Baseball Crank
Covering the Front and Back Pages of the Newspaper
August 26, 2004
BASKETBALL: Shooting By The Numbers

The miserable showing by the US Olympic basketball team has people talking about the decline of shooting in the NBA. It's certainly true that this team can't shoot. But is offensive efficiency and skill really in decline around the league? It's an appropriate time to unveil another of my long-standing research projects: a statistical history of offensive efficiency and tempo in the NBA. My apologies if someone else has done this stuff before, but I got tired of trying to find it somewhere; tip of the hat to for the numbers.

I'll run these in table form, decade by decade. The first four columns of the chart should be familiar enough: the leaguewide averages for team points per game (P/G), shooting percentage on two-point shots (2%), on three-point shots (3%), and on free throws (FT%). A key stat I use here is Points Per Field Goal Attempt (PPFGA), developed by John Hollinger of the Basketball Prospectus; the formula is (P/(FGA+.44(FTA))). Basically, Holinger started by assuming that a free throw is worth 1/2 of a field goal attempt (e.g., you get two shots for two points instead of a single field goal attempt), then cut the ratio from .5 to .44 based on an analysis of how often guys shoot an extra free throw after hitting a bucket, for a technical foul, etc. I use the denominator of this formula to estimate the number of team shot attempts per game (FGA/G). The last three columns seek to break down the components that go into offensive efficiency above and beyond the shooting percentages: the percentage of the league's points that were scored at the line (FT/P), the frequency of free throw attempts per field goal attempt (FGA/FTA; a higher number means less free throws), and (since 1979-80) the percentage of shots that were three-point attempts (%3).

I've listed league expansion and contraction under "Major Rules Changes," but I'm sure I've missed some actual changes in the rules that had some significant effects. Also, I haven't set out the blow-by-blow extension of the schedule; the NBA schedule rose gradually to 72 games in 1953-54, then went up to 75 in 1959-60, 79 the following year and wound up at its present 82 in 1967-68. I also haven't done a similar table for the ABA, for a variety of reasons; maybe another day. Let's begin:

The 1940s

Major Rules Changes: 1947-48, league contracts from 11 teams to 8; zone defenses outlawed


The NBA traces its official records back to 1946-47, although the league was known as the BAA (Basketball Association of America) for the first three years prior to a merger with another professional league. To the modern eye, a league-wide field goal percentage around .280 is almost inconceivable, although to the novice basketball fan at the time it may have seemed to make it easier to grasp basketball statistics (see! they're just like batting averages!). As you can see from the above and the seasons of the early 1950s, however, the offensive skill level of the league was improving rapidly as the league gathered the nation's best basketball players; look at the 60-point increase in the league's free throw percentage in a two-year span. Free throw percentage is a good barometer of basic shooting skill, since free throw shooting is basically just man vs. basket, with no adjustment for the level of competition. The pace of play reached a pre-shot-clock high of 107.9 shot attempts per game in the league's second season, when teams played just a 48-game schedule.

The 1950s

Major Rules Changes: 1951-52, size of foul lane doubled from 6 to 12 feet; 1954-55, shot clock introduced; 1957-58, ban on offensive goaltending


Basketball in the Fifties, especially early in the decade, was a bruising business, as earthbound forwards and centers dominated the game. The level of violence in the game reached a pinnacle in the 1952-53 season, with one foul shot for every 2.15 field goal attempts and a record 31.2% of all points being scored at the line. Perhaps the archetypical player was Dolph Schayes, who shot 40% in a season just once (.401 in 1959-60), but averaged nearly 8 free throw attempts per game for his career while shooting .849 from the line, and averaged 12 or more rebounds a game 11 years in a row. Bob Cousy debuted in 1950-51, and revolutionized the game by being the first true point guard, but took some time to foster imitators; Bill Russell arrived in 1956-57, although black players would not become a common fixture for several more seasons. You can see the immediate and dramatic impact on tempo of the shot clock, as well as the fact that it was introduced to arrest a decline in the pace of the game.

The 1960s

Major Rules Changes: 1961-62, league expands from 8 teams to 9; 1964-65, foul lane widened again from 12 to 16 feet; 1966-67, league expands from 9 teams to 10; 1967-68, league expands from 10 teams to 12; ABA begins operation; 1968-69, league expands from 12 teams to 14


1959-60, Wilt Chamberlain's rookie year, saw the league shoot above 40% for the first time and never look back; Wilt would be the first significant NBA player to shoot 50% the following year. The 1960s were the golden age of up-tempo basketball, which combined with stars who played more than 40 minutes a night is what gave us all those eye-popping individual stats - in 1961-62 alone, you had Wilt scoring 50.4 points and 25.7 rebounds per game, the Lakers with two 30/game scorers (Jerry West and Elgin Baylor), Walt Bellamy scoring 31.6 points and 19 rebounds/game as a rookie, Oscar Robertson averaging a triple double per game while scoring 30.8 points a game, Bob Pettit scoring a career high 31.1 per game while pulling down 18.7 rebounds/game, and Russell (the league MVP) hauling in 23.6 boards a game while scoring a career high 18.9. Those guys were good, but they weren't that good; they just played in a league with exceptionally favorable conditions.

The 1970s

Major Rules Changes: 1970-71, league expands from 14 teams to 17; 1972-73, ABA contracts from 11 teams to 10; 1974-75, league expands from 17 teams to 18; 1975-76, ABA contracts from 10 teams to 9, only 7 of which finish season; 1976-77, ABA folds, league expands from 18 teams to 22


As it had in 1959-60, the league took a great leap forward to usher in the 1970s, as the 1969-70 season saw the league's PPFGA shoot up from 0.981 (just off the prior year's record high) to 1.022, averaging more than a point per shot attempt for the first time. Why the sudden advance? Probably a combination of factors: with rapid expansion and rising player movement (especially if you count the ABA), team defenses were harder to sustain; Bill Russell retired, the Celtic defense collapsed, and the highly efficient scoring machine Kareem Abdul-Jabbar came into the league (compare Kareem's career PPFGA of 1.184 to Russell's 0.942 for an extreme illustration of the changes in the nature of the game and its dominant figures).

1969-70 also saw the league free throw percentage shoot up almost 40 points in one season, and free throw shooting would reach an all-time high of .771 in 1973-74. One factor was the injury and then retirement of Wilt Chamberlain. I'm not kidding; over his 14-year career, with the exception of the 1969-70 season (when he played only 12 games), Wilt missed an average of 440 free throws per year - about half the number of misses by an average team in those years. Particularly when the league was just between 8 and 11 teams, that can have an impact.

In a related development, the number of free throw attempts fell off sharply in the 1972-73 season, as the field goal/free throw attempt ratio shot from an all-time high of just over 3-to-1 to 3.832 to 1 in one year, and would only rarely again dip below 3-to-1.

The 1980s

1979-80, three-point shot introduced; 1980-81, league expands from 22 teams to 23; 1988-89, league expands from 23 teams to 25


The three pointer was the major rules innovation at the start of the 1980s, but coaches and players around the league clearly judged it a failure, as the number of attempts dropped by more than a third after the first season and didn't recover for five years (the player perhaps most responsible for its revival was Larry Bird, whose 3-point attempts picked up again in 1986-87 along with the league). But no matter; offensive efficiency reached historic highs in the 1980s, as field goal percentages soared close to 50% on the two-point shot, while rates of free throw attempts rose in the middle of the decade, the heyday of the sort of scoring-machine small forward that's almost extinct today (think Bernard King, George Gervin, Mark Aguirre, James Worthy, Adrian Dantley, Alex English, etc.). The Showtime Lakers were the leaders in this, of course. While we think of the 1980s as a great time for scoring, however, the slow decline in the pace of the game was continuing apace, as shot attempts dropped below 104/game in 1979-80 for the second time since the first season of the shot clock, and dipped below 102/game six times.

The 1990s

Major Rules Changes: 1989-90, league expands from 25 teams to 27; 1990-91, league awards 3 foul shots rather than 2 if a player is fouled while shooting a 3-pointer; 1994-95, 3-point line moved in from 23'9" to 22 feet; 1995-96, league expands from 27 teams to 29; 1997-98, 3-point line moved back again to 23'9"; 1998-99, lockout/strike shortens season to 50 games


The 1990s opened with another milestone: the first season below 100 shot attempts per team since the introduction of the shot clock. It should not be surprising, perhaps, that the 3-point shot's rise has coincided with the decline in shot attempts as well as - of course - free throw attempts, as the three places a premium on moving the ball around to get the open man. Offensive efficiency shot upward for a few years when they moved in the 3-point line, but collapsed when the league moved it back. The 1998-99 season proved to be a bit of an aberration, however; if you look at the percentages in context, you can recognize across the board that players were moving unusually slowly and shooting unusually poorly, no doubt showing rust from the long lockout.

The 2000s

Major Rules Changes: 2001-02, illegal defense rules eliminated as part of larger overhaul of defense rules


"Average" is the all-time average since the NBA's beginnings, or since 1979-80 for the two three-point-specific categories. When you take the current decade in context, you can see that three-point shooting and free throw shooting - the better measures of marksmanship - are as healthy as they have ever been; scoring is down today partly because of slow tempo, partly because fewer and fewer guys are getting to the line the past five years, and partly because shooting percentages inside the arc have dropped to levels not seen since the late 1970s. That is where the league's scoring issues lie; I'll leave it to someone who understands the game's nuts and bolts better than I do to diagnose more precisely why that is.

Posted by Baseball Crank at 09:00 AM | Basketball | Comments (1) | TrackBack (0)

Very nice work.

It's interesting that the number of 3-pointers took a big jump when the line moved in, but after it went back out, it was still significantly above where it used to be. And the 3-pt. shooting % is still well above the historical average.

It's only a guess, but the lower 2-point shooting percentage may have to do with the retirement and decline of the really good centers since the mid-90s.

Posted by: Devin McCullen at August 26, 2004 12:55 PM
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