Re: Athlon Sports on scoring efficiency

["Thomas Murphy" <tfmiii@worldnet.att.net>]

Thanks for the reply. You're going to make me work aren't you ;>) OK, so
I've actually run some date (below).

----- Original Message -----
From: Alexander Wang <awang@MIT.EDU>
To: Thomas Murphy <tfmiii@worldnet.att.net>; Celtic list <celtics@igtc.com>
Sent: Thursday, October 25, 2001 7:53 AM
Subject: Re: Athlon Sports on scoring efficiency


> At 05:40 AM 10/25/01, Thomas Murphy wrote:
> >During the '2nd half' both Paul and Ray were presented with each other's
> >situations from the 'first half' - Paul got three dunks and two wide open
3s
> >whereas the defense clamped down on Ray and he got one open look for 2
pts
> >but otherwise was presented with four tough possessions which led him to
> >pass the ball back to Sam Cassell. The final box score looked like this:
> >Pierce 6-6 6-8 20 pts
> >Allen 6-6 0-0 14 pts.
> >Now according to your formula for efficiency Ray Allen is supposedly more
> >efficient than Paul (2.3 to 2.0) despite having scored 6 less points in
> >exactly the same number of possessions!
>
> A couple of things here. When Ray passes off to Sam Cassell, his team
> doesn't lose possession of the ball, so this is fundamentally different
> from a scoring opportunity where the other team typically gets a defensive
> rebound.
>
> Second, somehow Paul dunked the ball three times and hit two three
pointers
> and his scoring efficiency dropped to a third of what it was. Isn't this a
> perfect indication of why PPS is flawed?

NO

First off, to quote the 'great communicator' - "there you go again!" ;>)
What I mean by this is you are using another example of an extremely odd,
atypical situation to try and prove your point. Now there is no real problem
with hypotheticals or thought experiments and I think your use of them has
been very instructive - but ultimately I think they are only instructive of
how statistics can be misinterpreted. Each of your examples deals with an
*extremely* small data set. This problem (the small N problem) is well known
to cause a breakdown of statistics. In other words statistical operations
are bound to produce wierd results (as you have shown) when there are only a
very few data points used for interpretation - like trying to take an
opinion poll of the entire US by only asking the seven people waiting for
the subway. It just doesn't work because with so few data points the margin
of error is simply way to high - so high that it includes any results you
may produce. That is why opinion polls require anywhere from 1000 - 2000
respondents - in order to avoid the small N problem and drive down the
margin of error to acceptable levels (3-5%). That is why you keep getting
screwy results in your hypotheticals. In other words it is a problem with
your examples, not necessarily with the statistics.
>
> Much of your remaining arguments rest upon the "role player vs. star
> player" distinction. The star players have the responsibility to generate
> points in difficult situations where role players can pick their spots,
> which is why Steve Kerr is never going to be an All-Star. And most of
these
> guys go to the line. This efficiency is not "washed out" as you say
though,
> because FTs are converted at a much higher percentage (and when they're
> not, like when Rodman shoots 30%, it didn't really benefit the team very
> much).
>
> Anyway, of course you have to separate these types of players; numbers
> won't give you everything. But lest you believe that the efficiency
measure
> I proposed "logically" leads to ridiculous results (like Steve Kerr > MJ),

Jordan vs Kerr, 1998 - who is the more efficient scorer?

Jordan
28.7 ppg
46.5 FG%
23.8 3pt%
78.4 FT%

Kerr
7.5 ppg
45.4 FG%
43.8 3pt%
91.8 FT%

When we use you proposed statistic for divining which is the more efficient
scorer - lo and behold - it is STEVE KERR!

Kerr: 376 pts / (302 FGA + (49 FTA / 2)) = 1.15

Jordan: 2357 pts / (1893 FGA + (721 FTA / 2)) =  1.05

By your measure Kerr is clearly the more efficient scorer.

> let me propose my own example. Let's say that Ted is a 4'6" third-string
> point guard who has no offensive talent, but he can get open in inbounds
> plays, take care of the ball, and hit free throws. Ted's coach puts him in
> during late game situations when his team is up a few points, to take the
> intentional foul. So over the course of the season, Ted goes 18-20 from
the
> line, all from intentional fouls. At the end of one game, Ted throws up a
> halfcourt shot for fun and misses it. So Ted's season efficiency score is
> based on 0-1 FG, 18-20 FT, for a PPS of 18! Obviously you wouldn't argue
> that Ted is far more efficient than Michael Jordan, just as I wouldn't
> argue that Steve Kerr is more efficient than MJ, even though Steve at
least
> had to hit a couple of three pointers in a real game situation.
>
> The main point is that there is a volume effect which isn't accounted for.

OK I'll buy that - and we can eliminate the problem of the volume effect and
the small N problem by only dealing with top scorers. That will eliminate
Kerr as Mr Basketball ;?)

But even after excluding the lesser scorers, shouldn't volume be accounted
for in some manner . . . hmmm, I've got no answer - just a question at this
point.

> Guys who convert at a higher volume are more valuable at the same
> efficiency level. But incorporating this volume effect into your formula
by
> arguing "Higher volume requires free throws so let's boost up the value of
> free throws a ton" is invalid. In terms of efficiency, the relative
> efficiency of free throws vs field goals is accounted for by their higher
> percentage. That's why Pierce is still #2 by my measurement after Shaq. By
> "excluding" the attempt from your calculation, you're missing a
fundamental
> point, which is that the other team gets the ball - you lose possession -
> always after a made FG or FT and most of the time off a missed one.

That is fair enough.
>
> Anyway, the thing is that big time scorers who go to the line a lot and
> shoot high percentages still rate extremely highly under the measurement I
> proposed, with Pierce still #2 behind Shaq. I just think that you avoid
> some weird anomalies that PPS gives you, like Eric Williams behind roughly
> as efficient as Vince Carter. Eric's not as inefficient as his FG% says
> because he does go to the line a lot, but in my mind it makes him
> relatively average (which he is under pts/(FGA+FTA/2)) rather than very
> good as he is under PPS.
>
> Alex
>
Yet isn't this 'anomaly' also eliminated when one excludes low volume\low N
players? Eric Williams vs Vince Carter is analogous to the comparison
between Kerr and Jordan you objected to above, no? So shouldn't you have
already excluded this example from your analysis rather than holding it as a
debit against PPS?

It sounds as if what you are arguing for is for the most part the
compression of the scale of values upon which the players will be ranked.
You feel that FTs are overvalued on a PPS scale and would rather see a scale
based on a "points per scoring opportunity" scale. My complaint about this
scale is that it fails to take into account the generation of additional
opportunities as an element of efficient scoring, which PPS does since every
shot is a potentially missed shot whereas FTs represent points above and
beyond the normal game context. You claim it does because FTs are
(typically) converted at a much higher rate.

So if this is so, does your proposed change actually change any of the
efficiency rankings of 20 ppg scorers? In other words how much 'distortion'
does your measure actually eliminate?

One last idea - have you thought of ranking players on a points/missed shot
scale? This would seem to get to the core of 'inefficiency' - potentially
losing the ball without scoring. I wonder if it would alter the rankings
significantly?

Here's how the top ten ppg scorers rank according to these three measures:

PPShot        PPScoring Opportunity       PPMissed Shot

1) Shaq                  Shaq                                Shaq
2) Pierce                Pierce                               Pierce
3) Kobe                Vince                                 Kobe
4) Marbury            Kobe                                Vince
5) Vince                Marbury                            Marbury
6) Stackhouse        Tmac                                Webber
7) Iverson              Stackhouse                        Tmac
8) Tmac                Webber                            Iverson
9) Webber            Iverson                            Stackhouse
10) Jamison            Jamison                            Jamison

Clearly the different measures alter some of the rankings depending on what
you want to emphasize:

PPS - how many points per 'offensive gamble' (shot)

PPSO - how many points per offensive opportunity

PPMS - how many points per failed 'gamble'

I think each of these measures can be useful if used intelligently. What I
objected to in the first place was completely discounting PPS as somehow
inherently useless.

Phew - that's enough for now!

cheers - TomM