• ## Reference for TENDEX, Pts Created, etc.

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• 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
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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
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
formula:

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
VBP.

"HoopStats: The Basketball Abstract" (which I know upset Dave
Heeren), this method just has different weights on the different
stats.

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
methods.

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
results.

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
Defense.

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
http://www.tsoft.com/~deano/articles/iwldef.html)
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

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
calculate.

Dean Oliver
• 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
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dean - thanks for the positive writeup...

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
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
bchaikin@...
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