewarded for having the higher mean -- but the difference
      is not too severe: 87.8 vs 63.4. Player 4 also has the same variance as player 2, but
      has a much lower mean. He is penalized more severely.

      I think this version of my formula captures more of what I think consistency is --
      certainly better than my first try. To show the difference, here are the top 10 CS in
      Manley Credits (tm), old ranking in the first column, and new ranking in the second
      column.

      Old New Player New CS

      3 1 wallace,ben 308 |---| + |----|
      1 2 duncan,tim 368 |---| + |------|
      18 3 miller,reggie 259 |---| + |---|
      12 4 mourning,alonzo 269 |--| + |----|
      138 5 mckey,derrick 152 |-| + |-|
      10 6 stockton,john 276 |---| + |----|
      16 7 robinson,david 260 |-----| + |------|
      4 8 payton,gary 305 |--| + |------|
      158 9 curry,michael 144 |-|+ |--|
      7 10 pierce,paul 298 |----| + |----|


      So here are the top and bottom twenty Consistency Scores version 2.0 performers:

      EffFG%

      1 mcgrady,tracy 4659 |---| + |--|
      2 robinson,glenn 4161 |---| + |--|
      3 iverson,allen 4082 |-| + |----|
      4 bryant,kobe 3682 |----| + |-----|
      5 jordan,michael 3639 |--| + |--|
      6 houston,allan 3582 |----| + |---|
      7 carter,vince 3503 |----| + |---|
      8 payton,gary 3363 |--| + |---|
      9 o'neal,jermaine 3349 |---| + |---|
      10 pierce,paul 3299 |---| + |----|
      11 webber,chris 3215 |-----| + |---|
      12 o'neal,shaquille 3162 |------| + |----|
      13 marion,shawn 3124 |------| + |----|
      14 malone,karl 3101 |-----| + |----|
      15 baker,vin 2965 |-----| + |----|
      16 finley,michael 2929 |-----| + |---|
      17 duncan,tim 2861 |----| + |-----|
      18 hamilton,richard 2839 |--| + |-----|
      19 garnett,kevin 2809 |-----| + |---|
      20 bibby,mike 2774 |----| + |---|

      [...]

      280 bowdler,cal 345 || + |----------|
      281 drew,bryce 342 || + |---------|
      282 anderson,shandon 341 || + |-----------------|
      283 bradley,shawn 337 || + ||
      284 stith,bryant 335 || + |--------|
      285 shaw,brian 334 || + |------------------|
      286 amaechi,john 333 || + |------------|
      287 palacio,milt 331 || + |--------|
      288 mitchell,sam 315 || + |-----------------|
      289 childs,chris 313 || + |-----------------|
      290 ferry,danny 304 |------| + |-------------|
      291 bell,raja 299 |----| + |----------------|
      292 torres,oscar 297 || + |----------------|
      293 mccarty,walter 295 || + |--------------|
      294 langdon,trajan 276 || + |-----------------|
      295 alston,rafaer 270 || + |------------------|
      296 cummings,vonteeg 252 || + |-----------------|
      297 lopez,felipe 249 || + |---------------|
      298 woods,loren 225 || + |---------|
      299 buechler,jud 199 || + |--------------|


      Manley Credits

      1 wallace,ben 44 |---| + |----|
      2 duncan,tim 43 |---| + |------|
      3 miller,reggie 43 |---| + |---|
      4 mourning,alonzo 40 |--| + |----|
      5 mckey,derrick 39 |-| + |-|
      6 stockton,john 39 |---| + |----|
      7 robinson,david 39 |-----| + |------|
      8 payton,gary 38 |--| + |------|
      9 curry,michael 37 |-|+ |--|
      10 pierce,paul 37 |----| + |----|
      11 brown,p.j. 36 |----| + |---|
      12 mason,anthony 35 |--| + |-----|
      13 brand,elton 35 |-----| + |-----|
      14 christie,doug 35 |---| + |---|
      15 coleman,derrick 35 |---| + |-----|
      16 weatherspoon,cla 35 |--| + |-----|
      17 bryant,kobe 34 |-----| + |--------|
      18 o'neal,shaquille 34 |-----| + |-----|
      19 cassell,sam 34 |-----| + |--|
      20 harpring,matt 33 |---| + |---|

      [...]

      295 kemp,shawn 13 |-| + |-----|
      296 rooks,sean 13 |-|+ |----|
      297 lopez,felipe 13 |-|+ |---|
      298 delk,tony 13 |--| + |--------|
      299 griffin,eddie 13 |---| + |------|
      300 solomon,wille 13 |-|+ |---|
      301 smith,charles c 12 |--| + |-------|
      302 amaechi,john 12 |-| + |----|
      303 glover,dion 12 |-| + |------|
      304 cummings,vonteeg 12 |-|+ |-------|
      305 stith,bryant 12 ||+ |----|
      306 mccarty,walter 12 || + |--------|
      307 alexander,courtn 12 |--| + |------|
      308 starks,john 12 |-|+ |-----|
      309 arenas,gilbert 11 |---| + |------|
      310 croshere,austin 11 |--| + |---------|
      311 wallace,gerald 11 |-|+ |------|
      312 wallace,john 10 |-|+ |-----|
      313 torres,oscar 10 |--| + |-------|
      314 langdon,trajan 10 |-|+ |--------|


      Minutes

      1 iverson,allen 315 |----------| + |--|
      2 snow,eric 214 |----| + |--|
      3 walker,antoine 210 |------| + |---|
      4 garnett,kevin 189 |--------| + |----|
      5 mason,anthony 181 |-----| + |------|
      6 payton,gary 174 |-----| + |---|
      7 sprewell,latrell 166 |---------| + |------|
      8 robinson,glenn 160 |------| + |---|
      9 bibby,mike 154 |----| + |----|
      10 stockton,john 149 |------| + |----|
      11 jamison,antawn 146 |-------| + |---|
      12 mobley,cuttino 145 |---------| + |------|
      13 bryant,kobe 141 |-----| + |-----|
      14 coleman,derrick 137 |-----------| + |-|
      15 szczerbiak,wally 135 |--------| + |----|
      16 davis,antonio 135 |---------| + |---|
      17 barry,brent 134 |--------| + |-------|
      18 robinson,cliffor 133 |-----| + |---|
      19 brand,elton 132 |-------| + |---|
      20 jones,eddie 131 |--------| + |----|

      [...]

      295 arenas,gilbert 16 |------| + |---|
      296 manning,danny 16 |--| + |--------|
      297 johnson,avery 16 |----| + |---------|
      298 doleac,michael 16 |---| + |----|
      299 alexander,courtn 16 |-------| + |---------|
      300 wallace,gerald 15 |-| + |----------|
      301 brown,kwame 15 |--| + |--------|
      302 morris,terence 15 |---| + |----------|
      303 thomas,etan 15 |-| + |--------|
      304 montross,eric 15 |--| + |------------|
      305 davis,hubert 14 |-------| + |---|
      306 lynch,george 14 |---| + |--------|
      307 solomon,wille 14 |--| + |------------|
      308 mccarty,walter 13 |-| + |--------|
      309 strickland,mark 12 |-| + |--------|
      310 alston,rafaer 12 |-| + |--------------|
      311 bell,raja 12 |-| + |-----------|
      312 cummings,vonteeg 11 || + |----------------|
      313 pope,mark 11 || + |--------|
      314 torres,oscar 11 |---| + |--------------|


      best,
      ed
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