On Fri, 29 Mar 2002, Dean Oliver wrote:

>

> One of the things I've done fairly recently is to look at how efficient

> players are as a function of how frequently they try to score. Since I do

> have estimates of how efficient players are that I trust, I have always

> felt that some of these efficient guys can increase their scoring rate,

> while others can't. I've taken a stab at looking at this by looking at

> boxscores and the "possession rate" of players. Basically, my hypothesis

> was that players are less efficient -- have lower offensive ratings -- as

> they have higher possession rates (possessions/minute). I've looked for

A good hypothesis, but only if qualified in certain ways. Such as

"ceteris parabus": holding all other things equal, if we ask one player

to do more things per minute, his efficiency is likely to decrease.

Although the graphs have efficiency on the horizontal axis, which seems

hard to justify...we can try to say that high efficiency nights put a cap

on a player's possessions per minute, but in reality there is no such cap.

We could shove the ball in his hands a few more times. That would

probably lead to more missed shots or turnovers, and lower efficiency, but

that simply shows that efficiency is not really the independent variable

here, it seems to me it should be the dependent variable.

I don't know if the hypothesis works as well if we look at all of a

player's games. There could be some causality that goes in the reverse

direction and leads to a reverse relationship: on nights when a player

is doing well (and I don't think we have to invoke potentially mythical

hot streaks to justify the existence of such games, it could simply be a

mistmatch that night), he is probably more likely to get fed the ball by

his teammates and will have more possessions. So on those hot nights

compared to regular nights, the relationship would be high effic --> high

possessions, instead of high possesions --> low effic.

> this a few ways. First, I looked to see whether there were "critical

> points" of possession rate, where players are statistically significantly

> better at lower possession rates than they are at higher possession

> rates. Second, I looked at moving averages (of every 10th percentile) to

> see whether there were general trends. Finally, I summarized the results

This is the part where I'm trying to follow. From the graphs, it looks

like you're doing calculations, or at least plots, at offensive ratings

values of 120, 115, 110, 105, etc. Are those the percentiles that you

speak of? What are you calculating a moving average of -- a moving

average of possessions per minute? and calculated over what set of

observations -- all of the preceding ones?

Are the critical points part of the graphs you drew up, or is that a

separate analysis?

> in a plot of possession rate vs. observed offensive rating. Those seem to

The plots and their labels are not quite clear. Are you looking at all

the games in which a player achieved, say efficiency of 120 or better, and

calculating the possessions per minute of those games, compared to this

games of <= 119 efficiency, and if the difference is significant plotting

the max possessions per minute among those games? I would expect an

occasional non-downward-sloping line segment, just from random variations,

even though the overall hypothesis of a downward-sloping could be (and

evidently is) correct.

Also, the interpretation above doesn't explain why most of the graphs dip

down into 0 possessions per minute, with efficiencies that are positive

(and large) rather than undefined. I would think that 0 possesions per

minute would require extrapolation, since it would almost never be

observed in any actual game, except for the occasional "trillion" game

where a player plays 1 minute and has a box score line that goes 1 0-0 0-0

0-0 0 0 0 etc.

So I'm not understanding what's behind these graphs.

The notion of looking at maxima brings up a possible statistical technique

to use: econometricians often estimate what is called a frontier

regression line, one which basically looks at the outer hull of a set of

data points -- possibly required to be convex, and usually with a

couple of random error terms assumed to exist, so that a player can

ocasionally perform at better than 100% of his long run potential, due to

the occasional random good night. I.e. it's not literally the outer hull,

just outside "most" of the point.

> be doing fairly well in matching up with observed season possession rates

> and observed offensive ratings. So I'm hoping to predict players who can

Aggregate statistics such as season stats don't always show the same

relationship as the underlying individual game stats. E.g. John Stockton

and Rashard Lewis probably had different, and lower, graphs during their

rookie seasons than they did later in their careers (Stockton shot a

career low 47%, Lewis scored fewer than 16 points per 48 minutes). Once a

player's career reaches maturity, then one could probably compare

different seasons -- although one could imagine changes in the quality of

the player's team and role could affect what his season stats were like.

> increase their productivity without significant loss of efficiency.

>

> A few plots are attached that show the relationships I'm seeing (based on

> last 2 years of data). Some players haven't shown any ability to maintain

> high possession rates. Some are about the same efficiency no matter what

> rate. Some show steep drop-offs, others more gradual. The plots just take

> a little bit of looking at. I've selected the players somewhat at

> random. Rashard Lewis, Ben Wallace, Jerry Stackhouse, Allen Iverson, Aaron

> McKie, Jason Terry, Antawn Jamison, Reggie Miller, Tim Duncan, David

> Robinson, Vince Carter, Kobe, Shaq, Derek Fisher, Rick Fox, Robert Horry,

> Michael Finley, Steve Nash, Dirk Nowitzki. That's enough for now.

I would've like to have seen a few more non-superstar non-scorer types in

the mix...e.g. Ben Wallace, whose graph wasn't in the set of attachments

that I received. Some of them high efficiency types such as Todd

McCulloch -- how fast would his efficiency plunged if he was given more

possessions? And for comparison, some players who are just plain bad.

Putting several of the plotted lines in a single graph would make it

easier to compare players.

It was surprising that Kobe's max possessions didn't max out at

particularly high numbers per minute. I would've thought that Shaq's been

absent enough for there to be a good number of Shaq-less and presumably

high possession nights for Kobe. Or ... was Kobe enjoying high efficiency

on those Shaq-less nights, which would cause them to not show up on the

plots (no statistically significant drop off in possessions per minute)?

If so, those games might not show up on the graphs but Kobe's high

possessions and high efficiency on those nights would be important

observations.

>

> I'm not sure how to summarize all of this in quick numbers, but I'm pretty

> pleased with where it's going and what it's saying.

It's comforting that the graphs show such strong consistent downward

slopes but I'd want to know more about the methodology before drawing

conclusions.

--MKT