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Reference for TENDEX, Pts Created, etc.

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  • Dean Oliver
    I want to provide a reference for some of the methods available for analyzing individual players. These include q Dave Heeren s TENDEX rating q Doug Steele s
    Message 1 of 2 , Feb 14, 2001
      I want to provide a reference for some of the methods available for
      analyzing individual players. These include

      q Dave Heeren's TENDEX rating
      q Doug Steele's TENDEX rating
      q Bob Belotti's Points Created formula
      q HoopStat Grades from Secour and Couzens
      q David Claerbaut's Quality Points
      q Martin Manley's Production Rating
      q Minkoff Player Rating
      q Bob Chaikin's simulation techniques
      q Doug Steele's defensive evaluation, and
      q Journal of Basketball Studies methods (multiple)

      The first six are very similar methods, ones that I call Approximate
      Value techniques or (for baseball folks) linear weights. They all
      pretty much sum the positive things and subtract the negative things
      to arrive at a number that can be approximately compared among all
      players in a league. Each one may have little variations, like
      adjusting for pace or position, but they are essentially the same.
      They all have the benefit of simplicity and they all can do gross
      comparisons of sets of players. The formulas, as best I can tell,
      are presented below for reference.

      Abbreviations Used:

      PTS: Points Scored
      REB: Rebounds
      AST: Assists
      STL: Steals
      BLK: Blocks
      FGM: Field goals made
      FTM: Free throws made
      FGA: Field goals attempted
      FTA: Free throws attempted
      FGMiss: Field goals missed
      FTMiss: Free throws missed
      TOV: Turnovers
      MIN: Minutes played
      GP: Games played
      Oreb: Offensive Rebounds
      Dreb: Defensive Rebounds
      PF: Personal Fouls
      FF: Flagrant Fouls
      TEC: Technical Fouls

      Heeren's TENDEX

      Dave Heeren has been using his TENDEX formula for a long time, since
      the 1960's according to his press releases. He has published aspects
      of it in his Basketball Abstracts, which he published for a while.

      Dave Heeren's TENDEX = (PTS + REB + AST + STL + BLK - FGMiss - FTMiss
      - TOV)/ (Game-pace factor)

      where his game-pace factor is kept private. (You can divide the
      total by minutes, as he typically does, or by games.) The game-pace
      factor is approximated by the following formula:

      Game-pace factor ~ (TMBallPoss)/(RefBallPoss)

      TMBallPoss = (FGA + 0.4*FTA + TOV)_TM

      with the subscript TM standing for the player's team, and RefBallPoss
      is some reference calculation of Ball Possessions (using the above
      formula for a league or all the league for all seasons). For sake of
      being definitive, let's say that RefBallPoss is given by

      RefBallPoss = (FGA + 0.4*FTA + TOV)_HAvg

      where HAvg means the historical NBA average since the advent of the
      24-second clock. (You actually need a RefBallPoss for each game or
      each season - any time period that you are interested in.)

      I am positive that this game-pace factor is not exactly what Heeren
      does, but it has the same general effect. I don't use this method
      because the game-pace factor is mysterious.

      Steele's TENDEX

      Doug's TENDEX is in fairly common use because he provides a lot of
      statistics (http://shell.rmi.net/~doug/) and because he publishes his

      Steele TENDEX = (PTS - FGMiss - FTMiss/2 + 1.25*STL + 1.25*AST + BLK
      + REB - 1.25*TOV - TEC - 2*FF - PF/2)/ GP

      Doug makes no claim as to the validity of the formula. I don't
      really use it.

      Belotti's Points Created

      Belotti's Points Created formula has been put out in his books (I've
      only seen the '92-93 edition). His technical version is

      Points Created = PTS + AST*(2-VBP) + (REB + STL + BLK)*VBP - (FGMiss
      + FTMiss + TOV)*VBP - 0.5*VBP*PF

      You can divide by minutes or games. VBP is the value of a ball
      possession, as he estimates apparently on a seasonal basis (perhaps
      on a team-season basis) as

      VBP = (Ball possessions)_LG/PTS_LG

      Ball possessions = REB + FGM + TOV + FTM/2 + BLK/2

      (Bob is a member of the group, so he can clarify my guesses here.)

      I generally don't use his method because I haven't calculated the

      HoopStat Grades

      Published by Joshua Trupin and Gerald Secor Couzens in their book,
      "HoopStats: The Basketball Abstract" (which I know upset Dave
      Heeren), this method just has different weights on the different

      HSG = FTM + 1.4*FGM + AST + STL + 1.4*BLK + 0.85*Oreb + 0.5*Dreb -
      0.6*FGMiss - 0.8*TOV

      No one really uses the method, though they did actually do some funky
      to obtain the weights. It is odd that nothing is taken away for
      missed free throws.

      Claerbaut's Quality Points

      David Claerbaut put out a few books by the name of The NBA Analyst.
      His Quality Points, though he seems to disguise it, pretty much comes
      down to

      Quality Points = PTS = AST + BLK + STL + REB + (FGM/0.5 - FGA) +
      (FTM/0.75 - FTA)*0.5

      Basically, David uses a target FG% of 50% and a target FT% of 75% to
      give guys additional credit. Not clear why. No one appears to use
      this method. Again, you can divide by games or minutes.

      Manley's Production Rating

      Manley put out at least three editions of Basketball Heaven, his
      basketball analysis book (that makes 5 different authors, if you're
      counting). He uses a simplified version of the above linear weight

      Credits = PTS + AST + REB + STL + BLK - FGMiss - FTMiss - TOV

      PR = Credits/GP

      Because of the extreme simplicity of this method, I will occasionally
      use it. I tend to view the additional "accuracy" of the other
      methods above as not worth the effort unless pace really is
      significantly different among the individuals being compared.

      Minkoff's Player Rating

      Developed by Tony Minkoff (who has done a bit of research on the
      web), my understanding of this stat is that it takes a linear
      regression of minutes per game against each per minute stat, then
      uses those coefficients to compute the number of minutes "earned"
      through a player's statistical performance. This may be modified by
      weighting it with actual minutes per game, a modification I'm not
      sure I like.

      This is one of the most interesting player stats I have seen and I
      have seen a lot. The concept of rating players by how much time they
      deserve is very innovative and conceptually simple. I am not
      convinced that linear regression is a great tool for a game as
      complex as basketball. I think this may be why the stat is fudged by
      weighting the actual minutes per game along with it. I think it is
      more interesting to compare the minutes earned with actual minutesÂ…

      Chaikin's Simulations

      Bob Chaikin is another member of this group. Bob has spent a ton of
      time developing his online database, which, if you look at it
      carefully, has numbers in it that indicate the percentage of time
      players shoot, shoot a three, pass, commit turnovers, or do something
      from the field (??). Very cool, though I have never been sure how he
      comes up with all these. He said that he took a bunch of
      measurements. I think he then developed estimation techniques for
      the factors so that he doesn't have to get carpal tunnel recording
      them for every game.

      With these factors, Bob has developed simulation software, B-Ball,
      which simulates games to some degree. I don't think it simulates
      every dribble, every pick and roll, but it simulates a lot and pretty
      quickly. I don't recall whether it does stochastic simulations
      (different results every time with the same teams) or deterministic
      simulations (same result every time). But I tend to believe the

      Unfortunately, Bob has to do the simulations and it's hard to dissect
      them. He does generate a boxscore that could be compared against
      reality. He also simulated for me the 1997 Finals with Chicago
      beating Utah (http://www.tsoft.com/~deano/articles/aa060197.htm).
      One of the first things I'd like to do is actually compare his
      predictions against the reality of that series. He predicted a 5
      game series victory for Chicago, but it actually took 6 games. He
      never predicted the famous Jordan Flu, but I guess you can't fault
      him for that. If anyone wants to take a closer look at his
      predictions vs. reality, feel free to do so.

      What I'd like to do with Bob's stuff is examine player strategies
      more. Can he suggest a player rotation for the injury-riddled
      Warriors this year? Should Dampier or Foyle start at center? Are
      there different teams that one should start against over another?
      Can Bob slightly modify his numbers to look at whether Isiah Rider
      should pass more for the Lakers?

      There is a lot of promise here, but it's not public enough to
      examine. It would be nice to trust the method a little, then test
      its limitations in making strategy predictions.

      Steele's Defensive Evaluations

      Doug calls his method Defensive Tendex. Defensive Tendex is actually
      quite a complex thing and Doug's own write-up doesn't explain it
      particularly well. So I'll give it a try.

      Half of Doug's method, the part I call Man Defense because it relates
      to shutting down a man, looks at how well a player lowers his man's
      Tendex rating (where Tendex is Steele Tendex above). Doug's algorithm
      for doing this is to approximate match-ups in a game -- starter to
      starter, sub to sub -- then evaluate whether a player is below his
      season average Tendex rating. The difference between what a player
      does in a game and his average is credited (or charged if the player
      has a good game) to the matched-up defender. Strictly, Doug only
      evaluates the offensive categories -- points, assists, offensive
      rebounds, turnovers -- in his Tendex formula for this.

      The second half of the formula accounts for the defensive statistics
      a player racks up, including defensive rebounds, blocks, steals, and
      fouls (even though we can't really distinguish between offensive and
      defensive fouls). I call this second half of Doug's formula the Team
      Defensive part because blocks, defensive rebounds, and steals often
      come as a result of teammate interaction.

      I think he pretty much adds these two parts together. For example,
      let's say that Kobe Bryant allows his defender an extra 2.0 Tendex
      points per game. Kobe's defensive rebounds, blocks, steals, and
      personal fouls work out to give a Tendex value of 8 per game, let's
      say. This adds up to be -2 + 8 = 6, so Kobe's defensive rating is 6.
      It doesn't really have a meaning - perhaps points, but it's really
      not clear.

      I think Doug's method is innovative
      (http://shell.rmi.net/~doug/00-01DefensiveTendex.html). Difficult to
      carry out and debatable in the match-up part, but useful. It looks
      at one of the things we all qualitatively see in his Man Defense
      part. Along with my own defensive methods, I always look at Doug's
      stuff as a cross-check because my stuff does nothing like his Man

      Journal of Basketball Studies methods

      These are mine and I have a lot of them. You'll get sick of them
      after a while. Fundamentally, I don't have any "rating" method, but
      a number of estimation techniques. These estimate the following
      properties for all players:

      q Scoring Possessions (number of possessions on which a player
      produces at least one point)
      q Possessions used (number of possessions a player contributed to the
      end of)
      q Points Produced (points produced through all appropriate routes,
      assists, field goals, free throws, offensive rebounds, NOT defensive
      stats; the sum of all players values on a team approximately equals
      the team total)
      q Floor % (scoring possessions divided by possessions)
      q Offensive Rating (Points produced divided by possessions times 100)
      q Defensive Rating (Points allowed per 100 possessions)
      q Individual Wins and Losses (Defined multiple ways, see
      q Individual Net Points

      Probably the closest things to an individual rating like those of
      TENDEX, etc. are a player's total Net Points in a season or the
      difference between his individual wins and losses. Very few of these
      have simple formulas, though the team versions are really simple.
      Over the near future, I'll document the team versions, then work on
      the individual versions, which require some rather advanced
      probability theory. The best reference in the short term for the
      individual methods are at
      http://www.tsoft.com/~deano/articles/JordanvsOlaj.html. The formulas
      there are the non-technical versions, but they will still probably
      make your head spin.

      Finally, note that one of the fundamental assumptions of most of the
      linear weights/approximate value methods is that a ball possession
      has a given value, whether it is 1 point (as assumed by Heeren and
      Manley, implicitly by Claerbaut) or calculated in a general sense (by
      Belotti, HoopStats, Steele). I think that this is assuming the real
      problem away. What is most important about a player is how many
      points he produces with his possessions and that's what I aim to

      Dean Oliver
      Journal of Basketball Studies
    • bchaikin@aol.com
      dean - thanks for the positive writeup... all the questions you asked about the B-BALL software concerning examining player strategies is exactly how i used
      Message 2 of 2 , Feb 14, 2001
        dean - thanks for the positive writeup...

        all the questions you asked about the B-BALL software concerning examining
        player strategies is exactly how i used the software when i consulted with
        the nets/heat in the mid 1990s. what players to play together, who to play
        against certain teams, who to sub when a certain player is out hurt, who to
        trade for, what free agents to sign, etc. the basic task was to plug the
        players into a team's lineup and let the computer play the games - the more
        games played the more certain the result. if the software is updated during
        the season (say at least once a week, every 3-4 or so games), the results are
        quite accurate..

        the possession factor (poss fact), or "touches per minute" number, is
        calculated by how often a player shot, passed, got fouled, or turned the ball
        over per minute that he played. think about it - once you stop your dribble
        you have to do one of the 4 (except for some rare exceptions - double fouls,
        technicals, flagrants, etc) - and divide that total by a player's minutes
        played and you get his poss fact. the key, of course, is determining how
        often players pass and that is based on me counting passes in over 1000 nba
        games (over a three year time span, the 88-89, 89-90, and 90-91 seasons -
        along with counting lots of other stuff like team and player possessions, off
        the ball fouls, you name it ). i've spot checked those numbers over the past
        decade frequently in "test" games, and while the total team possessions per
        game have steadily decreased all thru this decade the average passes per team
        possession haven't...

        actually the software is indeed public enough to examine (i welcome
        comments/criticisms), although i haven't updated it since the 97-98 season as
        i haven't had a gig with an nba team since then and other projects (the
        databases at www.bballsports.com) have taken precedence. its currently in
        hibernation waiting for an opportunity to awaken - hopefully soon. a free
        copy of the software with all of the teams from three seasons from the late
        1980s can be downloaded by anyone from "members.aol.com/bchaikin" and a
        version with any seasons from 77-78 to 97-98 can be purchased thru me ($30
        for three seasons, $10 per each additional season, $100 for all 21 seasons)...

        as for trusting the "method" of the software, i personally do not have to do
        the simulations - anyone can use the free demo mentioned above (you can't
        beat free) for evaluation purposes, or purchase some seasons more recent from
        me. i think you'd be pleasantly surprised by the results. i'm not sure what
        stochastic simulations are (i do remember stoichiometry in chemical reactions
        from my college chemistry), but i will tell you that you'll never see the
        same box score twice in hundreds of thousands of simulated games...

        bob chaikin
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