APBRmetrics

Eli W · Joined: 01 Feb 2005 Posts: 402

Several commentators have recently pointed out that Golden State ranks #1 in 3PA per game yet is #25 in 3P%. Their conclusion is that the Warriors take too many three pointers. I wanted to determine whether this was accurate, and more generally what the optimum ratio of twos to threes was for the typical NBA team.

To do this my goal was to calculate Golden State's points per two-point shot and points per three-point shot. The big complicator is figuring how often teams are fouled on twos compared to threes (a further complicator would be their different FT% on each due to guys who take threes tending to be better foul shooters, but I'll ignore that).

A = missed two not fouled
B = missed two and fouled
C = made two not fouled
D = made two and fouled
E = missed three not fouled
F = missed three and fouled
G = made three not fouled
H = made three and fouled

Some of these can be derived from known numbers such as 2PA, 2PM, 3PA, 3PM, and opponent shooting fouls (which is listed on 82games.com).

2PA = A + C + D
2PM = C + D
3PA = E + G + H
3PM = G + H
Opponent shooting fouls = B + D + F + G

Plugging in the numbers for Golden State:

1010 = A + C + D
477 = C + D
147 = E + G + H
457 = G + H
202 = B + D + F + G

From this you can derive A = 533 and E = 110.

The final formulas I would use are these:

Points off twos = B*2*FT% + C*2 + D*2 + D*FT%
Points off twos = FT%(2B + D) + 2(C + D)
Two-point shots = A + B + C + D
Points per two-point shot = points off twos/two-point shots

Points off threes = F*3*FT% + G*3 + H*3 + H*FT%
Points off threes = FT%(3F + H) + 3(G + H)
Three-point shots = E + F + G + H
Points per three-point shot = points off threes/three-point shots

Thus the key values that must be determined are B, D, F & H (since C + D and G + H are already known). Does anyone know how to calculate these? Or is there some easy way to do this that I missed completely? I suppose since it's still early in the season I could just comb through all the play-by-plays.

mtamada · Joined: 28 Jan 2005 Posts: 376

Mike G · Posted: Tue Dec 06, 2005 7:30 am Post subject:

There may be several other uncertainties. Since basketball games are seldom single-possession affairs, you want to optimize your lineup to include rebounding, defense, etc, and not just scoring.

Further, do we know the difference in OffReb% between the typical 3-pt'er and the typical 2? What about the relative frequency of putback (high-% followup) attempts? What about opponent OffRtg after a missed 3 vs. a 2?

Fouls not-in-the-act are of course not directly due to shot attempts; but how many guys are fouled while jockeying for position beyond the arc? Or when receiving a pass out there? And then, what is the real effect of causing foul trouble for the opponent?

A balanced attack is always optimal, in the long run. The threat of drives, or a post threat, sets up the 3s. The threat of the 3 opens the middle. Last year, teams ranged from 12% (Uta) to 29% (Phe) of their FGA being 3s. Both teams have sound coaching and could be assumed to be doing 'the right thing', in this regard.

The Warriors are trying 31% of their shots from 3-land. Disregarding OffReb and FT from this strategy, that is a .482 eFG%. On their 2-pt and FT shots (combined), they are converting at .533. Their OffReb% is only .265, 22nd in the league

Eli W · Joined: 01 Feb 2005 Posts: 402

mtamada, you're right that there are lots of other factors to consider. I seem to remember someone doing a study that contradicted the traditional wisdom that missed threes lead to more offensive boards than missed twos.

Mike G, those numbers you calculate include FTs from non-shooting fouls, right? So that's not really the eFG% for twos.

oprice · Joined: 25 Aug 2005 Posts: 2 Location: North Carolina

If you're seeking a ratio, then it seems that the solution would require at least some element of game theory (and I'm not sure how this can be quantified). I guess you could also use empirical data to come up with a ratio that has proven to work in the past. Otherwise, I think you're left with declaring either twos or threes as being optimal -- not a ratio.

If you're interested in the extremes of 3-point shooting, then there are a few examples of teams shooting about half their field goals from beyond the arc in NCAA Div 1 basketball (although I suspect the three is a far better prospect in college). Many of which use elements of the "Princeton Offense" (Princeton, Air Force, Samford, West Virginia, etc.) and have had success at producing an efficient offense. I can say that, from looking at these college teams, teams which shoot more threes tend to have trouble getting offensive rebounds. I think this's probably more a result of the offensive motions (pulling big guys out away from the basket) than shot allocation, but I think it's probably true that threes are less likely to generate offensive rebounds than twos. I'm not sure if this decrease is enough to offset the additional opportunities, however. These teams also shoot and make less free throws per possession than the average college team while turning it over at about the same rate or slightly less. I also believe that these teams have slightly worse defenses because the opponent has more "medium break" opportunities off of rebounds. The opponent spends less time retrieving the ball from the basket (or after free throws) than it would against an average team. Anyway, those are my amateur observations of the effect of threes on the college game.

Ed **Küpfer** · Joined: 30 Dec 2004 Posts: 785 Location: Toronto

Mike G · Posted: Tue Dec 06, 2005 2:34 pm Post subject:

That's nifty stuff, Ed. Which is the conventional wisdom: what we used to remember? or what we thought before that?

I may be biased against over-reliance on the 3. I lumped in all FT with the 2-pt attempts because, as I said, there isn't much fouling out beyond the arc. Being fouled before the attempt is usually (not always) closer to the basket.

The few FT that occur with 3-pt shots are likely offset by worse putback opps, etc. I guess I'm saying, Unless your 3-pt eFG% is greater than your overall TS%, you should be going inside more.

Further complicating things, a certain number of 3's are just desperation heaves that shouldn't really count against their %'s.

John Hollinger · Joined: 14 Feb 2005 Posts: 175

I had done some work on rebounding on 3s vs. 2s a few years ago as well, and my conclusion was that missed 3s are harder to rebound, not easier. Which makes sense -- the most dangerous offensive rebounder is the shooter, and on a 3 he's got quite a haul to get to the boards.

HoopStudies · Posted: Tue Dec 06, 2005 3:36 pm Post subject:

People simply forget that there are a TON of easy offensive boards off 2pt shots. On help defense on the interior, a man leaves his guy to stop a shot, leaving a very easy offensive board for the man he left. And if an offensive player gets inside position and misses a chippy, he's right there to try again. In this case, conventional wisdom needs modification -- 3pt jumpers are easier to rebound than 2pt jumpers (not 2pt shots).

The NBA understands this. Most teams act as though they know that 2pt shots are as easy to rebound as 3s even if people are saying otherwise. So this seems to be more a media thing than a true mistake in conventional wisdom. I never heard it from my coaches.
_________________
Dean Oliver
Author, Basketball on Paper
The postings are my own & don't necess represent positions, strategies or opinions of employers.

mtamada · Joined: 28 Jan 2005 Posts: 376

Wait a minute, when we say "easy" or "hard" to rebound, do we mean for the shooting team or the defensive team?

Also, what is the conventional wisdom? Here is my perception: most reporters and fans think that offensive rebounding rates are lower on 3pters than on 2pters. Some hoopstatisticians have found that the rates are similar, but I don't know if there has been a definitive study. 82games.com at this point probably has enough observations to make a real good estimate. I don't know what coaches think, but I trust DeanO's perception of their thinking. Except I don't know if he's saying they think rebounds of 3pters are harder for the O or harder for the D, compared to missed 2pters.

gabefarkas · Joined: 31 Dec 2004 Posts: 1313 Location: Durham, NC

mtamada · Joined: 28 Jan 2005 Posts: 376

gabefarkas · Joined: 31 Dec 2004 Posts: 1313 Location: Durham, NC

mtamada · Joined: 28 Jan 2005 Posts: 376

HoopStudies · Posted: Wed Dec 07, 2005 10:53 am Post subject:

Offensive rebounding percentage is higher off 2pt attempts than off 3pt attempts. It's been shown (though not a huge difference).

There are broadcasters who imply the opposite.
_________________
Dean Oliver
Author, Basketball on Paper
The postings are my own & don't necess represent positions, strategies or opinions of employers.