Sports Reference Blog

Estimating Pace and Per-Possession Ratings, 1951-1973

Posted by Neil on December 6, 2013

Today, we added a new feature to Basketball-Reference: historical team Pace Factors and Offensive/Defensive Rating estimates.

As of yesterday, we only had Pace and ORtg/DRtg for NBA teams going back to 1973-74, the first season in which the league tracked team/opponent turnovers and offensive rebounds (which are, of course, necessary to the possessions formula). However, it is possible to estimate possessions for years prior to '74 -- an idea I developed casually at the old BBR Blog in 2010, and one which was expanded on in more detail by ElGee35 at his (now-defunct) blog in 2012.

The basic idea is to estimate possessions by applying blanket league-average turnover and offensive rebounding rates that make sense within the context of the game as we might imagine it was played in the 1950s, 60s, and early 70s. To this end, we cannot use league-wide averages for all of NBA history up to and including 2013-14, because the game has undergone numerous radical changes since then (in particular, league turnovers would drop sharply in the 1980s, probably due to a combination of them being tracked and the introduction of the 3-point shot).

Instead, we look to the years immediately after turnovers and offensive boards began to be tracked, but before the ABA merger altered the NBA forever. In those seasons, the league averages were roughly a 30% offensive rebounding rate (which is the same constant we use in pre-1974 PER) and a 16.3% turnover percentage, rates which we apply to the rest of NBA history leading up to 1973-74.

The further back you go, more challenges emerge. Here's a handy chart detailing the statistical barriers to computing possessions at various points in history:

| League  |    Years     |         What's Missing?           |
| NBA     | 1974-present | Nothing.                          |
| NBA     | 1971-73      | Tm/Opp ORb, Tov                   |
| NBA     | 1965-70      | Tm ORb, Tov; All Opp stats        |
| NBA     | 1951-64      | Tm MP; Tm ORb, Tov; All Opp stats |
| ABA     | 1972-76      | Nothing.                          |
| ABA     | 1969-71      | Opp ORb                           |
| ABA     | 1968         | Tm/Opp ORb                        |

In the NBA before 1971, I had to drop the opponent side of the possession formula, making it:

Poss = Tm FGA + 0.4 * Tm FTA - 0.321 * (Tm FGA - Tm FG) + Tm TOV

(The 0.321 part comes from ORB being 30% of TRB; 1.07 * (3/10) = 0.321.)

This adjustment allows us to estimate possessions for the NBA going back to 1951, the first year they tracked rebounds.

In case you're curious, for ABA opponents from 1969-71, I used the league ORB/TRB rates for each season (since we know that number for those ABA years), and for the 1968 ABA I set ORB = .35*TRB, since the surrounding ABA rates were roughly 35%. (Incidentally, these are the only adjustments necessary for the ABA, since they counted turnovers in all of their seasons.)

The last step is to compute pace, which requires team minutes, which we don't know before 1965 (we can't aggregate individual minutes on a team because they inconsistently tracked split-season stats before then). Again using the surrounding seasons, I determined that team minutes can be estimated from 240*games + 23*overtimes_played (note: I have no idea why it's not 25*OTs, since there are 5 players and a 5-minute OT, but that's what the data says). Doing that for pre-1965 teams, we can calculate pace factors for teams going back to 1951 as well.

5 Responses to “Estimating Pace and Per-Possession Ratings, 1951-1973”

  1. Jason J Says:

    Very nice explanation, Neil. Excited to get a look at the results when I have the time.

  2. Mike G Says:

    Neil, this is intriguing work. We were recently debating this at APBRMetrics. An argument is that the Bill Russell Celtics were dominant defensively and barely average on offense.

    Note that in 1960, league avg pace is estimated at 126.1, the Celts at 136.3
    Avg ORtg (and DRtg) estimated 91.1
    They were dominant that year with 59 W and 7.62 SRS
    Boston is given ORtg of 91.0 (avg) and DRtg 84.5

    What if in fact a lot more than 31% of their rebounds were offensive?
    And what if their depth of players afforded them a sizable TO advantage?
    Wouldn't both of these mean they did not in fact play at a much faster pace than the rest of the league?
    And if so, their ORtg might be well above the avg. that year.

    It must be unusual for a team to be that much higher paced than league avg and also to be dominant on D.

  3. Frank Says:

    Great stuff, thanks for your hard work (the relative ORtg/DRtg numbers under the franchise indices are a nice touch as well).

    BTW, the Finals composite box scores pre-84-85 season have been broken for some time now. I'm wondering if you guys are aware of this problem?

  4. David Says:

    Frank - The Finals box scores have been fixed.


  5. Frank Says:

    Thanks guys! :)