Re: PPS vs. FG%

[Alexander Wang <awang@MIT.EDU>]

At 07:03 PM 10/18/01, Francis Hsu wrote:
>Points per shot is points scored / field goal attempts.  The reason why I
>like it is because it takes free throw points into account.  Warwick's
>example of Eric Williams is a good one.  If you used FG % to measure his
>offensive efficiency, he looks like one of the worst on the Celtics.  But
>if you used PPS, he's better than Walker.

I think when you're looking at FG% or points per shot in this context, 
you're trying to find a single number that represents a player's scoring 
efficiency, so that you can make comparisons. The inputs we're considering 
are two point field goals attempted and made, three point field goals 
attempted and made, free throws attempted and made. I think the intuitive 
notion of offensive efficiency can be roughly represented by: each time I 
give player X the ball, how many points do I get? If you're a professional 
on a coaching staff (or have a VCR and too much free time) you can kind of 
do what the baseball stats people do, which is find out someone's 
conversion percentage under almost any imaginable situation. But the rest 
of us have to use the inputs above and general judgements about the value 
of 3's vs 2's vs FTs.

The problem with points per shot is that free throws made count but free 
throw attempts aren't considered. If someone gets fouled on the shot, goes 
to the line, and sinks two free throws, is that any different than if he 
hit a 15 foot jumper? They're not exactly the same, because in the first 
case you've given an opposing player a foul, but intuitively they're pretty 
similar in that you've scored two points and given up possession of the ball.

A measure that I tried to promote a few years back was points / (FGA*2 + 
FTA). The idea is that most of the time, your points from free throws come 
from two shot fouls that are roughly equivalent to a conventional field 
goal attempt. It's scaled to look like a percentage.

Of course it's far from perfect, because among other things, a "basket and 
one" three point play counts as an attempt and a half here instead of one 
attempt as it should. Mark Berry's opinion is that a three-pointer is not 
worth 1.5 two-pointers because you give up long rebounds that leads to fast 
breaks and disrupt the offense. On the other hand, you also get more 
offensive rebounds and therefore second chance points. I agree on the whole 
that the three-pointer should probably be worth less than 1.5 two pointers. 
The guy who makes 50% FG is typically a lot more valuable than the guy who 
makes 33% 3pt FG. One reason is that the 50% guy usually goes to the line 
much more, but that is partially accounted for with the efficiency measure 
above. More importantly, a lot of offense in the NBA is generated inside 
out. The guy who shoots 40% on 3's usually gets open looks because the guy 
shooting 50% on 2's is drawing double teams.

But I disagree with Mark's approach, which is to ignore the issue and 
essentially consider them the same by using straight FG% to compare 
players, though it's certainly simpler.

Anyway, there's definitely a limit to what stats can tell you about a 
player, because you don't include stuff like "who does he play with?" that 
tend to be really important. It's more difficult to convert efficiently 
when you're the go-to guy that gets double teamed than when you're the role 
player. I remember that some economics professor had a study that stated 
that Allen Iverson wasn't a very good player because he is so inefficient. 
He's obviously missing the context of how the 76ers entire team is structured.

But I think both FG% and PPS have clear flaws if you're trying to use it as 
a single number that estimates a player's offensive efficiency.

Alex