APBRmetrics

schtevie wrote:...
I don't think that this is true. Where the variability? Why the variability? The distribution of talent should be expected to be stable, and if you look at Jeremias' xRAPM data, you see this to be the case. Yes, one should expect variability in the measured ability of the best of the best players, in any given year. However, these "excesses" and "deficits" are confined to only a very few players, and are small in magnitude (compared to the average) and represent very few possessions compared to the league total.

Suppose LeBron James gets injured early in the season (just bad luck) and misses a lot of games. How much does that change the per minute talent level? ... I guess a lot of it depends on how you calculate the talent baseline.

Nate wrote:

schtevie wrote:...
I don't think that this is true. Where the variability? Why the variability? The distribution of talent should be expected to be stable, and if you look at Jeremias' xRAPM data, you see this to be the case. Yes, one should expect variability in the measured ability of the best of the best players, in any given year. However, these "excesses" and "deficits" are confined to only a very few players, and are small in magnitude (compared to the average) and represent very few possessions compared to the league total.

Suppose LeBron James gets injured early in the season (just bad luck) and misses a lot of games. How much does that change the per minute talent level? ... I guess a lot of it depends on how you calculate the talent baseline.

Suppose the best player in the league (call him a +10) has a season-ending injury in the last pre-season game (and, for mathematical simplicity, whose minutes are replaced by a composite +0 player). Similarly suppose he would have played 3/4 of his team's possessions and we are looking at a team and a 30-team league average of 100 possessions per game. What you get is that the effect of this player's absence on league quality is 1/40 of his rating, or -0.25.

In terms of what has actually transpired, looking at the thirteen seasons between 2001 and 2013, in J.E.'s xRAPM, there was only one year where there was a big hit in possessions played by the top 3 rated players, 2005. Tim Duncan and Shaq weren't playing career-peak minutes and the third-rated player, Andrei Kirilenko, was injury-plagued. Collectively, relative to the 13-year average, 4,800 fewer possessions were played by the top 3 players. Doing the same math as above for the year in question, I calculate a hit, relative to the 13-year average of -0.21. And for context, the next most below-average year (as well as the most above-average year) shows a variation in top-3 possessions that is smaller by about a factor of three.

Pending any objections/clarifications/improvements on the (relatively small) factor adjusting for talent concentration, I would like to move on and address what is the penultimate, yet critical, and, in fact, dispositive issue for comparing the relative superiority of the 1996 Bulls and 2016 Warriors: 3-point shooting ability.

Prior to dealing with issues related to time-traveling (that is making arguments about how the differing rule regimes would, on net, benefit one team or the other) there is a vey basic question: how would the 1996 Bulls have performed if the 3-point line in that season were at the "regular" distance - that is where it has been for all but three of the years of its existence?

And this question is, in fact, easily answered, and with a high degree of confidence, so much so that it makes the whole exercise (of which team is better) almost absurd. The better team is clearly the 1996 Warriors because the 1996 Bulls simply didn't have the ability shoot the proper-length 3, and shooting 3s, um, matters a lot! Period. Full-stop. No question.

In fact, this answer is so clear, it makes one wonder why the Fifth Estate failed so conspicuously, when focusing on the comparison at hand, in articulating this basic fact. In fact, I've seen no explicit mention of it. (And if I am incorrect here, I would be very obliged for a reference to clarify the record; I have tried to follow what has been said in front of pay walls, but not behind.)

So, how do we know that the 1996 Bulls would be a mere shell of their offensive self were the 3-point line at its "proper" distance? Because we know how the 1998 Bulls - what was basically the same team - performed. And no aging adjustment for the two year difference can overturn the conclusion that the 1996 Bulls roster couldn't hit the 3. But this point can be sharpened, rhetorically.

The general perception of the greatness of the 1996 Bulls is entirely an artifact of the shortened 3-point line. Their skill set was specially benefited by the line moving in. At "normal" length, they would, of course, still have been a very good team. But not close to 72 wins. And, in fact, nothing of particularly special mention.

And then, of course, there is also wonderful irony in this reality (given Phil Jackson's - along with many of his contemporaries - general disdain of the 3-pointer).

So, let me pause now, before relating the straightforward facts supporting the argument, to see if there is any objection to the points made.

schtevie wrote:... The general perception of the greatness of the 1996 Bulls is entirely an artifact of the shortened 3-point line. Their skill set was specially benefited by the line moving in. At "normal" length, they would, of course, still have been a very good team. But not close to 72 wins. And, in fact, nothing of particularly special mention.

The 2016 Warriors don't have to defend the short arc. That works out pretty well for them! From 1995-97, that was a big issue with NBA defenses.
A team's roster is partly (or largely) created to accommodate the rules of the present time.

Meanwhile, the Bulls had SRS 10.70 in 1997, and 12th in 3ptrs made; when the arc went back to normal distance in 1998, they were exactly 1 year older (31.7 vs 30.7), 17th in 3's, SRS = 7.24

In other words, coincident with the re-normalizing of the 3pt line, they lost 3-4 ppg relative to their competition.
They also missed Pippen for 38 games, Kerr for 32 -- their top 2 distance shooters from '96 and '97.

The '96 to '98 Bulls were among the best (Opp 3fg%) at defending the arc, short or long. As are these Warriors.
Annual 3fg% Note that the shortening of the arc ('94 to '95) seems not to benefit da Bulls as it does the rest of the league.
If we give Kerr 80 games worth of 3-pt shooting in 1998 (at .438), the team shoots .333, and their advantage is a modest .011
But the team clearly peaks in '96, and aging becomes the terminal issue.

As threatened, here is the rock-solid, incontrovertible, empirical case that the 1996 Chicago Bulls, were the 3-point line to have been at its normal distance, would have been a very unspectacular offensive team (but, of course, still very good overall, think a 64-win team, thereabouts). There are three components to the argument. First, noting the offensive deterioration that occurred from 1996 to 1998: what is wholly (and I mean wholly) accounted for by the inability to hit the longer 3. Second, accounting for age-related deterioration: what best estimates suggest only offset a fraction of the observed deterioration. And finally, dealing with the effect of the (relatively small) changes in team composition between the 1996 and 1998 Bulls' rosters (an issue alluded to by Mike G above): what, interestingly, though it does serve to explain some of the deterioration in offense, does not explain at all the overall, observed deterioration, actually to the contrary!

(1) The 1996 Bulls just couldn't hit the proper-length 3; end of story. This fact is true and cannot be gainsaid.

In 1996, the Bulls offense was spectacularly efficient, scoring +7.6 points per hundred possessions more than the NBA average (whereas the defense was "only" +5.8 better than average). Two years later and the offense collapses. Offensive is +2.7, whereas the defense basically maintains its strength at +5.2.

And looking at the un-NBA-normed Bulls offensive data, the accounting of the offensive deterioration is very clear. Points scored per possession dropped 7.4 over the two years, what can be decomposed into a 9.1 drop in points from 3-pointers, offset in part by a 1.7 increase in 2-pointers (with there being no difference in the relative contribution of free throws). Let's let that sink in for a second. On the face of it, more than all of their decline was accounted for by the decline in 3-point scoring.

But that is an illusion, because the 2-pointer compensation was, of course, common across all teams, now having increased difficulty scoring 3s from the new/old distance. And, in fact, the Bulls offensive "reorientation" was entirely ordinary, with the NBA average adjustment being +1.8 more points per hundred possessions from 2-point range. But this leaves the very straightforward conclusion that all of the Bulls observed offensive deterioration owed to the inability to hit the longer 3! Period.

And just as a final point, about their team being relatively advantaged by the shorter line, the Bulls' decline in offensive efficiency owing to the longer line was twice as large as the NBA average, 9.1 vs. 4.6!

(2) You cannot blame this on aging.

So, how much of the Bulls being net +5.5 worse in 1998 than in 1996 can be blamed on player aging? Well, some, but by no means all. From the aging charts provided by J.E. (viewtopic.php?f=2&t=8308&hilit=aging+curve) extrapolating for a representative player aging from 30 to 32 (what pertains to the minute-weighted common roster over the two years) we would anticipate a total decline in Bulls' efficiency of about 2.0, three quarters of which on the offensive end and one quarter defensive.

So, with such an adjustment, the estimate is that the 1996 Bulls, with a longer 3-point line in place, would have been -3.5 worse than observed.

Now, is there anything in the actual record that might suggest that the average aging curve result ought not apply, and that greater age-related deterioration actually occurred? Well, if anyone believes this, I'm all ears. On defense, there was minor deterioration, almost exactly in line with the supposed -0.5. And it would be almost ridiculous to say that notional greater-than-expected offensive deterioration would express itself entirely in terms of decreased 3-point production. And, of course, one need not say that the 1998 Bulls won the NBA championship.

(3) And Scottie Pippen and Steve Kerr playing fewer minutes in 1998 doesn't change the story...well, a bit on offense...but definitely not overall...to the contrary.

To properly analyze the effect of changes in the Bulls roster between 1996 and 1998, it must be done comprehensively. That is, all player and minute changes must be taken into account. There were minute changes for players who were Bulls both in 1996 and 1998 (and not just Pippen and Kerr); and there were minute changes for players who played in only one of the two years in question. As the goal is to estimate how the 1998 Bulls would have performed if they played 1996 minutes, we can use J.E.'s imperfect (yet the best we've got) quarterly xRAPM for 1998 to "correct" for the changes in minutes distribution between the two years. And then for the new players in 1998, we can calculate the net xRAPM change between them and their 1996 counterparts. The results of this decomposition are as follows, for Offensive, Defensive, and Total Rating:

For 1996 players playing 1998 minutes: O -1.14; D -1.82; Total +0.63

What this says is that, yes, the 1998 Bulls would have been better offensively were Pippen and Kerr (and all other 1996 Bulls) to have played their 1996 minutes, but these offensive benefits would have been outweighed by losses on the defensive end, to a net worsening of +0.63.

Now is this result surprising? Well, no, not really (unless one chooses to be offensively-biased and incomplete in ones recollection of who played and didn't play, comparatively in the two years). Remember that in addition to Pippen and Kerr playing many fewer minutes, so did Bill Wennington and Jud Buechler - so the expected net gains in offense are offeset. And then on defense, there were more minutes for Rodman, and, again, addition by subtraction, with Kerr and Wennington playing fewer minutes.

Then the same exercise for the expected changes for minutes played by non-1996 Bulls in 1998 are: O -0.13; D -0.05; Total - 0.19.

So, here there is basically not much difference. The most notable non-1996 roster change being the presence of Scott Burrell. Not notable because he altered the overall balance much (though his was an estimated positive contribution on both offense and defense) but rather because he was actually a valuable, compensatory piece to the Bulls' 3-point offense. Said another way: he could actually hit the 3 in a meaningful way, whereas Scottie Pippen simply couldn't.

So, totaling the 1996 and non-1996 Bulls in 1998, the total effects are: O -1.28; D +1.77; Total +0.44

So, the long and the short of it is that the 1998 Bulls, playing 1996 minutes would have been expected to be worse overall by a small amount, not better. And this really ought not be a surprising result. (Happy to decompose the estimates further if anyone is interested.) Net roster/minute changes led to more defensive gains than offensive losses.

And one can end this long post with a final comment about this final adjustment. What is likely the case (were Phil Jackson to have been counterfactually astute) is that a 1996 Bulls team with a longer 3-point line would have seen fewer minutes for the Kerrs and Wenningtons and more for the Rodmans and Harpers. So, rather than subtract this factor from the supposed strength of the counterfactual 1996 Bulls, it is perhaps fairer to just ignore it, leaving the aforementioned result:

Based on the clearly demonstrated inability of the 1998 Bulls to hit 3s from the "proper distance" and adding in the expected age-related deterioration, the counterfactual 1996 Bulls would have been about 3.5 points per hundred possessions worse than they actually were.

Adding to this the previously discussed, talent concentration factor of about +0.6, and we're looking at the Bulls being about 4.0 points per hundred possessions weaker than the 2016 Warriors.

So all that remains (and please correct me if I've missed an important factor) is an explicit discussion of how rule changes over the twenty intervening years might have influenced this supposed margin of Warriors superiority.

First, noting the offensive deterioration that occurred from 1996 to 1998: what is wholly (and I mean wholly) accounted for by the inability to hit the longer 3...

The Bulls' 3fg% dropped .030 from '96 to '97, with no change in the length of the shot, nor in their personnel. Some other factors are definitely at work.
They dropped another .050 with the return to full distance in '98. The league at large dropped .016, so the Bulls lost another .034 relative to that. Seems like a consistent decline, from '96 to 97 to 98.

The 1996 Bulls just couldn't hit the proper-length 3; end of story. This fact is true and cannot be gainsaid.

I'll just gainsay that the Bulls hit .021 above the league norm in 1994 (proper 3), just .014 above the norm in '95; rocketed to +.036 in '96. But you know this already, 'cause I gainsaid it already.

Also, forcing more 1998 minutes onto the 34-36 year old Jordan, Rodman, and Harper does not make the team better on offense or on defense. You may be dreaming of automatons rather than players on their last NBA legs.

The '98 Bulls didn't have Pippen until the 36th game of the season, Jan. 10. He missed a couple more games later, but there are striking differences between those first 35 games and the last 47.
Here I've put them out of chronological order, because they weren't the same Bulls without Pippen:The team O-D lost 1.4 from '96 to '97, and 2.4 from '97 to '98-with-Pippen.
League eFG% dropped .015 from '97 to '98. Bulls lost .022 (wPip), but they avg'd almost 32 yrs old that year.
The league shot .346 from the arc in '98. Bulls wPip shot around .340?

Here are Jordan's 1st-35-games averages and shooting% vs last 47 games -- roughly without and with Pippen:Same points and minutes, but less shooting, rebounding, and turnovers with Pippen on the floor.

Mike G wrote:

First, noting the offensive deterioration that occurred from 1996 to 1998: what is wholly (and I mean wholly) accounted for by the inability to hit the longer 3...

The Bulls' 3fg% dropped .030 from '96 to '97, with no change in the length of the shot, nor in their personnel. Some other factors are definitely at work.

I agree that there's more going on, but you have to scratch a little just to get past the null hypothesis that the difference is due to luck. Suppose the "true" percentage is around .385. Then hitting .403 (or better) one year, and 0.367 (or worse) the next over 1400 attempts is roughly 1 in 120. Not that likely, but certainly not impossible.

Mike G, I am not exactly sure how the facts you present offer a criticism of the argument.

To briefly restate, as a factual matter, the collapse in the Bulls offensive efficiency in 1998 is (more than) fully accounted for by a decrease in points coming from behind the 3-point line. (This is also true, by the way, if you look at the change from 1997, but no mention was made of this as 1996 is the focus year). Furthermore, a significant fraction of the observed offensive decline can be assumed to be attributed to aging effects - how that would divide between decreased 3-point, 2-point and free throw scoring being an open question.

In reply you note that there was variation in Bulls 3P% in preceding years, neither controlling for team composition nor aging. No surprise there.

But let me address what I think is probably the underlying concern, that somehow I gave short shrift to the 1996 Bulls 3-point shooting ability, with 1998 perhaps representing an anomalously poor performance, hence an unfair baseline for "backcasting".

This concern can be directly addressed by seeing how proficient the 1996 Bulls (who also played on the 1998 team) were at hitting "long" 3s up until 1994.

Looking specifically at the four years prior (what begins with the Bulls' first championship season - an endpoint that is appropriate on a couple of accounts) what you find is that the group, shot-weighted 3P% is 31.1. By contrast, the same cast of characters in 1998 shot, wait for it...30.1%.

Note that this excludes Toni Kukoc who only had a rookie season to extrapolate on and that 27.1 would bias the result downward. But lest one think that this is a bit of legerdemain, please note that he was a career (excluding the three years of the short 3) 32.8% shooter.

So, can we now agree that the point stands? What reason is there to believe that the 1996 Bulls would have not taken a big hit to their offensive efficiency if the 3-point line had been at its "proper" distance?

OK, the Bulls in '98, with Pippen in the lineup, shot about .340 from the arc.
If Kerr also plays 80 games, rather than 50, they shoot another .010 higher -- so .350, if those 2 guys are healthy as they were in 1996.

The 1996 Bulls just couldn't hit the proper-length 3...

Yet .350 is better than the league shot in any season before 2000.
When the arc was shorter, the Bulls shot it better than the rest of the league -- particularly in 1996.
Should we assume they'd have shot the normal three worse than avg?

Points scored per possession dropped 7.4 over the two years, what can be decomposed into a 9.1 drop in points from 3-pointers,... On the face of it, more than all of their decline was accounted for by the decline in 3-point scoring.

Well, that is largely the result of their taking fewer threes as well as making a smaller % of them. Every team in the league went through some version of this; and on avg scored 5 ppg less on their 3's.

The Bulls suffered by 57% more than other teams because their 2 most prolific 3-shooters missed 70 games between them. Not because they "just couldn't hit" them.

We might assume the '96 Bulls excel at the 23' 9" shot as much as they excelled at the 22' version, relative to the rest of the league.
The 1994 league avg was .333; when the longer shot resumed in '98, it was .346.
Since league 3FG% had increased by about .004-5 per year for some time, let's assume without the shorter arc, the NBA norm is .340 for 1996.

Since the Bulls hit .403 vs a league that hit .367, we can just add that difference, +.036, to the expected .340, and they shoot .376 from the full blown 3pt line. This is right where the Spurs are this season, and behind only the Warriors.

It isn't the only time a stable lineup has inexplicably launched to new heights in their long range efficiency. In LeBron's 3rd year in Miami, the team went from .359 to .396 -- then dropped back to .364 in 2014.
Several players had their best 3pt shooting seasons. It wasn't a strategy to do that, most likely; just a happy convergence.

Mike, apologies for the belated reply. Let me first reply to your very optimistic conjectures about how proficient the 1996 Bulls would have been were they to have been obliged to shoot from the "proper" 3-point line. As I understand your last two comments, the structure of your argument is that the Bulls were better 3-point shooters when Pippen was available in 1998 and if only Kerr could have played more, they might have been as relatively good as they were in 1996.

This argument plus heroic assumption fails. And it doesn't just fail because the record clearly shows that Pippen and Jordan, given their roles in the Bulls offense, simply weren't able to hit the longer 3 (on this point, there can be no argument; just look at the collapse in their realized 3P%; they just didn't have the range.) It fails because there is direct evidence on the issue of how the "skilled" 3-point shooters fared alongside them at the longer distance.

You don't have to speculate about how the offense would have performed in 1998 were Pippen and Kerr to have played together. They did play together! Kerr played 25 games after Pippen's season started, and they played together in 22 of these, and the evidence speaks directly and clearly on this very point.

Looking at this 25 game bloc as a whole, what was the realized 3p%? Drum roll, please. Was it the 34% mentioned above as that obtaining for the entirety of the Pippen season? Nope. Was it higher? Nope. The answer is 32.8% What, for reference, in barely higher than the season average of 32.3%. In terms of 3PAr, yes, they improved from their slightly below-average rate of .141 (ranked 17th) to .178 (what would be ranked a tie for 8th).

So, returning the 1996 roster in full strength in 1998 yielded results along the lines of what I supposed. And the nail in the counterfactual coffin is that the 1998 team was advantaged by having Scott Burrell. He actually could shoot above-average being the longer line, and he wasn't on the 1996 team, and there was no one who replaced this skill.

So, the point really does stand. The offensive collapse is properly accounted for by the collapse in 3-point shooting, and there is no evidence to suggest that in 1996 they would have fared any better from long range. But at this point let me pivot. Again, the point of this stage of the conversation is to estimate the offensive and defensive efficiency of the 1996 Bulls, were the 3-point line to have been at its "proper" distance. Subsequent to establishing this baseline, a discussion of the effect of rule changes and all that (fun stuff!) can occur.

In this latter regard, I note that conducting the same exercise already performed for the entire 1998 season for the 25-game subset above yields basically the exact same result! This is to say, that looking at ORtg minus DRtg for the 25-game subset, then adjusting the minutes/players to bring them to 1996 season levels (then additionally adjusting for home/away schedules and quality of competition, as it is a partial season) what you get is essentially the identical margin of superiority as for the whole season.

I shall present these data in a subsequent post, but lets hash out the 3-point shooting issue first.

... Pippen and Jordan, given their roles in the Bulls offense, simply weren't able to hit the longer 3 ...

Saying this over and over does nothing to make it so. In 1990, Jordan hit .376 from the arc. Only 7 players in the league hit as many, at a better %. When he wanted to focus on this, or if it was necessary in the context of the team, he did it.

In '91 and '92, the Bulls were dominant, and he didn't need to make 3's for them to succeed. In '93, he hit .354 from the arc. Just 22 players hit more at a higher %.

If you want to cite Jordan's career 3fg% from 1985 to 1993 -- which was .301 -- it's worth noting that in his first 5 seasons it was .202
In his next 4 seasons, 1990-93, it was .343
Extrapolating beyond that -- imagine he didn't retire, and the arc wasn't shortened -- we could imagine this trajectory puts him in the upper .300's- .400's after that. An elite long-range marksman!

What we actually know is that he got as high as .427 in 1996. Only 6 players hit as many at such a high percentage that year.
He falls short of the extrapolation, and indeed well short of it in 1997, because he's getting into his mid 30s. In fact, only 3 older players hit as many in '96, and none with as high a % -- Dale Ellis (.412), Sam Perkins (.355), and Derek Harper (.372)

Pippen's 3FG trajectory is similarly spotty but lower at the beginning and the end. For him, 1996 is precisely the midpoint of his career. His first 6 years he shot the long ball at 25%. Then in 1994, he hit 32%. Good learning curve!
Run the reel backward from the end of his career to the middle: His last 3 years were at 29%. Four seasons before that, 1998-2001: 33%. Suggesting mid-upper 30's% before that, with the full-length arc.

Jordan and Pippen were both up-and-down as 3-point shooters. If we combine their shooting for each year, from Pippen's first to Jordan's last, we get larger samples and more consistency.
A simple straight-line extrapolation can suggest how their 1988 thru 1994 shooting might predict their 1995-97 shooting. Similarly, we can run it backwards from the end : 2003 thru 1998, and postdict the short-arc era.The 3rd column predicts great things, while the 4th predicts mediocre but not terrible.
Column 1 is the avg of 3 and 4.

Both '94 and '98 were anomalously bad years. They "should have" shot .344 in '94, based on the '88-93 trend; but Jordan retired. They "should have" hit .361 in 1998, but Pippen was hurt, etc.