Measuring the Quality of Basketball in the NBA Take 2: Adjusting for Pace

In the comments for the previous post on Measuring the Quality of Basketball in the NBA Commenter Dan said:

“I don’t think this kind of analysis makes sense. What you’re calling higher average team productivity probably just reflects factors like a faster leaguewide pace, higher scoring per possession, and maybe trends in some specific statistics. A faster pace allows players to accumulate more statistics, so it’ll lead to higher pre-adjustment WP. With many statistics the two teams’ change in WP cancels out (e.g., a steal for one team is a turnover for the other, a defensive rebound requires a missed shot), but not with scoring, so more offense will increase pre-adjustment WP. The 1990s saw a drop in both pace and points per possession, so that explains the drop in “basketball quality.””

Huh. He’s right. I did not think to adjust for pace when I did the Analysis. But to paraphrase  the immortal words of Herm Edwards : “We can definitely build on this”

Calculating Pace in the NBA

To calculate pace  in the NBA we need to estimate the number of possesions per game in the NBA. In the world of Wins Produced (and really in the world of basketball) possession of the ball is currency and what you do with it is what determines whether you win or lose. To quote another sage: “Ball don’t Lie”. So for any truly comparative measure of true basketball productivity and quality (our value delivered) adjusting for the possessions (our spend) is critical.

How do we calculate the number of possessions?    A standard formula used is:

Possessions = .96 * (FGA − ORb + TO + (.44 * FTA)) (source)

If we calculate possessions per game since 1978 looks like this:

Or as a pretty chart:

Damn you Pat Riley!!!!
This is not the Stock Market

So the pace of the NBA slowed significantly and at a consistent rate from 1978 (210 poss. a game) to a low of 174.5 poss a game in 1999 before picking back up to about 180 possession per game (90 per team) since. With this information we can now adjust  or quality measure accordingly.

Average Player Productivity

Some adjustments to the numbers from the previous post before we get to pace. As noted I was calculating average Team productivity per 48 minutes played based on simply adding the average production (ADJP48 click here for detail) for all 5 position (Center,Power Forward, Small Forward, Shooting Guard &Point Guard). It occured to me that the number would look more in line to typical Position Adjustment numbers for calculating WP48 if I divided by five. So I did, Here’s the new table:

Pace Adjusted Quality in the NBA

So we have pace and average productivity per player, let’s put them together shall we.

For the purpose of this exercise we will calculate :

Productivity per 200 possesions =  (Avg Player Productivity per Game (ADJP48)/Avg Number of Possessions per Game)*200

In table form this looks like:

As graph it looks like:

So once we adjust for pace, we see that we get a very different picture. 1991 thru 1997 was a golden era but the last three Years have actually been better for quality than anything in the data set.  The dip in 1999 and the early 2000’s remains . Post Merger basketball looks worse . I guess our memories can lead to view the past thru rose-tinted glasses.


A few notes before the end:

  • I realize that the introduction of the three point shot  to the league in 1980 skews the early numbers and the 95to 97 short three point line skews it as well. C’est la vie. I figure some sort of adjustment around the % of FGA that are 3PA is needed. Looks like something for take 3
  • Ditto for the handcheck rule. Need to think about this one.
  • The point of this exercise is to establish a way to compare historical performance by teams over time. Please hit me with questions and doubts so that I can help this puppy grow into a nice strong big dog.


To Guy in the Comments:

What I’m doing is closer to:

PROD =     2FGM*0.032 + FTM*0.017 + FGMS*-0.032 + FTMS*-0.015 + REBO*0.032 + REBD*0.033 + TO*-0.032 + STL*0.033 + FTM(opp.)*-0.017 + BLK*0.019 + AST*0.022

Than Pts per possesion. Pts per possesion looks like this :

Which is not the same.

Written by:


  1. Guy

    “Please hit me with questions and doubts so that I can help this puppy grow into a nice strong big dog.”

    I appreciate your effort, but this is a fruitless exercise. Now that you’ve asjusted for pace, you’re left with (basically) points per possession. If you correct for that, you will see every year is virtually identical. Or if you don’t, you are simply defining “better” as higher scoring.

    There is a reason fans continue to argue about whether today’s players are better than era “X.” It’s hard to figure out. You can try to measure change in overall competition by looking at individual players’ careers, but then there is the confounding issue of aging to deal with. But you can NEVER settle that debate by comparing statistics in one period to those in another, because every improvement in offense can be a decline in defense, and vice versa. What you are doing is logically impossible. I’m afraid this dog will never hunt.

      • Guy

        It’s your time, of course. But you really shouldn’t try, because success is impossible. Every single statistic you are using is zero-sum: every rebound obtained is a rebound missed by the opponent; every shot made is a failure by a defender; every blocked shot is a failure by the shooter. Unless you define “better” as higher scoring, this exercise cannot answer the question you are asking. Ask Berri — he’ll tell you the same thing.

      • 7/19/2010

        I’m going down that path. What I’m looking for is the quality of the talent pool. So the last three years offer the smallest difference in performance from the best to the worst players the mean is higher across the board. So if I took Lebron and magically transported him to 1999, his numbers would get ridiculous.

      • 7/19/2010


        Hmm.. Guy is right. These questions are difficult.

        So, on the AdjP48 side of things, you are adjusting by 48 minutes.

        On the pace side of things you are adjusting by possession.

        If you are adjusting by possession, shouldn’t that take all possession stats out of the picture (i.e. logically you can’t have 3 defensive rebounds per possession, each steal corresponds to a turnover so they cancel each other out, etc..). So you have to throw out Reb, OReb, TO, etc..

        This problem makes these results difficult to parse. It’s hard to say, but I have a feeling that if all of the adjustments are perfected, your results would potentially just be showing where the average team sits on the offense/defense continuum for a given year.

  2. Guy

    One interesting question your data could address, I think, is whether there has been any change in the distribution (variance) of talent in the NBA over these 30 years. That is, has the difference between the best and worst players grown or shrunk at all? You could measure this as a standard deviation at each position, or compare the top and bottom quintiles — whatever suits your fancy. I think that would be an interesting exercise.

  3. greyline

    Great work. I’ll be interested to see your future refinements. One ignorant question though–for each season, you only list one year. Is that the year the season began? Or the year the season ended?

    • 7/19/2010

      I think the year the season ended is the norm in this case. You know, we just had the 2010 NBA finals, rather than the 2009/10 NBA finals. I think that that’s possibly the reason for the convention.

  4. Dan

    I agree with Guy about this. One way to think about it: WP was designed (by regression) to approximate net efficiency (offensive efficiency minus defensive efficiency). It essentially started with a team’s net efficiency and divided responsibility between the team’s players by figuring out which box score stats predict net efficiency (and then translated the units into wins). It only measures productivity to the extent that it approximates net efficiency. But average leaguewide net efficiency has not changed over the years – it has necessarily remained at 0.0, just as average winning percentage has remained at .500 – so any changes to average WP cannot reflect any real change in productivity at producing wins. Changes in WP are just a side effect of what factors the WP calculation happens to include or exclude, along with leaguewide trends like changes in the balance between offense and defense.

  5. 7/19/2010

    WP and actual wins are fixed assets assigned to teams based on the marginal value of their players performances vs. the performance of their peers. My premise lies on the fact that the average value is shifting over time and thus the amount of ability required to obtain the same marginal result must also change. A higher level of competition means diminishing returns for the same net productivity.So what I’m arguing for is that it’s possible to build a model given that we know the marginal value and the absolute value for productivity that adjust for the average value of productivity.

    • Guy

      “My premise lies on the fact that the average value is shifting over time and thus the amount of ability required to obtain the same marginal result must also change.”

      You may very well be right about that. For example, if you looked at times in the Olympic 100m sprint over time, you would find that runners are faster today. But the number of medals given out (wins) has stayed exactly the same. The problem, though, is that basketball statistics are not like elapsed time on a track. They do not have meaning outside the context in which they happened. If players shoot more efficiently, you don’t know if it’s because they are better shooters, because defense is worse, or rules have changed (or all 3). Same thing for other statistics.

      The only stat I can think of for which this is not true is FT%. Shooting free throws basically hasn’t changed. So we know if players are better or worse at that. Unfortunately, no other stat is like that.

      BTW, baseball allows for one fairly constant reference point: hitting performance by pitchers. Since pitchers aren’t selected for their hitting ability (only their ability to pitch), it should be roughly constant over time. And what you see is that the gap between pitchers’ hitting and the hitting of position players grows steadily over time — confirming that today’s hitters are better than hitters of the past.

      • 7/19/2010

        I’m trying to measure the adjusted value of a win over time given how intense the level of competition is. By doing that I hope to answer questions like what was the value of a 65 win season in x Year. This is similar to trying to come up with adjusted hitting stats based on league averages for the year,parks etc. So the “quality” (or really net productivity by team really drives this). Comparing a 20 win season in 1996 vs 1999 is like comparing a $100 million dollar picture now vs. a decade ago. Again this model is not an end goal in itself but a tool to a desired end (season to season comparisons for wins).

        • Dan

          Normally, era-adjusted stats assume that every era was equally good. They judge each player relative to his peers who played at the same time, and then put players from all eras on a common scale so that we can see who was best relative to his peers. For instance, era-adjusted stats would show whether Peyton Manning outperformed the other quarterbacks of his era to the same extent that Fran Tarkenton outperformed the other quarterbacks of his era. Manning’s raw stats (passer rating, completion percentage, interception rate, etc.) look more impressive, but there have been leaguewide changes in schemes, rules, talent at other positions, and so on which have led to a leaguewide improvement in passing offense, so those raw stats aren’t that meaningful when comparing different eras, which is why you need era adjustments.

          But WP already includes an era adjustment – the player adjustment means that a player’s WP is defined relative to the other players at his position during that season. What you’re trying to do here is to UNDO the era adjustment and judge some eras as better than others based on some combination of their raw stats (your PROD formula). You can talk about some leaguewide trends (turnovers are down, offensive rebounding is down, points per possession went down and back up, etc.), but it doesn’t make sense to combine them into a measure of leaguewide “productivity” in the same way that WP measures a player’s productivity relative to other players within a single season.

          • 7/20/2010

            I concede the point on Wins Produced. What makes it such a good predictor is that it focuses on marginal productivity of a player against their peers. But I’m not trying to predict the good purchased (wins), I’m trying to evaluate the net return (productivity) on investment (possessions). What the numbers tell me is that on average players did more positive things per possession in 2008 than in other years so a team had to be a truly exceptional to win.

  6. Guy

    We’ll just have to agree to disagree on this.

    I do look forward to hearing any data you have on the distribution of talent. The idea that the last 3 years have had the narrowest best/worst gap is quite intriguing….

  7. 7/19/2010

    I’ll get to it. Got a post on the knicks and one on evaluating metrics before getting back to it.

  8. 7/19/2010


    Actually, now that I think about it, your comparison of possessions to currency is apt. Pace then, would map to the concept of inflation/deflation. Therefore, there is no contradiction in adjusting both for pace and minutes since all you are doing is increasing/decreasing the value of a possession lost/gained.

  9. 7/19/2010


    *Nodding* I’m quoting you on all further revisions.

  10. Alvy

    Ah shit, Five Star Post. And yes, describing it as comparing nominal and real values seems to make sense.

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