Re: Athlon Sports on scoring efficiency

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

> Date: Tue, 23 Oct 2001 16:00:20 +0200
> From: "j.hironaka" <j.hironaka@unesco.org>
> Subject: Re: Athlon Sports on scoring efficiency (or, the truth about
Toine)
>
>          Very interesting (nice to see Paul up there so high) but I'm not
> quite sure I understand the explanation of Scoring Efficiency Index. Does
> an SEI of .707 simply mean that Paul Pierce scored a higher points-per-FGA
> than the league average in 70.7% of the games he played in? <snip>

Yes, that is exactly what the measure indicates.

Note that unlike average measures that take each game and lump the totals
together this measure actually attempts to measure consistency from game to
game. What it demonstrates is that (in this example) Pierce is very
consistent in being above average in terms of point production given the
number of shots attempted. It is the exceptional game in which he falls
below the league average with respect to this measure. If one were to merely
look at points per shot this consistency might be obscured because those bad
games may be REALLY bad. Of course, the converse can be said for someone
with a low score on this measure. This measure is valuable because it
minimizes the distorting effects of 'outliers' - those performances that are
transcendentally good or pathetically awful - in evaluating the performance
of a player.

> Date: Tue, 23 Oct 2001 10:20:33 -0400
> From: "Jim Meninno" <jam@london.com>
> Subject: Re: Athlon Sports on scoring efficiency (or, the truth about
Toine)
>
>snip<
>
> Now, it's really a pity that Athlon Sports put so much effort into
refining
> PTS/FGA without addressing the real problem with the stat, which is that
> fouls that result in two free throws are not counted as attempts.  They
> didn't address it because they can't.  No one keeps track of how many
times
> a player is fouled and misses a shot, or goes to the line because the
> defensive team is over the limit.  For guys like Iverson, Shaq and, yes,
> Paul Pierce, this means that a great deal of their points come from
> "attempts" that aren't counted by this statistic.
>
I understand why Jim and Alex find this a 'failing' of the Athlon measure
(and of points per shot) but I disagree that this invalidates the measure.
While no measure is perfect I think PPS actually accounts more accurately
the importance of foul shots than any proposed revision.

Points per shot is simply attempting to record offensive efficiency -
period. Foul shots are the most efficient type of offense - no one can stop
you but yourself. It is well known that good offensive players will attempt
to draw fouls - *especially* when their outside shot is not falling - for
this very reason.

Both Jim and Alex seem to think this measure should record the individual
history of how each point was attained. Thus free throws should count as
'half a shot'. (By this logic three point shots should by all rights count
as a 'shot and a half' to indicate the inherent difficulty and consequent
reward involved in such a shot.) But this is not terribly accurate either
because free throws are much easier (and much more efficient) than 'half a
shot' - you have ten seconds (more if you're the Mailman), no defenders, and
a simple, straight-on attempt from 15 feet. One might argue that these
advantages should show up in higher conversion rates, but that is not the
only advantage of FTs. Unless there is a terrible defensive breakdown there
is no chance for an opposition fast break. You even get the ball back after
your first 'half shot' for a second. So calling free throws half a shot
actually *undervalues* their efficiency. (BTW proponents of hack-a-shaq seem
to miss these points - by slowing down the game they eliminate their own
attempts at easy baskets, allow the Lakers to set up their D, and give Shaq
a blow while he stands at the foul line. Dunleavy is a fool . . . but I
digress).

One might argue that while FTs may be valuable in setting the pace of the
game or fouling out opposing players these factors do not effect offensive
efficiency. The core of my objection to counting FTs as half a shot lies in
how such a measure fails to do justice to the art of drawing fouls - for the
simple reason that oftentimes the foul actually precedes the 'attempt'.
Reggie Miller may be the best but Pierce has also grown adept at faking the
opposing player into leaving their feet and drawing the foul - and only THEN
'attempting the shot'. In such instances it is clear that a shot would not
have been 'attempted' except that a foul was committed because it often
requires *several* fakes before the opposing player commits the foul. Bird
did this many times - and if he could not draw a foul on the perimeter he
would try to do so on a drive. (Another example: in Shaq's case many fouls
are committed before he even has a *chance* to make an attempt -  why should
his efficiency rating be penalized when he isn't even allowed to make a shot
attempt?) Drawing a foul is simply not the equivalent of taking a shot.
Taking a shot is actually relatively easy. Cultivating the skill of drawing
a foul, on the other hand, it is in truth much more difficult - but when
done correctly it is *much* more efficient. The attempt to draw a foul does
*NOT* require a shot attempt and therefore often allows the offensive player
MULTIPLE chances to attempt to draw a foul. In other words, when attempting
to draw a foul you don't have to surrender possession of the ball until you
actually succeed - now that's efficient! (Just imagine if that were true of
shooting). Arguing that the advantages of foul shooting are represented in
higher conversion rates for FTs fails to take this crucial fact into
consideration.

The plain fact of the matter is that it is difficult to overstate the
importance of the ability to draw fouls (that fouls are not distributed
randomly is obvious). Such an ability provides an extra dimension for an
offensive player that enables the best players to thrive offensively even
when their jumpshot has gone south for a game. This extra dimension cannot
be quantified simply by counting foul shots as 'half shots' - i.e., treating
two fouls shots as simply just another shot attempt. To do this not only
negates all the unique and special advantages that the ability to draw fouls
confers but more importantly it ignores the fact that an 'attempt' to draw
fouls does not surrender possession of the ball. While PPS undoubtedly was
not specifically devised to portray the advantages of drawing fouls I think
it does so fairly accurately. To say counting points from foul shots
(without adding 'phantom attempts') gives 'extra' points to such players is
like saying three-pointers also give 'extra' points to players. It is true
in both cases, but justified both by the difficulty of the skill required
and the impact of the *actual points* on the game. For these reasons not
counting two foul shots as an attempt actually better reflects the increased
dangerousness and offensive efficiency of players who have mastered that
skill than would be the case if foul shots were simply considered half of an
ordinary shot.

Basically what it all comes down to is how one values the relative
importance of FTs as a weapon in the offensive arsenal. Jim and Alex would
equate FTs a merely a 'shot' by another means. I would agree with this
assessment *if* FTs were randomly distributed among all players - but this
is clearly not the case. Some players cultivate the skill (and consequently
become much more efficient scorers) and others don't. The ability to draw
fouls and get to the line represents a skill over and above the ability to
shoot the ball. This ability results in a much higher offensive efficiency
than would be reflected if such points were equated with points derived from
shooting the ball because the player who has mastered the skill of drawing a
foul can - unlike the shooter - retain possession until he succeeds in
drawing the foul (or is forced by the clock to shoot the ball).

> I also question the whole premise that consistency equals a better chance
> for the team to win more games.  Maybe, maybe not.  But the way they
define
> consistency is completely arbitrary.  As I understand it, their rating is
a
> percentage of games that a player exceeds the league average PTS/FGA.  So,
> if you miss it by .001, you might as well shoot 0-30.  I mean, that's just
> an obviously worthless statistic, isn't it?

This statement is not only specious, it is downright misleading. The value
of the statistic lies PRECISELY in the fact that a 0-30 night is recorded
the same as missing by one one-thousandth of a percent. It is by valuing
each instance equally that one constructs what is in essence a bell curve or
normal distribution of the efficiency of each player's performance in games
over an entire season. This normal distribution can then be compared to the
average point per shot for the entire NBA by seeing what % of instances lie
above and below that average. If Pierce exceeds the average 70.7 % of the
time then we can deduce that the center of his bell curve lies well above
the average PPS. Conversely, if a majority of a player's games fall below
this average then we can deduce that the center of that player's bell curve
lies well below that average.

In other words, wild outliers do not skew the resulting measure as they can
do in straight averages such as PPS or shooting %. This is not arbitrary -
this locates where a given player's normal distribution of PPS per game
efficiency lies relative to the NBA average. This provides valuable info
regarding consistency and expected efficiency that is oftentimes distorted
when one consults mere averages.
>
> Is Shaq an effiecient scorer?  Of course.  Is Paul Pierce?  Yes.  Far more
> efficient than Antoine Walker.  But this statistic is extremely flawed and
> there's no point pretending it's not.
>
> Jim

Obviously we agree that Shaq and Paul are more efficient but disagree on
whether a measure that constructs a normal distribution based on PPS
portrays that efficiency with a fair degree of accuracy. My question then is
this:

How do you account for Shaq's and Paul's higher scoring efficiency if it is
not related to their consistently higher shooting percentages and consistent
ability to get to the foul line?
------------------------------

> Date: Tue, 23 Oct 2001 15:09:57 -0400
> From: Alexander Wang <awang@MIT.EDU>
> Subject: Paul vs Antoine - scoring efficiency
>
>snip<
>
> The measure of pts/fga overrates this as Jim notes. Anyway, I
> think that points/(FGA*2+FTA) is imperfect but still an improvement over
> pts/fga. As Jim notes, sometimes free throws don't come in a normal
scoring
> context so they are overrated in this formula (like when the opposing team
> intentionally fouls to get the ball back at the end of the game); <snip>

As I see it points are points whether they come in a 'normal' scoring
context or not. The mere fact that someone is fouled in the backcourt does
not invalidate the points they score, just as points from a halfcourt heave
count despite the fact that they do not result from a 'normal' context. If
we are going to start dissecting each context in order to rule some in and
others out then why bother with a statistical measure at all? In any case
the points that derive from such situations should be small when viewed
within the context of an entire season. This means that a measure that
devalues outliers through construction of a normal distribution should be
all the more valuable.

Cheers - TomM