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I am wondering if there's interest in having a focused, empirical conversation about the hypothetical results of a time-traveling match-up between this year's Golden State Warriors and the 1995-96 Bulls. If so, I would like to propose that we begin with a poll, where opinions are offered about the expected advantage enjoyed by either team in terms of underlying strength, expressed in terms of net points per hundred possession.

So, for example, if one were to believe that no adjustments should be made to actual performances in respective years, the "correct" poll answer would be Bulls +2.7 (or with rounding +3) what implies that on average, on a neutral court, the Bulls would expect to score 2.7 more points per hundred possessions than the Warriors.

How so? Well, the Offensive minus Defensive Rating of the Bulls in their 72-win year was +13.4 (115.2 minus 101.8) compared to the Warriors' 10.7 (114.5 minus 103.8). And differencing these yields Bulls +2.7.

But please note a very important stipulation about the poll question. IT IS ASSUMED THAT THE 3-POINT LINE IS AT ITS CURRENT LOCATION, not the shortened version seen in the Bulls' 72-win season.

Handchecking rules would be another key detail to stipulate.

I see that the Warriors won their games against their next best 3 competitors by about 10 points per game whereas simple SRS differential with them was only about 3 pts. In regular season and playoff games the Bulls beat their top 3 opponents by about 7.5pts but only about a point above the SRS differential. Warriors plus 8 on actual - expected wins, Bulls plus 2. Going by relative performance against top 3 opponents I'd give some points to the Warriors, maybe a lot for outperforming against their best tests. I am not sure what to do about the actual - expected wins difference. It might favor the Warriors too but I am less sure of that. I might include a league quality adjustment later.

If you assume current hand checking rules I'd take points from Bulls defense but give to the offense especially because of Jordan's drives. The difference between these might be negative for Bulls (impact on all of defense vs. Jordan getting a lot of calls anyways). Either team could rise up beyond their numbers in a pivotal test, if they had to. Bulls with the eventual 6 championships might have an edge there. Superstar bias of refs? Advantage Bulls. 3pt line difference deduction for Bulls on offense but add points of credit on D. Coach Kerr really knows opponent. A bias for better trained and conditioned athletes 20 years later.

Lots to consider... First guess bottomline- Warriors by 2. Maybe it should be by more. I might change with more time to think about it, if that happens later

Crow, quite right about it being important to stipulate rules of the game about "handchecking". I had meant, as the counterpart to stipulating the current/regular 3-point distance, that one should ASSUME RULES PERMITTING "MAXIMUM" FREEDOM OF OFFENSIVE MOVEMENT. How exactly to specify this (current rules?) I don't know. But the point of the exercise is to formulate an estimate of relative advantage, assuming that each team would have available what is generally perceived to be their comparative offensive advantage.

Otherwise, does anyone have the formula at hand for linking the probability of winning a seven game series to the preferred measure here of net points advantage per hundred possessions? I ask because a data point could be entered for the wisdom of the ESPN crowd, where about 70% thought the Bulls would prevail.

By own efg% and opponent efg% allowed vs. average (very small difference in league averages) the Warriors have sizeable advantages in both. To win, the Bulls would have to offset by going to line more or winning net turnovers or controlling boards. In their time Bulls were only 26th on ft/fgas. How much more could they get in max offensive freedom / handchecking called environment? Were the rebounding and steal conditions in 95-96 more favorable for Bulls than they would be now? Would the Bulls have turned it over less with less ball pressure?

I can identify the issues but I don't have a lot of confidence in ability to determine net results of an inter-era matchup.

Estimating an answer to my own question, a single-game win probability of p=0.6 pertains to a team having about a 70% chance of winning a seven-game series (71%). And using an average of the results of applying "Hollinger" and "Morey" Pythagorean coefficients (listed here https://captaincalculator.com/sports/ba ... alculator/) and assuming baseline point totals averaging the pace for both teams, the implied per hundred possession superiority of the Bulls is +2.9. So, call it +3.0 for poll purposes, for the wisdom of the ESPN crowd. Interestingly, not terribly far from the aforementioned, unadjusted simple differencing of net Ratings...

I tend to think that the general level of play goes up over time, but we're only looking at relative strength with measurements like SRS or offensive/defensive rating. So that the 1996 Bulls would be favored over the 1971 Bucks or 1972 Lakers and the 2016 Warriors (or Spurs) would be favored over the 1996 Bulls.

...
How so? Well, the Offensive minus Defensive Rating of the Bulls in their 72-win year was +13.4 (115.2 minus 101.8) compared to the Warriors' 10.7 (114.5 minus 103.8). And differencing these yields Bulls +2.7.
...

This year's Spurs have a better Offensive minus Defensive rating that the Warriors do. (The Spurs are +11.3 which is 0.6 better than the Warriors.) In some sense it's a real question if we should we be talking about the 1996 Bulls vs the 2016 Spurs instead.

If we really think that the Warriors are better than the Spurs, then we're saying that there's something more to the situation than offensive minus defensive rating.

Nate, a few points in reply. Most generally, one has to pick some measure as a basis for comparison, and I cannot think of a better one than net points per hundred possessions. The exercise then is to make considered and reasoned adjustments in these terms, e.g. talent concentration from 1996 to 2017 adds -X points to the differential, for all relevant factors.

And the +2.7 margin for the Bulls is a good place to start. In a very real sense the Bulls were the better team (within their respective years) and the Warriors were just "lucky" to get more wines. In close games (here defined as ones that went into OT or were decided by six points or less) the Warriors were "fortunate" to count three fewer losses (I count 17-7 vs. 17-4). But on average, in a slower-paced league, the Bulls won their wins by greater margins (15.0 vs. 13.8) and lost their losses by lower margins (-7.7 vs. -13.7).

As for the Spurs being a better team than the Warriors on these same terms, hence why not compare them to the Bulls? Well, that is another exercise to be sure. Obviously a primary motivation for focusing on the Warriors vs. the Bulls owes to the win records, but there is another very good reason to begin with this comparison. The comparative performance in three-point shooting, I believe goes a long way toward providing a clear answer to the question of which team was better (and by how much).

If we really think that the Warriors are better than the Spurs, then we're saying that there's something more to the situation than offensive minus defensive rating.

Somewhere (?) in the last few days, I read that after 3rd quarters, the GSW had a better avg lead than the '96 Bulls had. Maybe the biggest known/ever?

Offhand, it does seem as if a lot of their games were 'decided' after 3, Curry didn't play the 4th, etc.
In which case, they might be quite a bit better than their (ORtg-DRtg). Maybe add 10 to 20% to it, to simulate playoff minutes.

Looks like they were 19-3 in games decided by 6 or fewer, or OT. This much luck may certainly offset most or all of the 3/4 game SRS advantage. I don't believe in luck momentum.
The Spurs were 12-8 in close (6 pt) games. Probably about average luck involved -- they were 7-7 when it's 4 or less.

Looks like [the Warriors] were 19-3 in games decided by 6 or fewer, or OT. This much luck may certainly offset most or all of the 3/4 game SRS advantage. I don't believe in luck momentum.

So the hypothesis is that the Warriors just happen to have 19 out of 22 possible wins on "coin flip" games by chance? A 1 in 600,000 chance isn't impossible, but it's far enough out there that I think there's more than luck involved.

Mike G, I would like to thank you for your comment.

I couldn't find an article comparing the Warriors' to the Bulls' third quarter score differential, but there was this one where their superiority to that of the Spurs is noted:

http://www.slate.com/articles/sports/sp ... kable.html

So, I went about checking 82 box scores to get the comparable Bulls figure and the facts you relate are basically correct. The Warriors average end of third quarter lead this year (including the last game third quarter margin, what the Slate article omits) is +10.0 vs. 9.7 for the Bulls in 1996.

However, once you adjust for pace (and assume constant pace over all quarters) you get the following comparison of net points per hundred possessions at the end of the third quarter: GSW +13.6 and CHI +14.2.

So, the end of game +2.7 difference is substantially reduced, when comparing end of third quarter efficiency, to +0.6 .

And then there is another factor that one should apply that essentially clears the slate as a starting point (before getting to talent dilution, three-point shooting, other rule changes, and all the rest). Between 1996 and 2016 opinions have changed about how long to play star players. Reflecting this, Stephen Curry and Draymond Green last year played slightly fewer minutes than their considerably older star counterparts (Jordan and Pippen) did twenty years ago. And taking these few minutes into account actually matters...a bit.

For what its worth, by my calculation, giving Curry Jordan minutes and Green Pippen minutes (at the expense of the next best position players on their team) RPM data suggest that the Warriors would be +1.1 per hundred possessions better over four quarters. And this translates to what is an end of three quarter estimate for the Warriors of +14.4 - essentially identical to that of the Bulls.

So, there it is; the Bulls and Warriors were equally great in their own league years. Now let the arguments about intertemporal comparisons commence!

A <6-point game isn't a "coin flip", it's more a 2-3 possession contest.
Depending on the opponent, the Dubs have a 50-55% chance of "winning" a given possession.
Their odds of winning "best of 3" possessions might be 70% -- about the % the Spurs won.

This suggests they should have lost 6 or 7 of those close games, rather than just 3: About half luck?
What are the odds that a 70% FT shooter hits 19 of any 22 FT? Not 1:600,000

Anyway: When the GSW led by more than 15 thru 3Q's, their net points in the 4th averaged minus-4.3
They were 28-0 in these games.

When their 3rd Q lead was 1 to 15 points, their 4th Q's avg'd +1.95 pts. They were 32-1 in these contests.

When tied or trailing by no more than 10 after 3, they outscored opponents by 5.8* in the 4th. They went 13-4 in these, with avg MOV = 3.8

When behind by 11 or more thru 3, they also lose the 4th by 4 to 7 points -- 0-4 in these cases.

Their 82-game net thru 3 quarters was 10.08
Times 4/3, that would be 13.45 if they kept it up thru 4 Qs
In the 54 games when their 3Q lead was 15 or less, their 4th Q avgd +3.22, or 12.88/4

* -- should be "in the 4th and overtimes".

I shall recommence with an intertemporal adjustment that on the face of it would seem to have to be YUUUGE, but that, by my estimation anyway, despite appearances, turns out to not be that big of a deal. And here I speak of twenty years of talent concentration in the NBA, owing to effective population growth far in excess of league expansion.

These are the relevant, underlying facts, for comparing talent in 1996 and 2016:

(1) The league expanded from 29 to 30 teams, an increase of only 3.4%. Whereas...

(2) The share of minutes taken by foreign-born players increased from 4.7% to 21.9%, and

(3) The U.S.-born, NBA-relevant population growth (an estimate taking into account age cohorts, weighted by minutes played, and race) grew by approximately 13.6%

And what is the story these facts tell? Well, though we cannot know the effective growth rate in the entire NBA-relevant, foreign-born population, we can use the parity in minutes played between foreign and domestic players to quite confidently state that there was no difference in average quality between domestic and imported players, what, in turn, allows us to look at the data on U.S.-born players to give us the desired answers.

And these minute shares relate that whereas U.S.-born players were stocking 27.6 effective franchises in 1996, by 2016 this had dipped to 23.4 - a decrease of 4.2 franchises (or 15.2%). And this at the same time that the underlying talent pool increased by 13.6%!

But how should we think of this large, effective concentration of talent in terms of an adjustment factor for current purposes?

Well, we can get at this by describing the demography another way: imagine constructing a 1996-era league out of today's player population.

To do this, we begin with the ordinary and neutral assumption that the population distribution from which NBA-talent comes would be the same in both years, only the "thickness" of each slice changing in proportion to population growth.

So, if in 2016, there were 372 U.S.-born NBA players, in 1996 this number would be proportionately reduced to 327 of equivalent quality owing only to population growth (what you get by dividing by the 1.136).

But 327 players would be grossly insufficient in number to stock the 27.6 effective U.S.-born franchises that existed in 1996. Given that about 15.8 players are required per team, an additional 108 players (again proportionately culled from the next-best, 123 currently available players) would be required to recreate the 1996-era, U.S.-born NBA. That's 6.9 additional franchises worth. Said another way, it would be an equivalent talent dilution to the current NBA increasing its number of franchises by one third!

But the question remains as to what specific, plus/minus adjustment factor should one apply to the Warriors/Bulls so as to account for this YUUUGE talent concentration over the years in question? I suppose historical analogies could be drawn upon, though I think one would have to go back all the way to the mid-60s for such an equivalent expansion.

I took another approach, where I have to admit I was initially a bit surprised (though I really shouldn't have been) by the small, estimated magnitude of the effect in question. What I got was an adjustment factor of only about -0.6 points per hundred possessions (and this not changing much at all over the plausible range of underlying assumptions).

This perhaps seems too small of an effect for expanding the league by one third, until one notes how few minutes the worst players in the league play. So, basically, even if you assume a really large influx of replacement level talent, they will take disproportionately far fewer minutes with the preexisting talent distribution getting their minutes shifted upward. And the net effect of this, over the entire range of plausible estimates for newly-incorporated D-League player ratings and minutes, turns out to be small. (At least that's what I found when I did a simple exercise, using 2015 RPM data, sorting by minutes played and dividing into subgroups (having the respective average minutes and RPM), assuming an average value for "deep into the D-League" NBA replacement player ratings, then reallocating minutes according to the league expansion assumptions.)

Well, that's that. Perhaps others have different views about the framing of the issue of talent concentration, or its notional effects.

If not, we can move on to the more interesting issues of three-point shooting and all other rule changes...

If I estimate nominal strength based on the win loss record and an assumption of scoring along a normal distribution with 13 point standard deviation, and splitting home, away, and neutral then I get that GSW and 1996 CHI are ~+15.5 point teams, and SAS and 1971 MIL are ~+13.5 point teams. Of course all the teams are far enough into the tail that one home win more or less corresponds to about 2 points in inferred team strength so it's very noisy. Of course that doesn't speak to inter-era team strength at all.

schtevie wrote:...
This perhaps seems too small of an effect for expanding the league by one third, until one notes how few minutes the worst players in the league play. So, basically, even if you assume a really large influx of replacement level talent, they will take disproportionately far fewer minutes with the preexisting talent distribution getting their minutes shifted upward...

Doesn't that also mean that 'league talent level' is largely informed by the top talent which, because it's scarce, is also going to be a high variance thing - statistical reasoning is going to work better for estimating the aggregate performance of the ~150 starters than the top 30-60 players.

Nate wrote:

schtevie wrote:...
This perhaps seems too small of an effect for expanding the league by one third, until one notes how few minutes the worst players in the league play. So, basically, even if you assume a really large influx of replacement level talent, they will take disproportionately far fewer minutes with the preexisting talent distribution getting their minutes shifted upward...

Doesn't that also mean that 'league talent level' is largely informed by the top talent which, because it's scarce, is also going to be a high variance thing - statistical reasoning is going to work better for estimating the aggregate performance of the ~150 starters than the top 30-60 players.

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.