Backpicks GOAT: #30 Bob Pettit

Key Stats and Trends

  • Never played on a dominant team
  • Despite strong box stats, limited evidence for elite peak

Scouting Report

There’s almost no video of Bob Pettit – the closest thing we have to a continuous reel of game tape is probably the 1962 All-Star game – so this will be the briefest scouting report in this series. It’s clear from the limited evidence that Pettit was a fluid athlete who had a good first step and an effective outside jumper. (He hit two shots near 3-point range in the first half of that ’62 ASG.) He could drive and finish around the hoop, was an active offensive rebounder and seemed to constantly probe for better position off the ball. Pettit himself felt his offensive rebounding was his best attribute, discussed below in this wonderful video on his career:

In the limited archives, there aren’t many instances of Pettit finding a great pass. However, there are some clips of decent assists or outright creation, setting up teammates after drawing defensive attention. Combined with his typical assist per game figures (often in the 3s) it’s likely that Pettit was a moderate creator for his time.

On film, his defense looks like a mixed bag. He occasionally reached when guarding the ball, but otherwise constantly swiveled his head to check his positioning. His recovery and shot-blocking don’t pop in any available footage, and he wasn’t known for verticality. However, it appears he was a strong defensive rebounder, but not quite elite in that realm.

Using estimates of rebounding, it’s likely that he was around 17 percent in total rebounding rate during his best seasons, comparable to modern bigs like Anthony Davis or Pau Gasol. In the first five seasons rebounding percentage were officially tallied — when defensive rebounding rates were chronologically closest to the ’60s — Pettit’s numbers would have ranked about 10th in a given season, or around the 80th percentile among big men.

As his career unfolded, Pettit’s physical condition changed dramatically. According to his account, he was a slender 210 pounds when he entered the league. After taking punishment in the paint, including 140 career stitches in his face and a broken hand that forced him to wear a cast at times in 1957 and ’58, he added 35 pounds with weight training, bulking to 245 pounds (at 6-feet-8 in socks). Pettit retired at 32, tearing a ligament in his knee in his final season in 1965.

Impact Evaluation

The shot-clock was to the NBA what the Cambrian explosion was to biology. Before Danny Biasone’s timekeeping innovation, the league was in a dull place, contracting a team in 1953 (Indianapolis) before another disbanded in 1954 (Baltimore). In 1951, there was even a 19-18 game. With the clock’s implementation in the 1955 season, the league entered a period of exponential growth in which racial barriers eroded, rules evolved and money poured in, all of which attracted a larger talent pool. The game grew so fast (pun intended) that there were conversations about banning tall players.

One measurement of this growth is the prominence of new players, and as you can see below, an influx of rookies played larger roles at the outset of this period:

In the last 65 years, there have been only five seasons where rookies topped 13 percent of the 1500-minute players, and all five were between 1955 and 1963. The league was immature then, and the teams tightly packed; the hardest period in history to create any separation was in the late ’50s and early ’60s. So while parity prevented a dominant team until the Celtics empire, some of those 50-win teams were quite impressive.

Pettit entered the league in ’55 and immediately assumed a leading role, nearly doubling his second-best teammate in scoring. Despite frequent roster turnover and coaching turmoil during his first few years, the Hawks gradually improved, climbing from an also-ran to a .500 team, adding notables like Slater Martin and Ed Macauley. And a .500 team was good enough to win back then, as St. Louis took the ’58 title with a quotidian SRS of 0.8.

Pettit was the first great scorer of the shot-clock era and claimed two scoring titles in the ’50s. Thanks to his outside touch (visible on film), his efficiency was bested by only a handful of players during the post shot-clock explosion. Here’s how he stacked up in the first 15 years of the clock:

The Hawks peaked in 1959, playing at a 50-win pace (prorated to an 82-game schedule). Macauley moved to coaching and All-Star center Clyde Lovellette joined the team. More importantly, Pettit, free of his cast, spiked in scoring and efficiency while his assists ticked back up. Commensurate with Pettit’s individual improvement, the St. Louis attack finished first in the league in relative offensive rating in ’59. After two average seasons of offense, they posted +2.9 rORtg in ’59, a near identical number to their 1960 mark of +3.0. So while the defense remained steady, the offense turned them into potential challengers to Boston in those years.1

With rookie and future Hall-of-Famer Lenny Wilkens aboard in 1961, the Hawks produced another 50-win pace season. But the ’62 team fell apart, despite Pettit and Hagan logging big minutes. The defense betrayed St. Louis, dropping from well above average to well below it, losing 7.4 points in relative efficiency overnight.2 Lovellette was injured for half of the season, but the team wasn’t so hot with him either. Wilkens also missed most of the year for military service, and in the 20 games he played, St. Louis looked average (+0.6 SRS). Another key factor, along with any regression from aging, was St. Louis’s coaching carousel; the Hawks trotted out three coaches that season, including Pettit himself for the final six games! (He was the eighth Hawks coach in six seasons.)

After that, St. Louis strung together a few more runs behind Pettit (the player), Zelmo Beaty and Wilkens, playing at a 45 to 49 win pace for Pettit’s final three seasons while returning to defensive performances that were comparable to their pre-’62 numbers.

Unfortunately, we have limited data from those years to gauge Pettit’s impact. If we examine his missed time, his WOWY score in 35 missed games during his prime is unimpressive (+0.9), although some scaling of those numbers is required given how tightly compacted the league was then. Using a more robust method like WOWYR demonstrates decent positive impact, but his numbers are closer to Sam Jones than the giants of the era. Given his injuries, It’s likely these studies understate his peak play, although I do think they accurately reflect a lack of dominance compared to that period’s transcendent stars.

I could easily see Pettit a slot or two lower on this list. However, it’s harder for me to see him much higher. This is largely due to a lack of information and rapid change during the era; Pettit is really the earliest star of the shot-clock period, and because of that, some curving is required to account for the influx of talent that would hit the league in the ’60s. Still, I give him nine All-NBA type seasons with a peak that barely touched MVP status, good enough for the 30th most valuable career since 1955.


The Backpicks GOAT: The 40 Best Careers in NBA History

Welcome to the Backpicks GOAT, a list seven years in the making! You may have seen ESPN, Slam, Elliot Kalb and Bill Simmons take a crack at the top basketball players ever. Maybe you have your own list of the NBA greats. Or maybe you just like reading lists. Either way, this particular one is a little different.

This is less about The List and more about the exercise of player evaluation. It’s intended to be an historical reference, organized by player, that (hopefully) adds to the understanding and appreciation of players, coaches and teams over the years. If you like videos, charts and graphs, you’ve come to the right list.

What This List Is Not

This list will not make traditional “arguments” for players. I won’t attempt to balance Kobe’s championships without Shaq, nor do I care about accolades like All-Star teams or the number of Hall of Fame teammates someone played with. I also don’t care how many rings a player won; the very thing I’m trying to tease out is who provided the most lift. Sometimes that lift is good enough to win, sometimes it’s not.

There are no time machines either — it’s not about how players would do today if transported into the past or future. It’s about the impact each had in his own time over the course of a career.

What This List Is

This list also goes far beyond the box score — indeed, the box score is merely a reference for quantifying tendencies — so if you’re used to citing points per game and Win Shares, this will be a bit different.

Instead, this is a career-value, or CORP list; it ranks the players who have provided the largest increase in the odds of a team winning championships over the course of their careers. This means that having great Finals moments or winning the hearts of fans with innovative passes is irrelevant. You can make a great list with those criteria, but that’s not what this is exercise is intended to be.

This list is really about evaluating players based on “goodness,” not merely situational value. (If David Robinson backed up the two best centers ever, he wouldn’t be very valuable, but he’d still be very good.) Players do not earn credit for potential — Michael Jordan helped no one in 1994.

All told, in the last seven years I’ve evaluated over 1,500 player-seasons to compile this list.


Thinking Basketball

As you read player profiles, you will notice little mention of playoff performances or game-winning shots. That’s because sample-sizes are incredibly small; instead, playoffs are included as part of an entire evaluation. I’ll only call out the playoffs if they reflect something larger about a player. If you’re struck by the lack of discussion around clutch play or why “losing” players are ranked highly, all of these topics and more are explained in detail in Thinking Basketball. The book also examines critical components of team building (portability) and individual scoring that are foundational to these rankings. (Buying the book also supports the blog and is greatly appreciated!)

List Criteria

The first step is to evaluate a player season. My practice starts with film study in order to understand context.  Perhaps the most beautiful thing about basketball is that there are so many ways to skin the proverbial cat; 20 points per game for one player is not the same as 20 for another. Of course, some skills are more valuable than others. Here’s a guide to the major ones:

On defense, quality of rotations, court coverage, rim protection and length are all countermeasures to the above offensive criteria. (Rebounding counts too, separately for offense and defense.) I tracked these, shot selection, and passing habits in over 100 hours of video study specifically for this series. (To avoid winning bias, I watched segments of games from random quarters.)

After establishing the skill set and tendencies of a player (“Scouting Report”), I then leverage data to quantify the effect of these tendencies (“Impact Evaluation”). All of this ultimately leads to a numerical valuation that allows me to compare the impact of different seasons. The high-level criteria for determining “best career of all-time:”

  1. Evaluate how much a player impacts different lineups (Global offense and defense)
  2. Calculate the probability change in championships based on his health
  3. Add all his seasons together to determine CORP
  4. Adjust for longevity based on era
  5. Compare who has the highest impact

While the first step is my assessment of a player’s seasons, the next four steps are an attempt at an objective measure of career value using those assessments. To do this, I rely on a championship odds calculator I’ve developed over the years so I don’t have to worry about arbitrarily balancing “longevity” and “peak.” I then make an adjustment for era-based longevity, and typically sort out any close calls by defaulting to the player with the better peak or stronger era.

To simplify things, each player-season can be slotted into different tiers:

  • GOAT Season (30 percent or more chance of a title on a random team, or about +7 points per game on an average team)
  • All-Time Season (23-30 percent or +6)
  • MVP Season (17-23 percent or +5)
  • Weak MVP Season (12-17 percent or +4)
  • All-NBA Season (8-12 percent or +2.5)
  • All-Star Season (5-8 percent or +1)
  • Strong Role Player (3-5 percent or 0)
  • Role Player (1-3 percent or -2 to -0.5)

This allows for easy comparisons between multiple seasons; we can see if two MVP-level Bill Walton seasons are more valuable than, say, five All-NBA seasons from John Stockton.

Ranges, Not Absolutes

This is still only one person’s opinion. A “better” list would come from a group of diverse and highly knowledgable evaluators, like realgm’s top 100 list. I see my value here as a video and data curator and as an analyst of that data; obviously, mileage may vary on the rankings, especially depending on criteria.

With that said, I will try and highlight where there’s wiggle room and the ranges that I believe players fall into, but the final order is based on the most likely answers to me (i.e. gun to my head, how good I think a career was).

Stats Glossary

Throughout this list, I’ll use the following metrics regularly:

  • Efficiency (for individual players) – This is measured in true shooting percentage (TS), or occasionally points per scoring attempt (PPA). In the simplest terms, PPA estimates how many “attempts” were actually two-shot fouls, and takes the total number of points scored from 3-pointers, 2-pointers and free throws divided by attempts. True shooting divides PPA by two. In order to compare efficacy across years, this is almost always cited as relative to the league average (rTS). NB: Postseason rTS values are relative to the league (not the opponent) unless otherwise specified.
  • Efficiency (for teams)
    • Offense  This is an estimate of points scored per 100 possessions, or the team’s offensive efficiency. It is often cited as relative to the league average or “relative offensive rating” (rORtg). For the playoffs, rORtg is the difference between the team’s raw offensive rating and the opponent’s regular season defensive rating.
    • Defense – This is an estimate of points allowed per 100 possessions, or the team’s defensive efficiency. It is often cited as relative to the league average or “relative defensive rating” (rDRtg). For the playoffs, rDRtg is the difference between the team’s raw defensive rating and the opponent’s regular season offensive rating.
  • Creation – This is an estimate of how many shots a player created for his teammates per 100 possessions played. It’s also sometimes referred to as a percentage.
  • SRS – The “Simple Rating System,” it is a measurement of point differential for teams, adjusted for schedule strength. SRS is highly predictive of regular season wins and more predictive of games and playoff series than win percentage alone. For this series, a teams “win-pace” is based on its SRS.
  • The Big 3 / Big 4 – These are the three primary offensive dimensions of the advanced box score: Scoring rate (points per 75 possessions), efficiency (rTS) and creation. A fourth dimension — “The Big 4” — includes turnovers (modified for the presence of creation). “Scaled” graphics (sometimes titled “Normalized”) shrink each dimension on an axis of the same length for an equal comparison between them.
  • WOWY / APM – These are the non-box score, scoreboard-based family of plus-minus metrics and some of the most important measuring tools we have in basketball. Most of the references to these are summarized in the historical WOWYR series and this post on the historical compilation of plus-minus metrics.

Who Am I?

The Backpicks Top 40

The list will snake around a bit until the final eight players are revealed in order. The series is intended to be read in the order the profiles are released, which is noted next to each player. Players 31-40 are profiled in small blurbs, most players from 21-30 have limited video-based scouting reports, and all profiles in the top-20 feature full video-based scouting reports.

*Limited video-based scouting report 

  1. March 19
  2. March 19
  3. March 19
  4. March 19
  5. March 19
  6. March 19
  7. March 19
  8. March 19
  9. March 19
  10. March 19
  11. December 14*
  12. January 22
  13. December 28*
  14. March 15*
  15. January 25*
  16. January 29
  17. January 8*
  18. February 5*
  19. February 22*
  20. February 26*
  21. February 8
  22. March 1
  23. March 5
  24. December 18
  25. January 1
  26. March 12
  27. February 12
  28. February 19
  29. December 21
  30. January 11
  31. January 15
  32. Wilt Chamberlain (1)
  33. March 22
  34. March 26
  35. April 2
  36. April 5
  37. April 12
  38. April 16
  39. April 19
  40. April 23

Post-Mortem: April 30

Backpicks GOAT: #9 Wilt Chamberlain

Note: This is the first profile in a historical series on the most valuable NBA careers of all-time. 

Key stats and trends

  • Overrated offensively (scoring blindness) – didn’t create and score at same time
  • Underrated defensively – anchored multiple top-tier defenses
  • Inconsistent, changed game multiple times (overly focused on stat du jour)

Scouting Report

We have limited film of Wilt, so piecing together his game is a matter of pairing the possessions we have with numerous journalistic accounts. He loved the left block, but didn’t work feverishly for deep post position like we might see from someone like Shaq at his apex. When he did establish deep position, Wilt was explosive and difficult to stop, either dunking or quickly wheeling for a finger roll. He also liked the fadeaway, demonstrating that he wasn’t merely a brute.

However, Wilt wasn’t always a fluid athlete, especially as he added muscle during his career. His footwork is the first thing that stands out on film; it was sometimes awkward and led to a number of travels or off-balance plays.

Once he started passing more, he became black-and-white with his attack – when he received the ball in the post with his back to the hoop, he would often start in a “pass mode.” Pass-mode Wilt waited for an open cutter, and if his receivers were covered, only then would he start a deliberate scoring move. Below, he surveys briefly before setting up his fadeaway:

This inability to simultaneously threaten the defense with scoring or hitting open players held him back as an offensive force in my estimation. In other words, he wasn’t a good playmaker. In 1966, Sports Illustrated alluded to this zero sum, baseball-like approach like this:

“But the tactical demands of using [Wilt] to his best advantage severely diminish his own team’s versatility and generally create morale problems among those who want the ball as much as he does.”

Wilt struggled to combine his own scoring with creation, as the best offensive players do. Additionally, his tendency to park himself on the block and remain there for the entire possession clogged driving lanes for his guards.1

As he grew older and was exposed to Alex Hannum, Wilt was a very willing passer. However the film demonstrates how teams responded to this “passing mode” differently. In 1964 (and again in 1967) Wilt was often double-teamed, and thus his passes to open cutters created a 4-on-3 power play, if properly spaced. In other words, defenses reacted to Wilt and he could create.

However, on the back nine of his career, teams didn’t seem to double this action. They just let Chamberlain stand there and hold the ball.2 Wilt was then truly making a “Rondo Pass,” where he would simply wait for the other four players to materialize an opening instead of helping them create the opening. This shrank his playmaking and minimized his overall impact.

Passes like this have some value, especially when surrounded by quality teammates, but they are more like jabs, whereas creating an open shot is a power hook. Wilt also might have been turnover prone. On my most recent film-study, I tracked 47 of his post possessions and seven were turnovers (a whopping 15 percent of the time).

That’s a super small sample, no doubt, but consistent with reports like this from Sports Illustrated during the 1973 Finals:

“Against Reed, who is taller, stronger, heavier and quicker than Lucas, Chamberlain’s attempts to back under the basket for his finger rolls and dunks yielded almost as many traveling calls, three-second violations and offensive fouls as they did goals.”

Because of this, I wouldn’t call Wilt a “high-IQ player,” although he did have a great feel for certain game dynamics, particularly when he could survey the court. (He had a nifty behind-the-back wrap-around pass that in one highlight led to a dunk and in two others clanked off a leg or sailed out of bounds.) As his career evolved, he looked to score less and less — although he still had power and spin moves in the post — and in his final seasons, he wasn’t a focal point on offense at all. Here (in 1972), he’s in position to attack, but thinks nothing of it:

Defensively, Wilt was a monster. Here he is in his later years defending Kareem brilliantly, first with active hands and then sitting on his sky hook to prevent Jabbar from comfortably wheeling to his left:

His defensive weakness was block-chasing. He tallied goaltending violations constantly in the limited film we have on him and occasionally fell out of position by chasing blocks. In the stunning clip below we can see his otherworldly athleticism combined with a propensity to rack up goaltends:

Otherwise, he generally stayed near the hoop and was an absolute terror protecting it. There’s plenty of this on film:

This led to dominant defensive rebounding and some of the most incredible blocked shots you’ll ever see. He ate up space with his 7-foot-8 wingspan and altered a number of shots from guards as they entered his domain.

Impact Evaluation

In Thinking Basketball, Wilt is the case study for Global Offense. He produced unrivaled individual scoring numbers, but they did’t move the needle much for his team. It’s only when his game shifted away from volume-scoring that his team’s offenses flourished. He’s perhaps the ultimate illustration that individual offense does not automatically equate to successful team offense.

The simplest way to see this is to look at the correlations between his offensive outputs (the x-axis) and his team’s offensive efficiencies (the y-axis):

There’s a massive negative correlation (-0.76) between Wilt’s scoring attempts and his team’s offensive rating. So, the less Wilt shot, the better and better his team’s offenses performed. I won’t rehash what’s outlined in detail in the book, but needless to say, Wilt’s skill set described in the scouting report contributed to this phenomenon; not creating for teammates is extremely limiting.

Most volume scorers will taper down on good offenses, but Wilt is unique in that he completely shifts his style of play away from scoring on all of his successful offensive clubs. In some ways, Wilt was the original “Black Hole” – when the ball went in to him, it wasn’t coming out.3

To put this into perspective, we can look at his ratio of true shot attempts (TSA) to assists.4 Historically, Jordan’s ’87 scoring spree comes in at 7.2:1 and Kobe’s ’06 barrage at 7.0:1. Those are the two highest scoring seasons per possession in NBA history. Wilt’s ’61 and ’62 seasons had ratios just under 20:1, good for sixth and seventh all-time, behind such legendary offensive forces as Howard Porter (1974) and Charlie Villenueva (2015). Even 1982 Moses Malone was around 15:1, and his favorite pass was off the backboard to himself. Here are Wilt’s outlier seasons visually:

So we know that early Chamberlain shot the ball a lot, didn’t create much, and (predictably) his team’s offenses weren’t very good. Can we infer how much he was actually moving the needle for those teams?

When Wilt joined the Warriors in 1960, the offense improved by about a single point per 100 possessions.5 That offense was still 2.4 points below league average (relative offensive rating, or rORtg), the first major signal that Wilt’s volume scoring didn’t automatically equate to great offense.

This was inline with his lack of creation; Chamberlain scored at 21.5 points per 75 possessions that year on efficiency 3.0 percent better than league average (relative True Shooting, or rTS). For comparison, 2017 Kevin Love was 22.7 at +2.0 percent. It would counter every trend in NBA history for this kind of isolation scoring or finishing (from offensive rebounds or off-ball scoring) to automatically generate quality team offense. If we plug in turnovers for Wilt — from low percentage to high percentage — his averages during those volume scoring years were 24 points per 75, +5.0 percent rTS and about a 3 percent creation rate (3 shots created per 100), closest historically to 1981 Robert Parish, 2007 Carlos Boozer, 1981 Moses Malone and 1996 Alonzo Mourning.

The 1960 Warriors also had improved roster continuity, and as a result two of their better players logged more time (Guy Rodgers and the NBA’s first “Mr. Everything” Tom Gola). All-Star Paul Arizin was a year older at 31 and coming off an All-NBA season. Otherwise, they returned the same core from 1959.

However, on defense, the Warriors showed massive improvement, jumping nearly 3.5 points relative to league average. This is a trend that would repeat itself throughout Wilt’s career. Here’s his entire timeline with the Warriors:

In 1962, with Frank Maguire taking over as coach and a second-year Al Attles in the rotation, Wilt averaged 50 points a night and the Warriors jumped to a 55-win pace. However, (again) the team offense budged only slightly, sitting 1.7 points above league average, the highest of any of his first seven seasons.

In 1963, yet another coach entered the picture and the Warriors lost Arizin to retirement. Wilt still had a monster scoring year, boasting an rTS of +5.8 percent for the second straight season, but the offense sunk to below-average. Sports Illustrated described the year like this: “The whole dull show was Wilt Chamberlain, who averaged 44.8 points a game while the rest of his team forgot to score.”

In 1964, one of the great coaches in NBA history, Alex Hannum, entered the picture (along with rookie and future Hall of Famer Nate Thurmond). SI wrote this at the end of the preseason:

“Hannum’s teams move constantly, and everybody works for shots. Could Chamberlain, who sometimes seems an immovable object, fit into the new style? The answer appears to be yes. The new Wilt is moving. He is passing, playing alert defense, running and rebounding, but not scoring nearly as much. He is getting some help from rookie Nate Thurmond (6 feet 11), who will be Wilt’s first relief man in his four seasons as a pro. Thurmond, who could start at center for many NBA teams, is also working as a forward, where he will back up Tom Meschery and Wayne Hightower, both of whom look much better this year…Wilt is the Warriors. They cannot win without him. Hannum feels they might win with him if he is really changing his technique.”

They returned to a 53-win pace in ’64…but it was with a devastatingly good defense (5.9 points better than average). Wilt still scored at volume and the offense waned. Again.

1965 was one of the stranger results in NBA history. The Warriors played at a 28-win pace with Chamberlain. His scoring went back up, his assists declined, and San Francisco finished with the worst offense in the league (-5.9 rORtg). Wilt was traded midway through the year for 40 cents on the dollar (for a 27 and 17 minute-per-game player) and the Warriors were only slightly worse without him. Meanwhile, Philadelphia picked up Chamberlain and improved from a 40-win pace to a 48-win pace.

1966 was Wilt’s final year volume-scoring, although he began to reincorporate passing more. And in 1967, when Hannum reunited with Chamberlain, he successfully sold him on a more global approach. SI wrote this before the year:

“[Jack Ramsay and Alex Hannum] are two of the finest brains, unprotected or otherwise, in basketball. It is doubtful that any franchise ever improved its top management so spectacularly as the 76ers did this year. The team was already excellent…Philly gets Larry Costello back, and the 76ers are younger than Boston and have a full-time coach. Besides, Hannum handled Wilt Chamberlain, at San Francisco, better than any man ever did. Who else but Hannum could say that he plans to use Luke Jackson in the pivot for up to 10 minutes a game and add, ‘Wilt will be agreeable if it’s right for the team.’ This is not psychological skirmishing, either; Wilt and Alex respect each other. Chamberlain did not enhance the relationship by reporting late, but Ramsay promptly fined him $1,050, and all the special considerations that Wilt had been given last year—private suites, travel arrangements—seemed far away indeed.”

The results spoke for themselves, as the 76ers started the season 37-4 and never looked back, posting the highest offensive rating in history at the time. Wilt’s assists spiked to nearly 8 per game en route to the title.

In 1968 Philadelphia’s offense regressed slightly. At the same time, Chamberlain became fixated on leading the league in assists. (He did.) However, based on film and reports, it seemed he was letting defenses off the hook by looking to pass too much – this took pressure off the opponent and essentially turned more of his passes into low-leverage “Rondo Assists,” as illustrated above in the scouting report. Based on the footage, I think a reasonable interpretation for the team’s offensive dip is that opponents stopped doubling Wilt as much as he looked to pass more and more.6

There’s also evidence that the late 1960s 76ers were absolutely loaded. Chet Walker had a smooth offensive game, good outside shot and the ability to create his own scoring (he made seven All-Star teams). Hal Greer made seven straight all-league teams. Billy Cunningham would rise to MVP prominence when given the reigns in the following seasons. Without Wilt, and before Luke Jackson’s season-ending injury in 1969, the 76ers were playing like a 60-win team.

Meanwhile, in 1968, the Lakers were working on their own Super Team. Coach Butch Van Breda Kolff implemented a system based on the Princeton offense and his collection of guards flourished. With Jerry West, they played at a 62-win pace, with an offense to challenge the record-setting 76ers from the year before. However, without West they were pedestrian, and the result went largely unnoticed in NBA history.

Despite success in Philadelphia, Wilt wanted to move to the glamour of Hollywood. SI wrote this before the ’68 season:

“Now that Wilt Chamberlain has decided not to acquire the Los Angeles franchise in the ABA or become a split end for the Jets or the heavyweight champion of the world but instead to play basketball for a salary approaching $250,000, the 76ers must be favored to win again.”

So at the end of the year, long before the Heatles, Wilt forced a trade to LA and joined superstars Elgin Baylor and West. However, Wilt’s prodding offensive game didn’t exactly fit into Van Breda Kolff’s Princeton schemes that emphasized space and open lanes, and the Lakers regressed with the addition of Chamberlain.

They were still quite good when healthy – a 57-win pace.7 Still, they were better the year before Wilt arrived. The Laker offense, spearheaded by West, still finished a quality 3.0 points above league average, but it’s clear that Wilt’s low and mid-post game didn’t enhance what LA had previously synthesized. Van Breda Koff was infamously ousted at the end of the year.

In 1970 Wilt missed most of the season with injury and returned for the playoffs. There are only small-sampled lineups to compare (shown above), but they are similar with and without Chamberlain. His final three years were likely his least effective offensively, as his free throw rates dropped severely and his scoring rates were close to Tyson Chandler levels.

It’s not a problem, per se, to combine the packages of Chandler and Rondo; such passing can still be additive when surrounded by offensive weapons like West and Gail Goodrich. Additionally, Wilt’s offensive rebounding helped too. But he became fixated on setting the field goal percentage record and at the end of the 1973 season would pass up easy shots to preserve his shooting numbers.

“March 28, 1973, Chamberlain didn’t attempt a shot or take a single free throw while playing 46 minutes in an 85-84 loss to Milwaukee. Coach Bill Sharman, when asked why Wilt didn’t shoot, said, ‘I don’t know why. You will have to ask him. That really hurt, him not shooting’ -St. Petersburg Times, March 29, 1973

“Wilt Chamberlain, who entered the game with 24 successful field goal attempts in a row, kept the streak alive in an unconventional fashion. He took no shots at all” – The Milwaukee Journal, March 28, 1973”

By all accounts, his last few years were some of his best defensively. He was built like a tank at that point – he claimed over 300 pounds – and anchored the second and third-best defense in the league in his final two seasons.

When we regress lineup data from that period (WOWYR) Wilt still shows strong impact. This is because of all the excellent teams that he was a major figurehead on – ’62, ’64, ’67, ’68, ’72 and ’73. All told, Wilt’s four best teams, by far, come from his non volume-scoring years, and the last two come from his “Tyson Chandler” vintage. This arc makes sense if you remember the scouting report – he wasn’t creating easy shots for his teammates, and his propensity to park in the lane helped muck up spacing that was already mucked. (After all, he was described by SI as “an immovable object.”)

Meanwhile, his willingness to pass (even those Rondo Passes) helped skilled teams, as did his occasional post move and presence as an offensive rebounder. But the major contributions came on the defensive end. There, he’s one of the greatest defenders ever, only overshadowed in his time by the greatest defender ever, Bill Russell. From the film of these seasons and from the data, we see Wilt’s tremendous impact and ability to block and alter shots while inhaling defensive boards.

Finally, there’s this tidbit to drive home these trends: Most relative defenses in the postseason are slightly worse. But Wilt’s improved by 1.9 points, far more than any other all-timer. On the other hand, most relative offenses improve in the playoffs, but Wilt’s teams declined by a point…more than any other all-timer. So while a “scoring blindness” drastically overstates his offensive impact, it also masks his tremendous defensive results.

He’s great, just not in the ways that the original box score predicts.


IV. Historical Impact: The all-time MVPs from Multiple WOWYR studies

Triangulation is an important concept in the social sciences. It allows us to hone in on a result without having a singular, definitive measurement. In Part III of this historical impact series, I ran two huge regressions based on 60 years of game results to determine whose presence correlated the most with his team’s improvement. The differences in those WOWYR results — presented using a “prime” and career value — demonstrated some instability in the regression. So if we want to be confident about how valuable older players were, we’ll need snapshots from different perspectives. We could use a little triangulation.

How accurate is WOWYR?

Prime WOWYR can match a 17-year adjusted plus-minus (RAPM) study for predicting lineup results at the game level. WOWYR correlates well with players from that 17-year RAPM set (from 1997-2014, by Jerry Engelmann), with a correlation coefficient of 0.67 (for scaled results) and an average error (MAE) of 1.1 points. Every player was within 4.7 points of his RAPM value, although among higher-minute players the max error was 2.9 points.

In other words, over long periods of time, WOWYR data and RAPM are quite similar — all players will be within three points of each other and most will be within a point. We wouldn’t expect the values to be identical, because WOWYR and RAPM are measuring two similar, but slightly different, events. Still, despite the convergence, WOWYR is plagued by two major problems.

First, it’s sample size isn’t large enough for every player. Sometimes players log years with the same combination of teammates or even a single teammate (Stockton and Malone). Although they played hundreds of games, the play-by-play analogue would be Wilt Chamberlain logging 45 minutes a game, and then trying to infer his value based on 250 minutes of time off the court. It gives rise to the dreaded collinearity issue, and we’re less confident in those kinds of results.

Removing a season or three of data can alter a player’s values by a few points per game, which isn’t always a result of him playing differently in those seasons. In order to accurately solve for “what’s the most likely impact for Larry Bird on all of his lineups?” we need to know about the value of his teammates, like Reggie Lewis. And since Lewis only played a few years, his estimate is a bit fuzzy, and that in turn effects Bird’s estimate.

Second, like any RAPM study that’s too long, it smoothes over differences between peak years, ignoring aging and injury. There are some ways around this — one of which is to use smaller time periods — but other potential solutions are for another post.

10-Year GPM: Another perspective

WOWYR is one perspective; it’s a bunch of weighted WOWY data that is regressed. Building off of the the same idea, Backpicks reader Zachary Stone has tackled historical games with a slightly different approach that I’ll call GPM (Game-level adjusted Plus-Minus). GPM is more analogous to “pure” RAPM in that each game result is a row in the equation, whereas WOWYR combines games and weights the lineups. The details of Zach’s version of GPM:

  • It uses only players who played at least 25 minutes per game during a season, so those games where Draymond Green is ejected early still count as a game played for him.
  • It uses a “replacement” player cutoff of 260 games. (The other studies below use 82 games.)
  • It’s run on data from 1957-2017.
  • (Technical detail: This version of GPM chose a lambda using the computationally expensive generalized cross-validation, not the chunkier k-fold method used for WOWYR in Part III.)

But there’s still the issue of time to consider. We don’t want the model thinking that Michael Jordan in his Wizard years is actually the Michael Jordan. So Zach ran the regression in 10-year slices, from 1957-66, 1958-67, 1959-68 and so on, and then grabbed each player’s best 10-year run. Finally, he scaled the results to allow for apples to apples comparisons across eras.

In theory, this will yield a better ballpark of those players with relatively consistent 10-year primes. Combined with WOWYR, this will give us multiple snapshots of the past based on game-level results. Additionally, I’ve added an alternative version of WOWYR to the table below that uses 20 minutes per game as a cutoff for qualifying players — a version that was slightly worse at predicting lineup results than the prime WOWYR published in Part III, but contained enough variability to throw into the mix.

Together, this triangulation won’t produce retina display clarity of past players, but it’s not exactly fuzzy in most cases. Anyone who fares well in all three of these areas was likely impacting the scoreboard when they played. In the table below, I’ve averaged the three regressions and included the variability among the three as a measure of stability (smaller is better). The “GPM years” column is the period of time Zach’s model picked for each player – some of the lesser names like Don Buse have been excluded:

PlayerScaled WOWYRAlt Scaled10-yr Scaled GPMGPM YearsAvg.Variability


Because this lacks the granularity of play-by-play data, more interpretation is required per player. For instance, guys like Stockton and Malone suffer from small-sampled collinearity; based largely on the 18 games Stockton missed to start the 1998 season, the models have no choice but to solve for the two of them by giving Stockton a larger share of credit. (Utah improved in its final 64 games that year.) Meanwhile, Bird has lots of instability in his result because of Reggie Lewis; in the 1955-84 set from Part II of this series, Bird was first among all players based on his first five seasons.

Next, although Zach’s GPM doesn’t have this problem — he scaled the results of each 10-year run — WOWYR does not account for varying point differentials over the years . So someone like Bill Russell requires an upward mental adjustment, while Wilt Chamberlain’s WOWYR scores are inflated a touch compared to Russell’s because of the early ’70s expansion. GPM is the only regression above that accounts for era differences, and it peaks Wilt from 1960-69, slotting him behind Jerry West and Oscar Robertson.

About half of the MVP Shares in history belong to the first 22 players in the above table. John Havlicek, one of a few non-MVPs in the top 20, is likely aided by the collapse of Charlie Scott and premature demise of Dave Cowens. Still, his results are impressive. Paul Pierce’s are too, although his number is likely inflated by the models having no way to account for the true “replacement level” quality of Kevin Garnett’s teammates in Minnesota. And — scoring blindness alert! — I think we’ve all underestimated Dikembe Mutombo, who looks quite good in non-box metrics.

Then there are the decorated players who struggle in these regressions. Dwyane Wade’s disappointing number is likely the result of two injury-plagued seasons dragging down his value, along with two more years in physical decline. Allen Iverson, echoing his play-by-play numbers,  shows no evidence of playing at an MVP level. George Gervin, dampened by a few post prime years, posts a small value given his five consecutive top-six MVP finishes.

There are still future tweaks that can be made to these models. However, they will always have certain limitations, and at this point I’m confident in saying that there’s not too much mileage left from them. These results paint a fuzzy picture for some players, and compelling arguments for others. Even for players with strong signals, the precision of the models should not be overlooked; they are not for declaring that a player was exactly 1.2 points more valuable than a contemporary. However, for most players across NBA history, they provide a fairly accurate approximation of value.

A Visual History of NBA Spacing

We’re living in the Pace and Space era, so spacing is kind of a big deal. So much so that I’d guess nearly everyone who isn’t a coach still undervalues its importance and the role it has played historically in dictating NBA tendencies and strategy. There was a time when the lane looked more like a rugby scrum than a spacious ballroom dance floor, and this post is a visual chronicle of that transformation. Jump in a DeLorean with me as we go back to a rainy November 12, 1955 grainy 1962…

Our first screenshot is from the ’62 Finals. Offensive players have white circles under them to denote their location, defensive players blue ones, and the ball handler is white surrounded by blue.

This was what an “open lane” looked like for much of the 60s. There are four defenders on the edge of the modern (16-foot wide) key ready to help on that ball-handler if he attacks. Notice, also, that if he drives left toward the baseline, something convoluted happens: He will try to use his teammates as screeners like they are offensive linemen in football, but help defense was easy because everything so tightly packed.

Guard play in the ’60s was also characterized by a palm-down (pronated) dribble. The effect of this cannot be overstated — guards simply were not allowed to dribble in any modern capacity, which made penetration into this congested traffic difficult. Bob Cousy didn’t dribble like this for fun, the rules demanded it.

The next image is quite grainy, but it was so typical of the times that it must be included. The ball is on the far wing, at most, nine feet from the man posting up (Wilt Chamberlain). There are eight players in the modern key!

It was common at the time for certain post plays to start with this much traffic, and it led to a practice I call the “free double-team.” Modern double-teams usually pay a price by leaving a player open. The free double-team is a costless defensive trap, in which the help-defender’s own man is still so close that he can effectively guard two players at once. Thus, despite being doubled, the ball-handler can’t create a shot for an open teammate.

In the ensuing years, teams and coaches were certainly aware of these issues. The Princeton offense — which now comes in many flavors — had a large emphasis on balanced spacing and opening the lane. Still, it was a slow crawl to where we are today. The inability to break down defenders off the dribble didn’t leave coaches dreaming of clear-outs.

If we jump ahead to the 1970 Finals, you’ll notice there’s a little more breathing room.

The Lakers have pulled two players (somewhat) high and wide on the weak side, and there’s now sufficient space between the entry passer (Elgin Baylor) and Wilt in the post. However, any drive from Baylor will encounter two fundamental problems. First, there are three defenders in the lane. Second, it will be hard to punish any help defenders. The best option is likely a kick-out for a long two, but the two spot-up players are within feet of each other and can be covered by one man!

From the same game, L.A. runs a more modern type of isolation for Jerry West, who liked to back his defender down from the high post. The screen capture is from the moment New York sends a double at West.

It’s not “free” in that L.A. is spread out enough for him to swing it to an open teammate at the top of the key. Notice how pinched down the weak side players are, allowing the Knicks to form a wall in the lane, deterring penetration. It’s an improvement from the early 60s, but it’s an “economy to economy-plus” improvement. This isn’t business class space.

There isn’t much footage from the 60s, but from the publicly available film, it wasn’t until the 1970 season that the NBA started easing up on palming. Players still dribbled with mostly pronated wrists, but the contact point of the ball could be held a little longer. (I credit the ABA’s free style of play for slowly relaxing the enforcement of these rules.) More secure ball-handling made it easier to penetrate into space…if there was any.

By the early 70s, offenses were starting to expand the court. Here’s our first example of some business class roominess (from 1974):

That screenshot was taken as the entry pass reached Kareem Abdul-Jabbar at the elbow. This kind of space was a game-changer; there would now be a hefty price for doubling Kareem with either the baseline defender or the diagonal defender near the foul line. And of course, Kareem himself has a lot of room to operate in isolation, and you don’t want to play Kareem one on one.

The ’70s were a mixture of viable spacing like this and the crammed confines of the ’60s. However, like a frog in boiling water, the dribbling rules continued to slowly relax . You can see some wrist rotation during this open court dribble from David Thompson in 1977, and then a full 90-degree wrist when he hesitates on the following play. By the early ’80s, players were fully turning their wrists over from the side (or underneath) the ball. Isiah Thomas was perhaps the most notable perpetrator, and the technique can be seen on his left-to-right crossover here.

In 1980, the NBA introduced the 3-point line, but it took a few years for spacing to expand to the arc. Here’s a typical Laker set from 1983, in which Magic Johnson’s entry to Kareem was four feet inside the stripe and the entire Laker offense is indifferent to the 3-point line. (Yes, Magic’s defender is daring him to take that shot.)

Notice that there are still five Denver defenders in the lane. However, offenses in the ’70s and ’80s distributed players evenly among the strong and weak side, particularly after the introduction of illegal defense in 1982, which permitted offenses to pull shot-blockers out of the lane. More on this in a second.

By the mid ’80s, the combination of improved spacing and efficacious dribbling made penetration and isolation more of a threat. This coincided with a steady improvement in offensive efficiency — in just over a decade, league-wide ratings exploded from the mid 90s to 107 points per 100 in 1982, within two points of the all-time peak.

Let’s hop forward to 1990 and snap an image of Chicago’s famed triangle offense, which emphasized spacing and balance:

Right away it should be clear that this is business class roominess. Michael Jordan is initiating the offense here, and Chicago’s spacing allows for, at the least, a drive-and-kick by Jordan. More importantly — at least for Shaquille O’Neal 10 years later — the post player’s life is easier with three teammates out beyond the arc and the opposite side big near the high post. This kind of spacing means the defense has to cover longer distances to rotate and makes interior passing more realistic.

Compare this to, say, Hakeem Olajuwon’s Rockets, who liked to use “3 out” and “4 out” sets, pinning shooters to the 3-point line in order to punish an Olajuwon double. This next caption (from 1994) is snapped after the ball has been kicked out of the post.

Utah still has an amoeba-like wall in the lane, but the threat of the outside shot forces the defense to close out on the shooters, which can re-open a driving lane. This was very much a read-and-react game, in which the spacing allowed teams to move the ball to the best shot, and defenses scrambled to stop that shot. Here’s an example of a “4 out” set from the same year:

Now there’s only one Utah defender in the paint and some decent real estate to work with. At the same time, many teams were starting to abuse the illegal defense rules by pulling entire defenses out of the lane.

That group of Spurs bunched together on the right side of the screen cannot legally drop below the foul line because Utah has stationed the rest of its team above the arc. Some version of this play was run constantly in the ’90s, particularly by teams with good isolation players. As you can see, it frees up a ton of space to attack; David Robinson is on a basketball island defending Karl Malone. If something breaks down, defenders from above the foul line, like Tim Duncan, will have to race down to protect the rim.

At the same time, the seeds of the modern pick-and-roll dominant game were being sewn. NBA teams have been pick-and-rolling forever, but the 3-point shot and spacing have supercharged its power. Here’s a famous Malone-Stockton sideline pick-and-roll. Notice how much space is created by stationing two players at the 3-point arc.

This play is so difficult to contain that it forces the weak side defender to completely leave his man in the lower right corner. Just the setup can create an open shot with a skip pass.

Of course, by this point in time, you could completely supinate your hand when dribbling, pause, and continue dribbling some more. As a result, quick guards were nearly impossible to contain when given space to attack. Before 1995, hand-checking was permitted above the free throw line, which could somewhat mitigate this effect, but the flood gates opened in the mid-’90s. The defensive counter to eliminating true hand-checking was to bump and arm bar players when they moved off the ball, which was then eliminated in 2005’s rule change emphasizing “freedom of movement.” All of this laid the foundation for today’s game.

Let’s jump a few more years to an isolation-heavy offense, the 2006 Lakers, and a Kobe Bryant drive:

Look at all that beautiful open court to attack! If help comes from anywhere, Kobe should be able to find an open shooter or cutter. This was the same kind of read-and-react game from the ’90s, only with better spacing principles (increased 3-point shooting) and no illegal defense (abolished in 2002 for defensive 3 seconds). Some teams were even initiating offenses with all five guys around the arc.

This is really difficult to guard. The threat of the shooters, and the space needed to help off of them and then recover strains defenses, who must pick-a-poison whenever the player initiating the pick-and-roll is an offensive weapon (like Steve Nash). The NBA moved toward this approach during the last decade, as 3-point shooting became more prevalent and stretch bigs helped open up the court. This has driven up individual scoring rates, led to a rise in creation and helped the league set an efficiency record in 2017.

Finally, you’ve earned it. Let’s enjoy the first-class experience:

Ladies and gentlemen, that is a high pick-and-roll 10 feet beyond the 3-point line, with three shooters pinning the defense to the arc. This is the game today — lots of space, threats everywhere and minimal congestion on cuts. That wide-open shaded area in the above screenshot is at least 350 square feet, the size of a New York City apartment.

Or, in the old days, the home of most of the defenders on the court.

Offensive Load and Adjusted TOV%

Many years ago when I was stat-tracking games, I first started tinkering with the concept of “Offensive Load,” or how much a player “directly” contributes to an individual possession. The idea was simple: Traditional “usage” looks at how much a player shoots or turns the ball over, but some shooters warp defenses and make plays while others are the beneficiaries of such plays.

Usage has value in its own way, but it doesn’t necessarily capture who drives the most offense. Thanks to optical tracking, analysts are now extending the concept to represent who is “involved” more in the offense, but that information is only available since 2014. Historically, playmakers who create for others are underrepresented by usage, but now that we can measure creation with the box score, we can calculate an offensive load estimate that incorporates passing and creation all the way back to 1978.

Calculating Offensive Load

If we want to measure meaningful offensive actions, we need to define what constitutes a “meaningful” action. Let’s define them as:

  • Shooting
  • Creating
  • Passing
  • Turning it over (while attempting to shoot, create or pass)

Usage covers half of this equation. The question is how to fill in the other half.

Shooting and turnovers are given equal weight in the classic usage formula. Since creating an opportunity is an integral part of many shot attempts, let’s give creation equal weight as well. That leaves “passing” (i.e. assists) as the final component of the formula, but this part is a bit trickier.

It turns out that 38 percent of opportunities created are also assists, so the first step is to remove those from the assist component to avoid double counting. Of the remaining “non-creation” assists, a percentage are from “capitalization” assists — the original or extra pass in an offensive advantage — another chunk are Rondo Assists (a more idle, basic pass where the receiver does most of the work) and the remainder are quality passes that exploit weaknesses in the defense. (These are the riskiest of the bunch.)

Some of these assists are mere happenstance, and some of them require solid decision making. In 2017, 23.9 percent of assists were hockey assists, so as a simple, ad hoc adjustment, one quarter of non-creation assists are removed from the Offensive Load calculation. Thus, the four components for offensive load are true shot attempts, a creation estimate, turnovers and non-creation assists. Using per 100 data, the final formula is:

Offensive Load: (Assists-(0.38*Box Creation))*0.75)+FGA+FTA*0.44+Box Creation+Turnovers

This allows us to compare who has carried the largest load at times for the last 40 seasons. Unsurprisingly, it’s Russell Westbrook’s unique 2017 season, an outlier at 74 percent and one of only three seasons above 60 percent. (Since load is a per 100 rate statistic, “percent” here refers to the percentage of plays that the player was “meaningfully involved” in while on the court.) The median load since 1978 is 27.1 percent, and everything above 32.4 percent falls in the top quartile.

The beauty of the stat is illustrated at the team level, where the partitioning of responsibility is more accurately reflected. Take a player like Steve Nash, who had the third-highest usage rate among Phoenix’s starters in 2005, but led them in Offensive Load by a landslide, which makes sense, because he directed the offense most of the time:

Thus, usage can more accurately be thought of as a team’s “shot distribution,” whereas load is reflective of who is responsible for the heavy lifting. Using Offensive Load, perimeter players with large ball-handling and playmaking responsibilities (like Nash) are no longer underrepresented, as they are in traditional usage. And now that we have load, we can come up with a more accurate estimate of turnover percentage as well.

Adjusted Turnover Percentage (cTOV%)

Traditional turnover rates are based off of usage, which, as previously mentioned, is mostly about scoring attempts. Because of this, playmakers are hammered in turnover percentage. In Phoenix, Nash’s turnover percentages were in the low 20s, whereas a scoring-centric player like Carmelo Anthony had rates between 8.9 and 12.7 percent for the heart of his career. By these accounts, Nash looks like a butterfingery Jeff George while Anthony a trusted gatekeeper of possessions. But this is simply a reward for Anthony throwing the ball at the rim a lot instead of setting up teammates.

Instead, if we use Offensive Load — which incorporates critical non-shooting functions — we can see a more accurate representation of how turnover-prone each player really was. Adjusting turnovers, which I’ll denote as cTOV% (creation-based turnover percentage), is a basic calculation:

cTOV% = Turnovers per 100 / Offensive Load

Now we can compare Anthony and Nash on a level playing field, one that accounts for the turnovers incurred when playmaking and passing:

As you can see, they now look quite similar. And, I suppose, it could still be argued that this adjustment is too small since taking pull-up jumpers is less likely to result in turnovers than any creation endeavors. But we’ll leave that for another time and place.

Either way, Offensive Load gives us a far more accurate representation of responsibilities than traditional usage, and adjusting turnovers based on it a fairer gauge of how turnover prone players really are.


Augmented Plus-Minus: Evaluating Old PM Data

There was a legendary statistician named Harvey Pollack who worked for the Philadelphia 76ers for years. He was decades ahead of his time, and it turns out that Pollack actually kept plus-minus data long before the NBA officially did. While it’s rumored other teams like the Celtics and Lakers tracked plus-minus in the 80s — and oh, what I would do to see that — we have Pollack’s 76er data as far back as 1974. He also started tracking it league-wide in 1994, three years before the publicly available NBA data.

Although Pollack never published any lineup data (which would allow for far deeper analysis than seasonal aggregates), there’s actually a lot we can glean just from having plus-minus data. It allows us to know how well a team played with a player on the court, off the court, and the net “on/off” impact of that player. Even though we can’t access play-by-play data to adjust for teammate and opponent strength, there’s a pretty strong linear relationship between net on/off and RAPM:

As you can see, there are no anomalies in that data (just large errors) which is good for setting up a prediction model. A longtime poster on APBR and realgm named Colts18 was the first person I’ve seen to try and map raw plus-minus to RAPM. And after encountering all of the Pollack data (thanks to the great poster fpliii), I thought I’d give this a whirl. Instead of using a single-year set, I ran a regression from 2005-10 with some hand-selected variables to predict RAPM using plus-minus as a base.

And the results were pretty good (details below). Combining on/off data with some box score data allows us to pretty accurately guesstimate a player’s RAPM. The more pedestrian the predicted RAPM, the more accurate the result; for high-performing players, almost all values are within plus-or-minus three points from their real RAPM (none over 4.0) and for moderately performing players, most are within 2.0. Not bad given the lack of play-by-play data.

We can think of this regression of plus-minus data (which is regressed onto regressed plus-minus data!) as an “augmented” plus-minus. Interestingly, because it’s using a blend of box score data and plus-minus data, the model is more stable than standard year-to-year RAPM (and certainly more stable than non-prior RAPM).

This means that for players with huge shifts, it will likely underestimate them in one year and then overestimate them in the following season. And this isn’t necessarily a bad thing, because while the metric will not give us the “true” RAPM value in such cases, it’s less subject to vagaries that might be caused by factors outside of the player’s control. Food for thought.

Of the 1391 1000-minute players I used from 2005-10, the best augmented season (AuPM) belonged to LeBron‘s 2009 campaign, at +8.9. No one besides LeBron was over +7.0 and only 1.3 percent of seasons were above 5.0. In other words, a typical top-5 season is somewhere between +4.5 and +5.0 using this metric.

Anyway, what does the augmented plus-minus tell us from Pollack’s data? I’ve compiled all the results in a google doc alongside known RAPM to give a historical perspective of this kind of data from 1994-2013 (and back to 1977 for a select group of 76ers). Check it out for yourself — for my money, David Robinson looks like the king of plus-minus in the 90s, Karl Malone, Scottie Pippen and Mookie Blaylock look great, and Julius Erving takes a huge hit. I’ve also created an interactive visual with some notable players — it’s easy to compare players if you deselect everyone.

Finally, this kind of stuff is only possible because of the great work of statisticians and historians that have paved the way, and I find myself perpetually in awe of their work. In this case, using Pollack’s data like this is only possible because of pioneers like Wayne Winston, Steve Ilardi, Joe Sill and Daniel Myers and Pollack himself.

Regression Details

Data set used was 2005-2010, using PI RAPM from Jeremias Englemann and plus-minus from Variables were hand-selected. I played with the relationship between a player’s on/off and his teammates, and while many made minor improvements, the largest came from simply summing the difference of the 1000 MP teammates ahead of a player. For instance, take the following group of teammates:

Player A = 2.0

Player B = 5.0

Player C = 6.0

Player A’s “summed above” value would be the difference between himself and B plus the difference between himself and C, or 7.0. For the box score, there’s already a composite (regression-based) metric that maps to RAPM, which is Box Plus-Minus (BPM). Adding it significantly improved accuracy. Finally, a team’s actual “on” value was important. The coefficients look like this:

AuPM = -0.0185 + Net * 0.2064 + 0.1113 * On  + 0.2343 * BPM – 0.0209 * SumAbove – 0.0017*(Net * SumAbove)

R-Squared was 0.76. Mean Absolute Error (MAE) was 0.92. Max error was 4.5 with a standard deviation of 0.71. Errors were larger among larger values:

  • For players +3.5 or better, 40 percent of predicted RAPM’s were within 1.0 of actual RAPM, 74 percent were within 2.0 and 96 percent were within 3.0.
  • For players between +1.5 and +3.5, 57 percent were within 1.0 points of actual RAPM, 89 percent were within 2.0 and 98 percent within 3.0.

Nylon Calculus Podcast

Just a quick status post today — I had the pleasure of sitting down with Kevin Ferrigan on the Nothing But Nylon podcast last week. For the uninitiated, the NBN cast has featured some of the best non-mainstream writers and analysts in basketball (Andrew Johnson, Ian Levy, Krishna Narsu, Andre Snellings and Nick Restifo).

We discussed Thinking Basketball, Box Creation, a general state of fandom-ness and the Kyrie Irving trade. The podcast can be heard here.

How Valuable is Creating Open Shots for Teammates?

Since we now have a good way to measure creation historically, I wanted to explore the relationship between creating shots for teammates and performance. Theoretically, we’d expect there to be some positive relationship between creation and the scoreboard — the more a team can breakdown a defense, the more higher-efficiency looks they’ll have. Using Box Creation, we can test this hypothesis.

Sure enough, there is a moderately strong relationship between a team’s creation rate and its offensive rating.* In 2006, the league started moving toward its current pace and space, 3-point centric game. Since then, the correlation between Box Creation and a team’s offensive rating was a healthy 0.66. (It was 0.56 since 1980.) For some perspective, turnovers have about a 0.4 correlation with offensive rating and effective field goal percentage has about a 0.8 correlation.

Remember, a team’s creation rate is not an estimate of the percentage of open shots a team takes — teams will end up with open shots when the defense breaks down, in transition or even just from setting a bunch of screens and forcing the defense to concede a deep jumper. Instead, Box Creation is a pace-adjusted estimation of how often a team created an opportunity (per 100 possessions) that led to an open shot. So why isn’t the relationship super strong?

First, creation is about drawing defensive attention and moving defenders as a reaction to a threat. But the ball still needs to find an open shot for this to be counted as an opportunity created, and that doesn’t always happen. Poor spacing or a slow pass (or ball stoppers!) can terminate the offense’s advantage, failing to capitalize on an opening that the creator provided. In this sense, passing is a separate but related component. While it’s the next step in creation, good passing, in general, is about capitalizing on or exploiting an advantage that already exists. (That advantage can come from creation or some defensive error.) So creation rates are not entirely independent of teammate quality.

Second, teams that excel in isolation, at offensive rebounding or by screening for long shots do not rely as strongly on their creators. This speaks to one of the wonderful parts of basketball; there are many ways to skin the cat! Because of that, we wouldn’t expect the relationship between shots created and offensive performance to be that strong. However, as you can glean from the plot above, the majority of historically great offenses create a lot of shots for each other. Fourteen of the top 15 creating teams since 1978 have finished with offensive ratings at least five points better than league average.

There’s a similar, moderate relationship for individuals between Box Creation and Offensive Adjusted Plus-Minus (ORAPM). Using Jeremias Engelmann’s 2006-2011 single-year prior-informed set, the correlation between creation and ORAPM is 0.52 for individual players. Again, this is expected — being a good creator helps, but it’s not the only way to defeat defenses.

Still, the moderately strong relationship between creation and performance reflects the importance of having centerpieces on the roster who can generate easier shots for players who can’t create for themselves.

*Because of the way basketball-reference data is organized, note that this method underestimates teams that made trades. A team swapping two strong creators will be severely underestimated. 

Are Older Players Getting Better? Aging throughout NBA History

Tim Duncan retired last year at 40 years old after 19 seasons. Kevin Garnett was 40 and played 21 seasons. Kobe Bryant was “only” 37, but bowed out after 20 years in the League. Are these oddities, or are players today playing longer and having more success in their twilight years than ever before? Is everyone eating Tom Brady’s avocado ice cream?

The Quantity of Older NBA Players is Increasing

*For the rest of this post, all ages referenced will be determined by a player’s age on February 1 of a given season.

In 1955, there wasn’t a single NBA player who logged 1000 minutes over the age of 35. Only three percent of 1000-minute players — a good proxy for rotational players — were over 33. Fast forward to the year 2000 and 17 percent of 1000-minute players were at least 33, a testament to improvements in sports nutrition and health. Below are all of the elder statesmen — 33-year old players and older — as a percentage of players who logged at least 1000 minutes in a season since the shot clock (1955):

There’s a steady upward trend in all age groups (represented by the thick trend lines), with the exception of the 39 and 40-year olds. Otherwise, beginning in the late ’60s, more players were able to contribute into their mid 30’s and by the early ’70s, the occasional 35 or 36-year old was still kicking around. By the end of the ’80s, seniority rapidly crept in and a larger portion of rotational players were between 33 and 36. Those players spearheaded a group of 37 and 38 year olds (the gray line) that have made up a small percentage of contributors since the late 1990s.

In 1955, about three percent of the 1000 minute players in the league were at least 33 years old on Feb. 1. Today, it’s the 36 year-olds that are hovering at about three percent. In other words, 36 is the new 33.

So there’s been a clear uptick in the quantity of contributing older players from the last century. But what about quality? Are players maintaining all-star level performance at older and older ages?

The Quality of Older NBA Players is Increasing Too

In order to evaluate this, we need a metric to estimate quality players. Let’s use Win Shares, which allows us to go back to the shot clock, and let’s set the mark at a 7 Win Share season. While this is a bit crude, it gives us a good approximation of all-star (or near all-star) level performance; in the 3-point era, 81 percent of all-stars (760 of 935) have had at least 7 Win Shares. In 2017, 40 players finished with at least 7 Win Shares.

In the early days, older players were never good players. Between 1955 and 1968, there was only a single 7 Win Share season from someone at least 33 years old (Bill Sharman, 1960). Then, the aging legends of the ’60s left their mark with monster seasons: Bill Russell (at 34) posted 11 Win Shares in 1969 while leading Boston to its 11th championship, Jerry West (33) finished with 13 en route to the 1972 title and Wilt Chamberlain (36) produced a whopping 18 in his final season in 1973.

12 years later, Kareem Abdul-Jabbar raised the bar, posting an 11 Win Share season in 1985 at 38. Tracy McGrady just turned 38.

Jump another decade-and-a-half and John Stockton set the standard again, hitting double-digit Win Shares at 39, in 2002. (Karl Malone did it the year after at 39 too). While this latest crop of aging players hasn’t quite had the same box-score success at the end of their careers, Duncan, Garnett, Bryant, Dirk Nowitzki, Ray Allen, Paul Pierce, Jason Kidd and Steve Nash have all had all-star level seasons at advanced ages.

Let’s look at all of the 7 Win Share contributors to approximate all-star or near all-star quality players in their mid to late 30’s:

All of these age groups still show positive trends, but the story is a little fuzzier since the samples are so small. There were more 33 year-olds logging these kinds of seasons in the late ’60s and early ’70s than there have been in the last few years. (The same trends hold if we use a rate state like WS/48.) While there were clear longevity gains from the original players of the ’40s and ’50s, the prevalence of talented graybeards hasn’t budged too much since the ’70s.

If we plot a linear trend line starting in 1970 running to today, it’s still positive in every age category. However, the slope of every line is gradual, closer to zero. Not one 33 year-old notched 7 Win Shares this year, whereas in 2010 there were eight. The 35 and 36-year olds have progressed slightly, although the graph looks cyclical. Perhaps were entering another upward trend of older players who produce big seasons.

Oh, and don’t look now, but LeBron turns 33 this year.

Note: Players come into the game at a younger age today, and this might be contributing to some of the regression seen in older players since peaking around the early 2000s. In other words, today’s 35-year olds logged more minutes than 35-year olds from the ’70s. Of the 33 players in the NBA’s 40,000 minute club, nearly forty percent entered the league recently after 1995.