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 basketball-reference.com. 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.

The Lonestar Problem: The Need for Multiple Offensive Stars

In Thinking Basketball, I discuss a bias called “The Lonestar Illusion,” when stars receive extra credit because they have no other notable teammates. This often occurs when a high-scorer is surrounded by defensively inclined teammates, whose value is lost in the traditional box score. But what happens when teams really only have one good offensive player?

Think of the legendary clubs of the last few decades: Jordan and Pippen. Shaq and Kobe. Curry, Durant and Thompson. It’s rare for these juggernauts to leave the offensive heavy lifting to only one player. But how rare? Are there any elite teams with only one? What happens when teams have two or three good offensive players?

To answer these questions, we first have to define “good” offensive players, which can be tricky over a large data set. For simplicity, I’ve chosen an Offensive Box Plus-Minus (OBPM) of at least 2.0, or roughly a top-40 offensive player in a given season (players must also qualify for the MPG leaderboard). For this question, it passes the smell test well because it allows passers/creators to have their due, takes into account team context and doesn’t overly credit inefficient scorers.

Using that definition, we can look at the makeup of good teams based on how many offensive stars they have. (The “3-star” offenses in this post have “at least” three players with an OBPM of 2.0.) Here’s what the pie charts — pie charts! — look like:

So single-star offenses account for about as many 4 and 6-SRS teams as three-star offenses. But, when we reach 8-SRS teams (63-win pace) — where the odds of winning a championship start to rapidly increase — single-star offenses are rare. About one in ten of these teams will only have one “good” offensive player.

It might seem like lone star offenses are decent, but their prevalence obfuscates how truly problematic they are. 42 percent of teams from 1999-2017 were single-star offenses, while just ten percent had at least three “good” offensive players.  If we view the distributions based on number of stars, the shortcomings of single-star teams come into focus:

Yes, about two thirds of three-star offenses posted SRS’s of four or better (53-win pace). But only twelve percent of single-star offenses reached that mark.

This is a lone star problem.

Only one team in the last 19 seasons has crossed the 8-SRS barrier with a single “good” offensive player, the 2016 Spurs. (They had two “good” rotational players eliminated due to the minutes restriction.) So while a team with at least two good offensive weapons was about twice as likely to post a 4-SRS when compared to the single-star units, they were five times more likely to eclipse the 8-SRS mark.

Having at least three good offense guys is even more multiplicative: Such teams were five times more likely to hit the 4 or 6-SRS mark, and twenty two times more likely to reach an SRS of 8. Three-star teams averaged 5.8 playoffs wins, whereas one-star teams averaged only 2.8.

While it’s plainly obvious that it’s better to have more good offensive weapons, what’s surprising is how disadvantageous having only one good offensive piece is. It’s quite difficult to build a contender with only one offensive star, and near impossible to construct an elite team that way.

Supporting Casts are More Important Than Stars

A while back I used 2002-2012 PI RAPM data to quantify differences in the “supporting casts” that surround a star player. The results were largely what we’d expect: That the players who surround a star (including other all-stars themselves) are hugely important in determining a team’s performance.

In the chart below I’ve graphed a team’s best player and his support based on how far they advanced in a season. I’ve also included min/max ranges for the supporting casts based on the data:

The data reflects common sense. As teams grow better, the players surrounding the star grow better. Improvements to the star himself are correlated with more team success, but the supporting players on a team are more important to the team’s success than the star player. This is expected; basketball is not a one-on-one sport. Still, it’s nice to be able to quantify this with a decade of non-box score data.

The importance of supporting casts can be seen most clearly in the correlations. The correlation between the entire team’s individual RAPM values and its Margin of Victory (MOV) is nearly perfect (0.95). The correlation between the “supporting cast’s” RAPM and MOV is 0.91, but the correlation with a best player’s RAPM is only 0.68. So if we removed the star player from every team in the league, we could still reasonably predict who the best teams were based on the performance of the other players. We could not make this prediction by only looking at the stars themselves.

Graphically, we can see the relative lack of relationship between the top player and team MOV compared to the strong relationship between the supporting players and team MOV:

Finally, note the vast disparity in supporting cast among non-playoff teams. The floor for a playoff team and the floor for a non-playoff team are separated by 10 points! Literally, off the chart.


  • “Best Player” is defined by the player with best minute-weighted RAPM for a team for a season. For example, if Player A has +5 RAPM and Player B a +4 RAPM but Player B plays 100% of the minutes and Player A 50% of the team minutes, Player B is credited with a “4” lift to the team and is thus considered their best player. (B would have a +2.5 lift).
  • “Supporting Cast” is defined by the minute-weighted totals of all other players on the team, summed together.
  • For traded players, the total season RAPM value was used
  • For minute-weighted totals, only players with 300 MP were considered

Specific Players

I’m always asked for notable players across a period, so this is how they shook out based on this metric. First players with at least 3 seasons as the “top player.” The second table has all players.

Dirk Nowitzki1.0-
Kevin Garnett-0.4-
Tim Duncan2.
LeBron James0.1-
Luol Deng-0.3-4.54.3-1.1-1.61.5-4.5-
Steve Nash-0.1-
Baron Davis-1.7-3.00.9-0.50.9-3.0-2.7-2.6-2.0
Dwight Howard-0.1-4.53.7-4.5-
Elton Brand-2.2-4.8-0.3-3.8-0.3-1.1-2.2-4.8-0.9
Jason Kidd0.3-
Kobe Bryant-0.1-3.74.5-2.7-1.7-
Brad Miller-3.2-
Dwyane Wade-4.5-9.6-0.9-0.9-3.6-9.6-4.0-4.5
LaMarcus Aldridge-0.4-2.92.6-
Rasheed Wallace0.1-1.42.6-0.40.9-1.42.6-1.1
Andrei Kirilenko-1.1-6.42.8-1.9-
Chris Bosh-2.6-3.8-1.6-1.8-1.6-3.8-3.2
Chris Paul-2.5-3.6-0.5-2.7-3.3-3.6-0.5
Gerald Wallace-3.9-6.6-0.3-6.2-2.4-0.3-6.6
Josh Smith-2.7-7.21.2-7.21.2-2.9-1.8
Paul Pierce-3.0-5.4-1.5-1.7-1.5-3.6-5.4
Ray Allen-1.8-6.02.6-5.01.1-6.02.6
Shaquille O'Neal1.4-
Shawn Marion-0.9-3.11.8-3.10.5-3.01.8
Steve Francis-2.3-4.7-1.0-4.7-1.2-1.0-2.4
Allen Iverson-1.7-3.9-0.4-0.9-3.9-0.4
Andrew Bogut-2.7-3.4-2.2-2.2-2.3-3.4
Antawn Jamison-4.4-7.2-1.3-1.3-4.6-7.2
Ben Wallace-2.0-6.43.0-2.43.0-6.4
Bobby Simmons-5.4-9.2-3.0-4.1-3.0-9.2
Brendan Haywood-4.9-6.8-1.7-6.8-1.7-6.2
Carlos Boozer-0.4-1.72.3-1.7-1.62.3
Chauncey Billups3.
Danny Granger-2.3-5.4-0.1-1.5-5.4-0.1
Jermaine O'Neal-1.2-4.01.7-1.21.7-4.0
Kevin Durant1.
Marcus Camby-5.9-9.6-0.9-0.9-9.6-7.2
Metta World Peace-2.9-6.41.1-6.41.1-3.5
Nene Hilario0.5-1.51.9-
Pau Gasol-1.1-8.14.1-
Rashard Lewis-2.8-8.63.7-3.53.7-8.6
Shane Battier-0.2-
Theo Ratliff-6.6-9.7-4.1-4.1-6.0-9.7
Vince Carter-7.2-7.2-7.1-7.2-7.2-7.1
Al Harrington-2.5-2.5-2.5-2.5
Allen Iverson-1.7-3.9-0.4-0.9-3.9-0.4
Alvin Williams0.
Amir Johnson-6.4-8.5-4.3-8.5-4.3
Anderson Varejao-7-7-7-7
Andre Iguodala-2.3-2.3-2.3-2.3
Andre Miller-0.4-
Andrei Kirilenko-1.1-6.42.8-1.9-
Andrew Bogut-2.7-3.4-2.2-2.2-2.3-3.4
Andrew DeClercq-5.9-8.5-3.2-3.2-8.5
Antawn Jamison-4.4-7.2-1.3-1.3-4.6-7.2
Anthony Morrow-8.6-8.6-8.6-8.6
Anthony Parker-11.1-11.1-11.1-11.1
Anthony Tolliver-8.2-8.2-8.2-8.2
Antoine Walker0.
Baron Davis-1.7-30.9-0.50.9-3-2.7-2.6-2
Ben Wallace-2-6.43-2.43-6.4
Beno Udrih-2.4-2.4-2.4-2.4
Bob Sura-4-4-4-4
Bobby Simmons-5.4-9.2-3-4.1-3-9.2
Boris Diaw-13.9-13.9-13.9-13.9
Brad Miller-3.2-8.300-1.2-2.3-4.2-8.3
Brendan Haywood-4.9-6.8-1.7-6.8-1.7-6.2
Brevin Knight-5-5-5-5
Brian Skinner-2.1-2.1-2.1-2.1
C.J. Watson-4.6-4.6-4.6-4.6
Carlos Boozer-0.4-1.72.3-1.7-1.62.3
Charlie Ward-5.8-5.8-5.8-5.8
Chauncey Billups32.
Chris Andersen-4.3-4.3-4.3-4.3
Chris Bosh-2.6-3.8-1.6-1.8-1.6-3.8-3.2
Chris Paul-2.5-3.6-0.5-2.7-3.3-3.6-0.5
Chris Wilcox-9.4-9.4-9.4-9.4
Corey Maggette-8.6-8.6-8.6-8.6
Corliss Williamson-1.9-1.9-1.9-1.9
Danilo Gallinari-1.1-3.61.4-3.61.4
Danny Granger-2.3-5.4-0.1-1.5-5.4-0.1
Darvin Ham-3-3-3-3
David Lee-3.1-3.1-3.1-3.1
DerMarr Johnson-3.5-3.5-3.5-3.5
Deron Williams-1.5-
Derrick Coleman4.
Desmond Mason-2.2-2.8-1.7-2.8-1.7
Devin Harris-3.6-3.6-3.6-3.6
Dirk Nowitzki1-
Doug Christie31.
Dwight Howard-0.1-4.53.7-4.5-
Dwyane Wade-4.5-9.6-0.9-0.9-3.6-9.6-4-4.5
Earl Boykins-2.2-2.2-2.2-2.2
Earl Watson0.
Eddie Jones-3.4-4.8-2-4.8-2
Eddie Robinson-6.8-6.8-6.8-6.8
Elton Brand-2.2-4.8-0.3-3.8-0.3-1.1-2.2-4.8-0.9
Eric Gordon-5-5-5-5
Eric Snow-0.6-
Etan Thomas-4.9-4.9-4.9-4.9
Gerald Wallace-3.9-6.6-0.3-6.2-2.4-0.3-6.6
Gilbert Arenas-3.9-3.9-3.9-3.9
Greg Ostertag2.
Horace Grant-4-4-4-4
Ime Udoka-5.5-5.5-5.5-5.5
Jackie Butler-7.9-7.9-7.9-7.9
Jamal Crawford-5-5-5-5
Jason Collins-3.3-3.3-3.3-3.3
Jason Kidd0.3-
Jason Richardson-4.9-6-3.9-3.9-6
Jason Smith-4.1-4.1-4.1-4.1
Jason Thompson-5.8-6-5.6-5.6-6
Jeff Foster-1.9-2.4-1.5-2.4-1.5
Jermaine O'Neal-1.2-41.7-1.21.7-4
Jerome James-1-1-1-1
Jim Jackson-1.9-1.9-1.9-1.9
Joe Johnson-3-4.7-1.2-4.7-1.2
Joe Smith-1-1-1-1
John Stockton-0.7-0.7-0.7-0.7
Josh Smith-2.7-7.21.2-7.21.2-2.9-1.8
Kevin Durant1.
Kevin Garnett-0.4-
Kevin Love-4.4-4.4-4.4-4.4
Kirk Hinrich-1.5-1.5-1.5-1.5
Kobe Bryant-0.1-3.74.5-2.7-1.7-
Kurt Thomas-4.2-4.2-4.2-4.2
Kyle Lowry-0.6-0.9-0.2-0.9-0.2
LaMarcus Aldridge-0.4-2.92.6-
Landry Fields0.
LeBron James0.1-430.9-1.8-1.7-42.6-0.432.4
Luol Deng-0.3-4.54.3-1.1-1.61.5-4.5-
Manu Ginobili1.
Marc Gasol-3.1-3.1-3.1-3.1
Marcus Camby-5.9-9.6-0.9-0.9-9.6-7.2
Marko Jaric-6.3-6.3-6.3-6.3
Marvin Williams-5.8-5.8-5.8-5.8
Metta World Peace-2.9-6.41.1-6.41.1-3.5
Michael Jordan0.
Michael Redd-6.4-7.7-5.1-5.1-7.7
Mike Conley-0.1-0.40.3-0.40.3
Mike Dunleavy-4.3-5.4-3.3-5.4-3.3
Mike James-5.1-5.6-4.6-4.6-5.6
Nate Robinson-7.4-7.4-7.4-7.4
Nene Hilario0.5-1.51.9-
Nick Collison-6.6-6.6-6.6-6.6
Nick Van Exel-4-4-4-4
Othella Harrington-5.2-5.2-5.2-5.2
Pau Gasol-1.1-8.14.1-
Paul Millsap-4.4-4.9-3.9-4.9-3.9
Paul Pierce-3-5.4-1.5-1.7-1.5-3.6-5.4
Quentin Richardson-3.3-3.3-3.3-3.3
Rafer Alston-0.3-3.52.9-3.52.9
Ramon Sessions-9.5-9.5-9.5-9.5
Rashad McCants-8.8-8.8-8.8-8.8
Rashard Lewis-2.8-8.63.7-3.53.7-8.6
Rasheed Wallace0.1-1.42.6-0.40.9-1.42.6-1.1
Ray Allen-1.8-62.6-51.1-62.6
Raymond Felton-3.1-3.1-3.1-3.1
Richard Hamilton3.
Rodney Stuckey-6.6-7.7-5.5-5.5-7.7
Ronny Turiaf-3.7-3.7-3.7-3.7
Ruben Patterson-3.4-3.4-3.4-3.4
Rudy Gay-5.1-5.1-5.1-5.1
Ryan Bowen-4.4-4.4-4.4-4.4
Samuel Dalembert-4.7-4.7-4.7-4.7
Sebastian Telfair-5.3-5.3-5.3-5.3
Shane Battier-0.2-
Shaquille O'Neal1.4-
Shawn Marion-0.9-3.11.8-3.10.5-31.8
Speedy Claxton-3.8-5.4-2.1-2.1-5.4
Stephen Curry-4.2-4.4-4-4-4.4
Stephon Marbury-2.5-2.5-2.5-2.5
Steve Francis-2.3-4.7-1-4.7-1.2-1-2.4
Steve Nash-0.1-
Stromile Swift-2.1-2.8-1.5-1.5-2.8
Thaddeus Young0.3-1.92.6-1.92.6
Theo Ratliff-6.6-9.7-4.1-4.1-6-9.7
Tim Duncan2.
Tracy McGrady2.213.413.4
Trevor Booker-7.7-7.7-7.7-7.7
Tyson Chandler0.2-2.52.9-2.52.9
Vince Carter-7.2-7.2-7.1-7.2-7.2-7.1
Vladimir Radmanovic0.
Wilson Chandler-0.8-0.8-0.8-0.8
Yao Ming-1.2-4.31.9-4.31.9
Zach Randolph-6-6-6-6
Zaza Pachulia-5.1-5.1-5.1-5.1
Zydrunas Ilgauskas-7.6-7.6-7.6-7.6

Star Player Effects on Teammate Efficiency

I had some fun playing with nbawowy.com last night. I promise, it’s not as dirty as it sounds.

Using available data from the last three seasons, I set out to answer a simple question: How does teammate efficiency change when star players are on or off the court? In other words, what impact does the presence of a player have on his teammate’s shooting?

There are a number of players we could do this for, but I wanted to visualize five in particular, four of whom are ball-dominant creators (James, Paul, Harden and Westbrook) and Steph Curry, who is renowned for his court-warping gravity off the ball. Here were the results using players who played at least 1,000 minutes with the player in question, with all five player graphs stacked side-by-side of comparison:


Surprise! LeBron had the largest effect of the group (expected based on more holistic analysis like RAPM. Eight of his ten teammates improved by at least 0.05 points per scoring attempt (or at least 2.5% in True Shooting efficiency). Of the five players who improved by at least 0.15 points per attempt, three played with LeBron. Of course, all the normal caveats apply here as there may be cofounds within the lineups and these numbers aren’t opponent-adjusted. Still, it’s a nice snapshot to have.

Steph Curry had the highest floor (no regular teammate below 1.12) and the highest ceiling (1.34) — no surprise there, as the Warriors have a strong candidacy for greatest offense in NBA history. He also had a hugely positive impact on Kevin Durant this year, who scored at 1.24 per attempt this year without Curry, right in the ballpark of his previous two seasons without Russell Westbrook. (Note that Durant was less efficient alongside Westbrook.) Among star teammates, only Kevin Love (with LeBron) came close to the boost Durant and Klay Thompson experienced when on the floor with Curry.

Finally, I’ve included the individual graphs below for all five players in order to see each specific teammate.