Hello,
everyone.
My
name
is
Kevin
O'Donnell.
I'm
a
JMP
Global
Customer Reference Intern,
and
today
I'll
be
presenting
on
a
personal
analytics
project
that
I've
done
that
is
the
NBA
Player
Matchup Model.
So
just
to
get
started,
I
would
like
to
go
over
my
idea
and
the
motivations
for
building
the
model.
I've
always
been
incredibly
interested
in
basketball.
I've
been
a
huge
basketball
fan
for
my
whole
life,
and
I
was
looking
for
a
new
analytics
project
to
dive
into,
so
I
ended
up
asking
this
question
here:
Could
we
model
a
player's
offensive
success
based
on
their
averages
and
the
strength
of
their
opponents
as
well?
So
as
most
of
us
know
from
watching
any
sport,
player
performance
varies
greatly
from
game
to
game.
It's
based
on
a
variety
of
factors
and
one
of
these
being
a
player's
average
points.
That
will
be
a
very
strong
predictor
for
points
in
an
NBA
game,
but
it's
far
from
the
only
influence
on
a
player's
offensive
performance.
So
going
into
this
project,
I
wanted
to
build
a
model
that
predicted
the
players
points
in
the
game
based
on
the
points
per
game,
but
also
a
lot
of
other
variables
which
we
will
look
into
on
the
next
slide.
So
ideally,
this
will
be
helpful
for
coaches
and
team
analysts
to,
for
example,
determine
which
of
their
offensive
players
are
likely
to
over
perform
or
able
to
perform
really
well
based
on
their
match
ups
and
vice
versa,
which
of
their
players
they
might
want
to
avoid
on
offense
because
they're
being
guarded
by
some
of
the
best
defensive
players
on
the
other
team.
This could
inform
play
calling
and
game
planning,
so
if
a
particular
defender
is
weaker,
coaches
may
look
to
target
that
match
up
or
look
to
force
a
switch
onto
their
best
scorer.
In
the
entertainment
realm,
fantasy
basketball
players
could
use
this
data
to
figure
out
who
to
start
or
who
to
pick
up
off
the
Waiver
Wire,
so
it
has
a
broad
range
of
applications.
So
here's
a
little
bit
of
the
overview
of
the
data.
I'll
go
through
this
quickly,
and we'll
see
this
as
I
go
into
the
JMP
demo
a
little
bit
more
in
detail,
but
we're
going
to
predict
points
per
game
based
on
seven
main
categories
of
data.
So
we're
going
to
use
player
offensive
averages
for
the
season,
this
includes
things
like
points
per
game,
3.2
point
percentages,
and
advanced
metrics
such
as
usage
rate,
which
records
how
often
an
offensive
player
is
used
on
their
team.
Player
attributes
such
as
height,
wing
span,
vertical
leap
will
also
be
included
for
both
the
offensive
and
defensive
players
because
these
physical
attributes,
I
would
assume,
also
contribute
to
how
many
points
a
player
will
score.
Finally,
in
terms
of
the
offensive
players,
we'll
use
career
averages.
The
same
averages
that
we're
using
for
the
season,
we'll
also
use
for
the
career
to
add
a
little
more
robustness
to
the
model,
and
overall
team
pace
and
offensive
rebounding
percentage
is
also
going
to
be
a
predictor
because
that
will
determine
how
many
possessions
there
will
be.
If
there
are
more
possessions
in
the
game,
it's
more
likely
that
any
given
player
will
have
more
points.
And so, on
that
same
token,
defensive
team
pace
and
defensive
rebounding
percentage
will
also
be
used.
In
terms
of
individual
defensive
stats,
things
like
steals,
blocks, fouls,
and
other
advanced
metrics
such
as
defensive
win shares,
which
measures
an
individual
player's
contribution
to
the
team's
wins
on
defense.
Those
are
also
going
to
be
predictors
to
probably
negate
the
amount
of
points
that
are
scored
by
an
offensive
player.
And
then
finally,
the
defender
attributes
will
be
used
as
I
mentioned
earlier.
So
before
we
get
right
into
the
data
and
the
modeling
and
JMP,
I
would
like
to
go
over
the
matchup
data
that
I
was
using
for
the
bulk
of
the
model.
So
the
NBA
recently
implemented
some
new
personal
match
up
data
collection
and
it's
based
on
detailed
player
tracking.
So
it
tracks
the
closest
defender
at
every
point,
not
just
the
primary
defender
on
a
play.
It
only
tracks
front
court
time
and
it
will
track
partial
possessions.
So
what
this
means
is
that
a
player
could
be
guarded
by
as
many
as
five
different
players
on
a
single
play,
and
each
defender
would
be
awarded
the
respective
amount
of
matchup
minutes
for
that
possession.
So
here
we
have
an
example
of
Terry
Rozier
for
the
Hornets
being
guarded
by
four
different
players
on
different
teams.
In
the
first
row,
Steph
Curry
is
guarding
him
in
only
one
game
for
2.7
minutes
and
allowed
two
points.
So
if
we
think
of
a
hypothetical
where
the
Hornets
are
playing
Steph
Curry's
Golden
State
Warriors
and
Curry
guarded
Rozier
for
10
seconds,
and
then
Klay
Thompson
switched
on
to
Rozier
for
another
10
seconds,
both
would
be
awarded
those
10
seconds
of
matchup
time.
However,
if
Rozier
scored
a
two
pointer
at
the
end
of
this
possession,
the
points
would
be
marked
for
Klay
Thompson.
This
is
really
cool
tracking
data
and
I
love
how
specific
it
is,
but
it
did
cause
some
problems
when
I tried
to
model
the
points
per
minute
for
each
player
and
defender
combination,
which
was
my
original
plan.
So
I
was
originally
going
to
use
the
offensive
player
stats
and
defensive
player
stats
that
I
mentioned
in
the
previous
slide
in
every
individual
matchup.
But
since
many
defenders,
like
you'll
see
here,
logged
very
small
amounts
of
time,
like
Stanley
Johnson
only
guarded
Rozier
for
an
average
of
under
one
minute
a
game,
that's
not
enough
time
for
some
of
these
points
per
minute
measurements
to
be
normal.
So
going
back
to
that
Klay
Thompson
hypothetical,
if
Klay
only
guarded
Rozier
for
10
seconds
the
whole
game
and
Rozier
having
to
score
two
points
in
that
possession,
then
Rozier's
points
per
minute
against
Klay
in
that
row
would
be
12.
So
obviously,
extrapolating
that
to
a
full
game,
even
excluding
the
back
court
time
as
this
data
does,
it's
very
unrealistic.
So
I
had
to
go
with
a
slightly
different,
less
ideal
approach.
Instead
of
using
the
individual
defensive
stats,
I
actually
averaged
them
out
for
each
combination
of
player
and
defensive
team.
So
instead
of
using
Rozier
versus
Curry
and
Rozier
versus
Thompson,
I
would
use
Rozier
versus
the
entire
Golden
State
Warriors
average
based
on
the
amount
of
matchup
minutes
that
each
player
defended
Rozier.
So
for
example,
if
Steph
Curry
and
Klay
Thompson
both
guarded
him
for
half
the
amount
of
possible
match
up
minutes,
then
the
team
average,
let's
say
steals
per
game,
would
just
be
the
arithmetic
mean
of
Curry
steals
and
Klay
steals
per
game.
The
same
would
go
for
every
defensive
variable
and
that's
obviously
a
simple
example,
but
the
same
goes
for
every
player
versus
every
team.
So
obviously
this
is
not
ideal
because
it
minimizes
the
individuality
of
the
matchup.
But
I
had
to
abandon
that
points
per
minute
approach
because
the
samples
were
too
small
and
the
response
was
heavily
distorted.
So
this
model
that
I've
created
with
the
aggregated
data
is
more
accurate
than
my
initial
attempts,
even
though
it
sacrifices
some
individuality.
So
at
this
point,
I'm
going
to
switch
into
JMP
here
and
do
a
little
bit
of
the
demo
on how
I
built
the
model
and
some
exploratory
data
analysis
to
begin.
So
to
begin,
we're
just
going
to
look
at
some
marginal
relationships
with
points
in
the
graph
builder,
and
I'm
able
to
choose
any
I
want.
But
for
now
we're
going
to
look
specifically
at
three
variables,
the
first
being
points
per
game.
So
we
see
here,
we
have
a
moderate
relationship
with
points
and
points
per
game,
and
it
is
positive
as
we
would
expect.
The
average
points
that
someone
puts
up
in
a
game,
or
over
the
course
of
the
season
rather,
is
going
to
obviously
influence
how
many
points
they
score
in
a
game.
Similarly,
something
like
usage
rate,
the
advanced
statistics
that
I
was
discussing
earlier,
also
has
a
positive
relationship,
just
slightly
weaker
than
the
relationship
between
points
and
points
per
game.
Finally,
if
we
look
at
some
of
the
career
stats,
if
we
look
at
career
points
per
game,
then
again
we
see
a
positive
relationship,
but
that
is
a
little
bit
weaker
because
it's
averaged
over
the
course
of
a
player's
career
rather
than
the
season
that
we're
currently
in.
But
hopefully
this
could
help
adjust
for
some
major
differences
in
the
points
per
game
totals
or
averages
rather.
So
now
that
we
have
a sort
of
an
idea
of
the
data
itself,
we
can
move
into
the
simple
linear
regression
with
points
by
points
per
game
as
a
benchmark
for
this
model.
So
as
I
mentioned,
you
can
predict
based
on
just
points
per
game
and
it
will
give
you
a
decent
prediction.
But
we're
looking
to
improve
that
prediction
by
adding
some
of
these
different
variables,
offensive
and
defensive.
So
if
we
run
this
script
here,
this
is
just
comparing
some
runs
of
a
simple
linear
regression
on
the
training
and
validation
set
using
KFolds
validation
throughout.
And
if
I
run
here
using
the
Hidden
Validation 2
column
that
I'll
be
using
for
the
remainder
of
these
models,
then
we
can
see
the
regression
here.
So
here's
a
regression
plot.
It
looks
pretty
scattered.
There's
not
a
clear
linear
relationship,
but
the
RS
quare
is
moderate,
meaning
that
46.5 percent
of
the
variation
in
points
is
accounted
for
by
this
average
points
per
game,
which
is
pretty
good.
And
the
Root Mean Square Error
is
about
5.
27.
The
Root Mean Square Error
is the
standard
deviation
of
the
residual,
so
it's
essentially
the
variation
in
how
well
our
model
is
predicting.
Its
standard
deviation
is
around
five.
And
we
can
also
look
at
some
other
measures,
such
as
the
AIC,
which
is
used
to
compare
models
for
predictability.
So
AIC
is
another
important
measure,
and
it
measures
how
well
the
model
will
predict
relative
to
the
number
of
predictors
put
in
the
model,
just
to
make
sure
you're
not
adding
way
too
many.
So
in
this
case,
the
AIC
is
very
high,
and
we
can
come
back
to
this
number
as
we
look
at
the
comparison
between
this
and
the
multiple
linear
regression
that
I
will
show
later.
So
while
I
was
trying
to
pick
the
model
that
I
was
going
to
choose,
I
decided
to
use
the
model
screening
feature
in
JMP,
which
allows
you
to
select
your
response
variables
and
all
the
factor
variables.
I
ended
up
putting
in
all
of
the
numeric
variables
that
I
had
for
a
full
model
just
to
see
initially
which
models
perform
the
best.
And
I
was
able
to
choose
from
a
variety
of
these
different
methods,
including
XGB
oost
and
Generalized R
egression,
and
then
of
course,
just
the
normal
Lease
Square.
In
the
interest
of
time,
this
would
take
forever
to
run
because
it's
using
some
of
these
machine
learning
algorithms.
So
I'm
instead
just
going
to
pull
up
a quick
screenshot
of
the
model
screening.
So
here
we
have
the
output
from
this
model
screening.
It
shows
the
RS
quare.
Again,
I
was
using
KFold
validation
with
ten
folds
here.
So
this
shows
the
RS
quare
and
the
Root M
ean
Square
Error
for
each
run.
So
we
can
see
that
the
Least
Square
Fit
actually
had
a
very
strong
fit
compared
to
some
of
the
machine
learning
algorithms,
which
I
was
surprised
by.
But
it
actually
helps
for
interpretability
because
some
of
these
machine
learning
algorithms,
they're
more
of
a
black
box.
And
if
I
were
to
use
those,
it
wouldn't
be
as
easy
to
interpret
the
coefficients
or
see
which
variables
are
truly
significant
or
which
are
just
being
used
for
prediction.
So
because
the
fit of
Least Square
and
the
Lasso Regression,
which
I'll
get
into
a
little
bit
later,
were
so
high,
it's
actually
a
good
sign
that
I'm
able
to
use
that
for
better
interpretability.
So
as
we
can
see,
the
most
accurate
model
is
this
multiple
linear
regression
with
Lasso
Regularization.
Lasso
Regularization
is
a
statistical
technique
that
regularizes
the
model
and
selects
features
to
minimize
multicollinearity.
Multicollinearity
is
the
correlation
between
predictors
and
that
can
negatively
affect
the
model.
So
using
this
technique,
we're
able
to
take
the
full
linear
regression
model
shown
here
and
remove
some
of
the
variables
to
minimize
the
multicollinearity
and
maybe
satisfy
some
of
the
linear
assumptions
better.
So
with
that
information,
I
was
able
to
take
the
variables
selected
with
Lasso
Regularization
and
then
create
a
multiple
linear
regression
using
those
variables.
So
as
you
can
see
here,
the
Actual
by
Predicted
Plot
looks
pretty
similar.
It
might
be
slightly
closer
to
the
line
of
best
fit
here,
which
is
a
good
sign.
And
we
can
see
our
effect
summaries,
but
we're
going
to
scroll
a
little
bit
past
that
so
that
we
get
to
the
summary
of
our
fit.
So
compared
to
the
simple
linear
regression,
the
RS
quare
and
the
Adjusted
RS
quare
are
very
similar
and
that's
probably
because
points
per
game
is
such
a
heavily
influential
factor
in
this,
as
well
as
the
simple
linear
regression,
obviously.
So
the
fit
is
not
too
much
different.
However,
adding
these
different
variables
shown
here
does
improve
the
Root M
ean
Square
Error
a
little
bit.
It
went
from
about
5.3
to
little
over
5.2,
which
is
not
a
drastic
improvement,
but
an
improvement
nonetheless.
But
the
real
difference
here
is
in
the
AIC
and
comparing
these
models
in
terms
of
their
predictability,
the
AIC
dropped
significantly
from
the
simple
linear
regression
to
this
multiple
linear
regression
with
Lasso R
egularization,
which
is
definitely
a
good
sign.
We
see
some
of
these
Parameter
Estimates
down
here
and
of
course
the
results
for
RS
quare
and
Root
Mean
Square
Error
in
cross
validation.
So
looking
at
some
of
these
Parameter E
stimates,
the
points
per
game,
again
very
significant,
it's significant
at
the
.05 a
lpha
level
and
many
below
that.
And
this
is
to
be
expected,
as
we've
explained
already.
Turnover
percentage
is
also
significant
and
this
has
a
negative
relationship
with
points.
As
one
would
expect,
if
you're
turning
the
ball
over
more,
that's
less
opportunities
to
shoot
the
ball,
less
opportunities
to
score.
So
that
checks
out
with
just
our
knowledge
of
basketball.
Here
we
have
the
defensive
pace,
or
the
pace
of
the
defensive
team,
and
this
has
a
slightly
positive
relationship
with
points
conditional
on
the
other
factors
in
the
model.
Again,
that's
to
be
expected
because
the
faster
a
team
plays,
that's
generally
more
chances.
However,
it
might
not
have
such
a
strong
effect
as
turnovers
or
points
per
game.
And
then
finally,
defensive
rebounding
percentage.
This
is
just
how
often
the
defensive
team
hauls
the
defensive
rebound.
Again,
this
is
preventing
second
chance
points
for
the
offense,
so
it
should
have
a
negative
relation
ship,
which
it
does.
So
all
these
things
check
out,
and
then
some
of
these
other
variables
are
insignificant
conditionally,
but
included
because
they
improve
the
predictability
of
the
model.
So
something
like
usage
rate
might
not
be
significant
at
the
.05
level,
but
it
nonetheless
improves
our
predictions.
Now,
knowing
that
points
per
game
might
not
be
available
at
the
beginning
of
the
season,
to
the
extent
that
it
is
near
the
end
of
the
season,
meaning
that
points
per
game
might
be
a
little
less
reliable
with
a
smaller
sample
size.
I'd
look
to
create
an
alternate
model
without
that
to
see
if
I
could
still
predict
better
than
the
simple
linear
regression
and
similar
to
the
Lasso
regression,
but
without
dependency
on
a
points
per
game
for
the
season
measure.
So
this
alternate
model,
I
created
using
backward
selection
by
AIC.
And
again
I
left
out
the
season
points
per
game,
so
it
still
includes
the
other
points
per
game
measurements,
or
other
per
game
measurements
rather,
like
field goals
attempted
from
three
and
from
two,
which
along
with
some
of
these
other
variables
can
be
a
proxy
for
that
average
points
per
game.
So
it'
s
not
completely
robust
against
early
season
fluctuations
and
small
sample
sizes.
But
it's
possible
that
these
variables
might
be
a
little
bit
more
representative
of
how
a
player
is
going
to
perform
in
the
long
run.
I'm
thinking
that
maybe
players
might
be
a
little
more
consistent
with
their
attempted
stats,
or
the
rate
at
which
they're
shooting
the
ball,
rather
than
just
the
amount
of
points
they
get
that
could
vary
based
on
just
a
small
sample
size.
These
could
as
well
but...
Just
using
this
model
as
an
alternative,
and
it
turns
out
that
it
actually
predicts
pretty
similarly
to
the
model
with
points
per
game
in
it.
So
it
might
not
be
favored
necessarily
if
points
per
game
is
available.
Inappropriate
but
it
provides
a
similar
prediction.
So
we
can
see
that
the
RS
quare
is
pretty
similar,
may
have
increased
a
little
bit,
and
the
Root
Mean
Square
Error
is
again
similar.
The
AIC
suggests
that
the
other
model
is
a
better
model
for
predicting
based
on
the
amount
of
variables
included,
so
that
is
definitely
something
to
note.
But
each
model
has
its
advantages.
This
one,
particularly,
we
can
see
some
of
the
conditional
relationships
of
the
other
variables,
particularly
those
on
the
defensive
side,
that
we
couldn't
see
as
much
in
the
other
one
because
points
per
game
was
dominating
so
much.
So
we
see
here
that
two
pointers
and
three
pointers
attempted
are
weighing
insignificantly
for
points,
which
again,
that
makes
sense
because
the
more
shots
you're
taking,
the
more
likely
you
are
to
score
more
points.
And
then
there
are
some
other
variables
that
make
sense,
and
some
others
that
maybe
are a
little
confusing
at
first
sight.
So
offensive
win shares,
that
being
a
significant
variable
makes
sense
that's
measuring
how
much
a
player
is
contributing
to
wins
on
the
offensive
side,
it
makes
sense
that
that
has
a
positive
relationship
as
we
can
see
down
here.
So
offensive
win shares
right
here
has
a
positive
relationship.
And
also
the
defensive
rebounding
percentage
down
here
decreases
the
estimation
again,
so
that
is
pretty
consistent
with
what
we've
seen
in
the
previous
model.
Average
fouls
per
game,
average
personal
fouls
per
game
down
here,
has
a
negative
effect
which I thought
was
interesting.
So
a
player
or
team
with
a
higher
foul
total
is
going
to
negatively
affect
the
points
scored
for
the
offensive
player.
This
might
mean
they're
more
aggressive.
I
would
assume
that
they
are
playing
more intense
defense
in
limiting
points
through
steals,
blocks,
or
heavily
contested
shots,
and
as
a
result,
they're
getting
more
fouls
called
on
them.
However,
this
is
not
all
good
for
the
defense
because
since
the
player
can
foul
out
with
six
fouls,
there
is
a
certain
balance
to
strike
in
the
defensive end.
You
don't
want
to
be
too
aggressive
because
then
you
could
be
giving
up
easier
points
or
you
could
be
leading
your
players
into
foul
trouble.
So
that's
an
interesting
variable,
I
think,
to
consider.
And
of
course,
this
is
a
conditional
significance,
so
it
might
change
slightly
based
on
the
removal
or
addition
of
certain
other
variables.
And
finally,
a
couple
of
defensive
relationships
are
particularly
confusing
at
first
glance,
I
think.
Specifically
involving
blocks
and
defender
height.
So
we
think
of
basketball
as being
very
dependent
on
height.
If
you
are
taller,
you're
more
likely
to
go
to
the
NBA.
Seven
footers,
I
think
you
have
a
20 percent
chance
of
just
going
to
the
NBA
even
if
you
are
seven feet.
So
this
is
something
that
we
think,
if you
block
shots
more
and
you're
taller,
you're
going
to
be
affecting
the
offense's
points
negatively.
However,
we
see
that
these
relationships
are
actually
conditionally
positive,
which
is
very
interesting
that average
blocks
per
game
and
the
defender
height,
as
well
as
the
blocking
rate,
are
all
positive
relationships.
And
so
initially,
I
was
confused
by
this,
but
I
think
this
has
more
to
say about
the
players
that
these
players
are
guarding
rather
than
the
actual
variables
themselves.
So
what
I
mean
by
this
is
when
you consider
that
taller
players
with
better
blocking
stats
are
big
men
playing
power
forward
or
center,
they're
guarding
other
big
men.
And
so
that
makes
sense
a
little
bit
more.
Guards
tend
to
put
up
more
points
in
the
NBA
with
the
emphasis
on
three-
point
shooting
now.
And
a
lot
of
offenses
are
run
through
some
of
these
smaller
players
who
tend
to
be
guarded
by
other
smaller
players.
Whereas
these
taller
players,
with
more
blocks,
are
guarding
big
men
who
maybe
aren't
the
focal
point
of
the
offense,
aside
from
certain
players
like
JokiÄ
and
Embiid
and
Giannis.
But
this
causes
a
positive
relationship,
but
it's
really
more
a
function
of
the
position
that
these
players
are
playing.
So
I
thought
that
was
an
interesting
conditional
relationship
to
highlight
within
the
model,
and
it
involves
a
little
bit
more
deeper
thinking
about
the
relationship
between
blocking,
height,
and
the
points
that
an
offensive
player
puts
up.
So
in
terms
of
the
model
overall,
we
can
see
that
this
one
and the Lasso regularized
model
are
very
similar
in
their
predictions.
We'll
see
that
in
more
detail
soon
when
I
flip
to
the
2021
predictions,
but
the
choice
then
might
not
be
too
significant.
Both
have
their
advantages.
Of
course,
this
one
allows
us
to
see
the
significance
of
more
of
the
variables,
specifically
the
defensive
variables,
whereas
the
first
one
has
a
slightly
lower
AIC
and
might
be
better
for
predictions
if
the
data
is
available.
So
both
leave
a
little
bit
to
be
desired
in
terms
of
predicting
much
more
reliably
than
the
simple
linear
regression.
I
would
have
liked
to
see
this
Root
Mean S
quare
Error
decrease
more,
and
it's
something
I
would
look
into
as
I
continue
this
project,
looking
to
gather
better
data,
trying
to
make
the
matchups
more
individualized
without
sacrificing
the
normality
of
the
response
variable,
things
like
that.
But
with
that
being
said,
these
are
the
models
that
I
have
now,
and
we
can
look
to
test
these
on
the
2021
season
thus
far.
So
if
I
switch
over
here
to the
matchups
for
2021,
we
have
the
same
data
table
just
with
this
year's
matchups.
And
so
I'm
just
on
Josh
Hart's
matchups
right
now
because
I
go
to
Villanova
and
he's
a
Villanova great,
so
here
we
have
him
as
a
player,
his
team,
and
the
defensive
teams,
his
stats,
their
stats.
As
we've
already
seen,
these
are
all
the
variables
that
could
be
included
in
the
model.
Apologize
for
the
quick
panning,
but
here
we
have
the
predictions
at
the
end.
So
these
prediction
variables,
or
rather
these
columns,
are
the
model
predictions.
So
our
first
one,
our
first
model,
is
the
Optimal
Multiple L
inear
Regression
that's
using
the
Lasso
regression
and
including
the
points
per
game
variable.
As
you
can
see
in
this
game,
he
is
predicted
to
put
up
12.8
points
and
the
residual
here
is
about
five.
So
in
reality
this
residual
is the
points
minus
the
prediction.
So
he
actually
put
up,
this
is
around
13
and
this
is
around
five,
so
he
put
up
about
18
points
here
instead
of
our
predicted
13.
So
that's
obviously
not
a
great
measure.
And
then
we
can
look
at some of
the
alternative
model.
The
alternative
model
prediction
is
very
similar,
and
we
will
see
this
in
greater
detail
as
I
flip
back
to
the
PowerPoint
and
show
you
kind
of
a
condensed
version
of
this
data
table,
because
right
now
I
know
that
this
in JMP
is
a
little
bit
overwhelming
because
there's
so
many
variables,
so
many
random
numbers
being
thrown
at
you.
So
I'm
going
to
switch
back
into
the
PowerPoint
to
show
you
some
of
the
predictions
for
both
Josh
Hart
here
and
for
Kevin
Durant.
All
right,
so
now
that
we
have
our
two
models
and
the
simple
linear
regression
to
compare
it
to,
we
can
apply
these
predictions
to
games
that
Kevin
Durant
has
played
this
season.
So
here
are
four
games
played in
Atlanta,
Charlotte,
Chicago,
and
Cleveland.
In
the
first
one,
he
scored
31
points.
In
actuality,
both
our
models
predicted
close
to
26
points,
so
the
residual
is
just
around
five.
However,
we
see
that
when Kevin
Durant
is
close
to
his
average
points
around
28
or
29
points
per
game,
when
he
actually
scores
that,
the
predictions
are
very
close
because
points
per
game
weighs
so
heavily
in
these
models.
So,
for
example,
in
this
Cleveland
game,
our
first
model
predicted
26.2
points,
he
actually
scored
27.
Therefore,
the
residual
is
less
than
one.
And
similarly
here,
the
residual's
less
than
one
for
the
alternative
model
as
well.
So
we
see
that
the
model
excels
when
players
perform
close
to
average,
which
they
will
do
most
of
the
time.
But
there's
obviously
variation,
like
in
this
game
against
Charlotte,
he
had
a
particularly
good
game.
He
scored
38
points.
It's
a
great
game,
but
particularly
good
game
by
Kevin
Durant
standards.
And
so
the
model
predictions
are
much
farther
off.
And
we
see
the
same
thing
with
Josh
Hart.
His
points
average's
a
little
bit
lower
because
he, again,
carries
a
lighter
load.
Kevin
Durant
is
a
star
player
on
the
Nets,
so
he's
getting
a
lot
of
touches
and
taking
a
good
portion
of
those
shots.
So
here
we
have
Hart's
production.
Again,
his
points
average
is closer
to
these
12
and
14
range.
So
the
residuals
here
are
very
small.
When
he
puts
up
14,
our
models
predicted
around
13.5
and
the
residuals
are around .5
.
So
we
have
really
good
predictions
for
when
he
scores
an
average
amount
of
points
or
close
to
an
average
amount
of
points.
But
when
he
scores
less
or
much
greater
then
the
predictions
tend
to
suffer
a
little
bit.
So
with
all
this
being
said,
I
know
I
ran
through
these
models.
Let's
take
a
step
back
and
look
at
the
limitations
in
detail
and
some
further
study
that
I
could
embrace.
So
first
of
all,
these
are
using
averages
by
the
offensive
player
and
defensive
team
as
opposed
to
offensive
player
and
individual
player.
As
I've
mentioned,
that
would
be
the
ideal
scenario,
but
as
I
was
doing
it,
it
didn't
work
out
like
that.
So
that
could
be
causing
some
problems
because
it's
duplicating
some
results.
Instead
of
being
sort
of
a
one
to
one,
if
a
player
is
being
guarded
by
this
player,
this
is
how
many
points
they
will
score.
If
a
player
is
being
guarded
by
a
combination
of
players
on
this
team,
this
is
how
many
points
they
will
score.
So
it's
easier
to
predict
but
maybe
a
little
less
accurate.
Additionally,
the
averages
are
for
the
entire
season,
which
means
predictions
toward
the
beginning
may
be
less
accurate,
as
I
mentioned,
which
is
something
that
I
think
the
career
values
try
to
remedy
a
little
bit.
It
could
be
worth
adding
things
like
points
per
game
in
the
season
variables
with
a
lag
of
maybe
five
seasons.
So
taking
the
average
points
per
game
for
the
last
season,
two
seasons
ago,
three
seasons
ago,
and
so
on
to
try
to
add
some
more
variables
and
maybe
predict
a
time
or
a
trend
in
player
performance.
Additionally,
player
performance
is
dependent
on
countless
other
factors
such
as
cold
or
hot
streaks,
how
well
they've
been
performing
as
of
late,
injuries
on
their
own
team,
Injuries
on
the
opposing
team
that
could
increase
or
decrease
their
role,
minor
injuries
that
they
are
dealing
with
themselves
that
could
decrease
or
increase
their
role.
And
then
things
like
rest
days,
travel
time,
and
a
lot
of
other
intangibles
like
NBA
players
are
human
and
we
all
know
some
days
we're
not
feeling
the
best,
other
days
we're
feeling
great,
more
energetic.
Those
types
of
things
could
lead
to
better
performance
or
worse
performance.
So
these
intangibles
are
not
going
to
be
something
that
I
can
factor
into
the
model
but
it's
important
to
recognize
that
they
could
still
affect
the
points
in
a
given
game.
In
terms
of
further
study,
I
would
love
to
kind
of
rectify
all
these
limitations
and
look
to
predict
a
more
holistic
variable
such
as
offensive
rating.
So
offensive
rating
is
going
to
predict
a
player's
points
per
100
possessions
contributed
to
the
game
instead
of
just
one
aspect
of
the
game
in
points.
I
would
love
to
predict
something
like
this
or
flip
it
to
the
defensive
side
and
predict
a
defensive
rating
based
on
who
they're
likely
to
go
up
against
on
offense.
So
something
like
that
I
think
would
be
really
cool
and
it
would
extend
the
application
of
this
more
toward
coaches
and
team
analysts
instead
of
maybe
some
of
the
fantasy
basketball
players
who
are
looking
for
a
strict
measurement
like
points
or
something
like
that.
So
with
all
this
being
said,
I'm
definitely
going
to
continue
working
on
this
project.
It
was
a
lot
of
fun
and
I
love
looking
at
these
models
and
interpreting
from
a
basketball
standpoint
what's
going
on.
If
you
have
any
questions,
please
feel
free
to
put
those
questions
in
my
community
post
in
the
comments.
I'll
be
happy
to
answer
them.
And
if
you
have
any
suggestions
as
well
for
further
study,
I
would
also
be
happy
to
take
those
on.
Thank
you
so
much
your
time.
