RE: [APBR_analysis] New file uploaded to APBR_analysis
- Two excellent points that Stuart McKibbin has made: Prof' Berri's
adjustment's by position are indeed an attempt to correct for players'
roles on a team. And correcting for touches in some way is also an
How best to do this, I don't know, but they are excellent points.
Stuart made a third excellent point, about the ability to score even when
closely covered or double-teamed. I remember thinking about this when
comparing James Donaldson's 60-some% FG% to World B Free's 44-some %.
Seemingly, Donaldson is not only the better shooter (which is fallacious,
as we've repeatedly mentioned here). But not only that, but seemingly,
the team ought to have Donaldson shoot more and Free shoot less (not that
they were ever teammates, but if they were on the same team, who would you
want to give the ball to?).
But that second claim is almost certainly incorrect also. If we look at
what economists would call each player's "marginal field goal percent" --
their probability of making the shot if given the ball one more time --
then it is quite possible that Free's marginal FG% was higher than
Donaldson's. Donaldson could obviously do fine on dunks and putbacks,
but if you said to him "here's the ball, go do something with it" he'd
probably end up bricking an 18 footer, assuming he didn't dribble it off
his foot and get a turnover. Whereas you could give the ball to Free,
anytime, anywhere on the court, and he could dribble in or let fly with a
shot which would have at least some chance of going in. And unlike, say,
Steve Kerr or John Paxson, do so with 2 or 3 guys hanging all over him.
Many years ago I tried to model this by assuming that players' FG% were,
not single parameters, but rather FUNCTIONS of the number of shots per
minute that they attempted. Anyone who reduced himself to a minimal
number of shots per minute would have a FG% of 100%, because they shot
only cripple layins. But if they attempted more than that, the FG% on
those additional shots would be lower than 100%. Where players differed
was in how fast their FG% declined: players like Donaldson would have
fairly rapid declines, but because they shot so rarely, they still had a
high overall FG%. Players like Free or nowadays Iverson or Payton would
have slow declines, but because they shoot so often, their overall FG% is
low. And some players, such as Manute Bol, would have very rapid declines
so even with their small number of FGA per minute, they still had low
FG%s, compared to say the James Donaldson's of the league.
The problem that I encountered and could not solve was: finding a good
functional form for the player's FG% as a function of FGA per minute. The
main problem was that in most functional forms, it was still the case that
the equations said Donaldson should shoot more and Free should shoot
less. Whereas I suspect that in reality, either the opposite was true,
or, if we're willing to make strong assumptions about teams' ability to
optimize their offense, all players should have the same marginal FG%.
But I couldn't come up with functions which didn't require all sorts of
additional assumptions and parameters which would exhibit that sort of
On Thu, 10 Jan 2002, McKibbin, Stuart wrote:
> I think Mr Berri's done us all a great favor by crunching the appropriate marginal value of wins out of each statistical category the NBA compiles. As others (Dean) have pointed out, Berri's linear method is better than TENDEX because it converts offensive and defensive stats into wins instead of some dimensionless and meaningless production number. Points for and points surrendered determine wins. Baal James uses Win Shares, so should we.
> I'm no statistician, but I'm sure it's hardly a settled matter in his profession if one can use quasi-R-squared tests to decide which model (each using equations estimated via differing functional forms) offers the greatest explanatory power. But who cares? His marginal values work well enough for teams, Berri's Table 11 is good enough proof for me. So let's figure out what can be done to better convert them to individuals.
> Berri adjusts his per minute production numbers for team tempo, team defense, position and another one to add in the league average of minutes per win (0.0052).
> I think Berri's position adjustment tries to do what all you guys want, but doesn't go far enough. It's the nature of basketball that the taller, stronger players (Centers, Power Forwards) operate closer to the basket and are more likely to get more rebounds than the guards. Berri says why over-reward the big tall guys for getting more rebounds than guards? That's why the coach has big guys close to the basket and his guards getting back on defense or leaking out for the outlet pass. Similarly, the nature of basketball is that SOMEBODY has to advance the ball up the court---usually that somebody is a guard, with the occasional exception of a Pippen or Pressey. Berri says why punish the advancer? Advancing and handling the ball is a dangerous job, a guard has more opportunities to turn it over, whereas Rodman runs down the court and leaves the guards to their fate and doesn't blemish his own turnover ratio. Because he sees guards, forwards and centers as complementary rather !
> an substitutes, Berri thereby tries to factor ROLE into the model. The position adjustment, while a good start, might be improved upon.
> I think (rightly or wrongly) that the most valuable skill in basketball is the ability to get, and make, a shot even if a player is guarded closely by one guy, or guarded by two or three guys. This ability CUTS ACROSS POSITIONS. A coach sees that ability in a player and puts the ball in that players hand's much more often than a Rodman, Outlaw or Jayson Williams. SOMEBODY has to score, SOMEBODY has to take the chance of missing a shot. Therefore, Karl Malone or Michael Jordan should not not be penalized compared to Rodman because his coach relies on him to be the focal point of the offense. They are penalized in Berri's model because they miss more shots in the aggregate than DRodman and have a correspondingly greater negative marginal value from those missed shots.
> What adjustments might Mr. Berri make to the model so it won't over-penalize the offensive players? One suggestion I have is that he could adjust for how much a player handles the ball. For example, in 1998 Rodman had 360 FGA's, 111 FTA's, 1201 rebs, 230 asts, 47 steals and 147 TO's. He touched the ball in a statistically measured way roughly 2040 times. Karl Malone had 1472 FGA's, 825 FTA's, 834 rebs, 316 asts, 96 steals, 247 TO's. That's roughly 3377 touches. The rate of turnover per touch is about the same for Malone and Rodman, yet because Malone had 100 more aggregated TO's he is overly penalized in Mr Berri's model. Perhaps a rate of TO's to total touches should be used to evaluate individual players instead of just the gross amount of TO's; or maybe Berri could add an average production number for groups of players with certain ranges of touches per minute to the individual players Win totals.
> Another way might be to take an average production number for players that shoot 0-5 times a game, for those that shoot 6-10 times a game, and so on---and add that to a players win total.
> This was just a thought experiment.
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