II. Historical Impact: Introducing WOWYR – top players of the 50’s, 60’s & 70’s

So you want to compare the all-time greats but have limited historical data? Not sure what to make of players before the Databall era, when plus-minus wasn’t available and, depending on how far back you go, the box score wasn’t even complete? Don’t worry, you’ve come to the right place.

In the first post in this series, we looked at WOWY data – a simple concept that isolates a player in order to gauge his value by using game-by-game results. But we were left with a fundamental problem — how do we estimate impact for players who weren’t injured or traded? It’s clear Jerry West provided significant lift, but what about someone like Bill Russell? How do we measure his non-box impact?

The answer? Regression, the same statistical method used on play-by-play data in the last few years to create irreplaceable impact metrics like RAPM (Regularized Adjusted Plus-Minus). Since comprehensive play-by-play does not exist before the late ’90’s, WOWYR instead regresses WOWY data, or game-by-game plus-minus data. (It’s better than WOWY, so it’s “wowier,” and stands for “With or Without You Regressed.”)

Evidence Beyond Injuries

WOWY score is almost always predicated on injuries, isolating lineups with-and-without players. But there’s far more evidence in the data beyond that.

First, there is indirect evidence for a player when his teammates leave the lineup. Let’s say we wanted to know how much Scottie Pippen contributed to the Bulls +9 point-differential in the early ’90’s. In 1994, when Michael Jordan left the Bulls, we could infer something about Pippen based on the change caused by Jordan’s absence. How?

If Jordan left and the team remained a +9 team, then it would be fairly safe to infer that Jordan was not the reason the Bulls were +9…which tells us that key remaining players on the team, like Pippen and Horace Grant, were the ones responsible for the large point differential.

WOWY Regression Graphic

Conversely, if Jordan left the Bulls and they unraveled into a -5 team, not only does that say amazing things about MJ but it would mean that the players left behind, like Pippen and Grant, weren’t integral to that +9 differential. Thus, we can make inferences about other players, even when they don’t leave the game-by-game lineup. So while Bill Russell didn’t miss as much time as Jerry West, there’s a bevy of evidence about Russell left by his teammates and all of the time that they miss over the years.

Similarly, when two players leave the lineup, it’s not a pure WOWY instance. But again, we can gain valuable insight here too: If the combination of two players leaving caused a team to fall apart, then we can infer that (a) one of those players was making the team excel, or (b) both of them were. Even though it’s unclear who caused it, it’s yet another piece of evidence that can be incorporated with direct and indirect game-by-game information about a player.

Indeed, regression parses all of these scenarios and provides an answer to how much different players impact the game. The result is a single, points-per-game value that estimates a player’s impact over multiple years.

Introducing WOWYR

Much like the first generation of adjusted plus-minus stats used Ordinary Least Squares (OLS) regression, so does version 1.0 of WOWYR. Follow-up versions will refine the method, but I wanted to start with OLS both for simplicity and so we see standard errors for each player; a smaller standard error indicates less variability in the player’s estimate.

Below are the WOWYR values for every player from 1954-1983 who played at least 450 games. All data is from basketball-reference, however their data changes slightly after 1983, so I’ll be incorporating 1984-present in a future post.


Keep in mind that the only data fed into this statistical model is (a) who played in a game and (b) what the score of that game was. Yet, more than half of the MVP’s claimed during the time period fall in the top-11. A search of similar criteria for the time period produces a list of similar All-NBAers. Pretty cool, eh?

Despite filtering for players with a good five seasons or more of playing time, there are still instances where multicollinearity and uncertain rear their ugly heads. Fortunately, some of these ambiguities — for instance, the early 80’s 76ers, Bucks, Spurs and Sonics — will be ironed out when more seasons are added. Other players, like Walt Frazier, just have a fuzzier signal than most.

Detailed methodology for OLS WOWYR can be found below. I’ll go into more detail in the next post in this series when WOWYR is improved.

Method Summary


  • ~25+ mpg to qualify for a lineup (aka ignore lower-minute players)
  • Exceptions: if 5th-highest minute player is below 25 mpg, will often take that player and any other in the same mpg range (usually 23-24 mpg) to complete the “lineup.”

Point Differential

  • Take the average, unadjusted strength of schedule (based on the full 82-game SRS value of a team)
  • Add a home-court advantage factor (3 points)
  • All postseason data is included

The Regression

  • Players who fail to qualify for more than 82 games worth of lineups are treated as a “replacement rotational” player
  • “Prime” and “non-prime” seasons are treated as separate players — more on this in the next post.
  • Technically, this is Weighted Least Squares (WLS), where weights are determined by games played (using the standard square-inverse of the variance).
  • Regression is performed on all lineups and their point differentials.


From the Vault: Brady vs. Manning, Superclutch

On the cusp of football season, a look back at a comparison of two of the all-time greats. This was the second post in a two-part series,  originally published on January 25, 2012. 

In the last post, we improved on the “game-winning drive” metric by looking at 4th quarter drives when the game was tied or within one score. That post examined drives starting between the 1:00 mark and the 15:00 mark of the 4th (and OT). Let’s define “Super Clutch” drives as those starting in the last five minutes. (Again, excluding desperation drives starting under a minute.)

Below are the Super Clutch results for Peyton Manning and Tom Brady. Included are the other MVP-level QB’s of this era, Drew Brees and Aaron Rodgers:

Super Clutch Years Drive Pts/Dr TD% Score% Avg. Yds Avg. Start Avg. Time TOL % at Home
Tom Brady 03-07, 10-11 19 3.95 47.4% 68.4% 47.6 33.0 02:29 1.68 26.3%
Peyton Manning 03-10 31 3.52 38.7% 64.5% 44.6 32.5 02:31 1.84 45.1%
Drew Brees 06-11 17 2.94 35.3% 47.1% 47.5 26.1 02:55 1.29 41.2%
Aaron Rodgers 08-11 16 1.63 18.8% 25.0% 28.3 27.8 02:57 1.94 25.0%

NB: If New Orlean’s placekicker had converted all of his field goals, Brees would boast a 64.7% score rate and 3.47 points per drive.

So Brady has been better — otherworldly, really — in the final moments of games. This, despite playing mostly on the road. Manning continues to look amazing as well, and so does Drew BreesAaron Rodgers has a long way to go in this regard.

And for those in the mood for some small-sampled data, here are the Big Three QB’s performances on regular clutch drives in the postseason:

Clutch Playoffs Years Pos Pts/Dr TD% Score% Avg. Yds Avg. Start Avg. Time TOL % at Home
Tom Brady 03-07, 10-11 9 2.89 22.2% 66.7% 37.3 33.3 07:06 2.78 11.1%
Peyton Manning 03-10 11 2.09 18.2% 45.6% 33.2 25.3 05:23 2.73 81.8%
Drew Brees 06-11 7 4.14 42.9% 71.4% 36.0 36.1 10:13 2.00 28.6%

And alas we see where Manning earned his (unjustified) reputation as coming up short in the postseason. It’s unjustified because, as anyone who has read this blog knows, the sample size is too small to conclude anything, and these figures don’t control for defensive strength. Brees has been magnificent, scoring on five of seven playoff clutch drives, and Brady has failed on only three postseason drives: early in the 4th against the Colts (2006), the Giants (2007) and in the final minute against Indianapolis again in the 2006 AFC championship.

One final note: After examining a number of clutch performances in basketball, it’s particularly interesting to observe that these quarterbacks seem to perform so well in clutch (and super clutch) situations. In basketball, shooting and scoring typically decline later in games. Yet, at least with Manning and Brady, they’ve performed as well (or better) than the best offenses in NFL history in these situations.

I. Historical Impact: WOWY Score Update

How valuable is a player? How many points per game is he worth? In sports, these are Holy Grail questions that play-by-play data has helped estimate. But how do we compare Magic and Bird when they played before play-by-play was available? How do we compare Russell and Chamberlain when they don’t even have a complete box score?

A few years ago, I circulated a method that takes a stab at these questions by using injuries, trades and free agent signings to compare teams with and without a given player. The result is an historical, (mostly) apples-to-apples comparison of value between players, called WOWY. (There’s a full primer on WOWY attached to the end of this post.) The lineup data — not from play-by-play, but from game-by-game — gives us the same insight into players for the last 60 years.

Take Bill Walton’s legendary rise and fall in Portland. All other things being equal, how did the team fare with and without him in the lineup? It turns out, Walton’s missed time from those years produces the best WOWY score in NBA history. (See the third tab, titled “Top WOWY Runs.”) In other words, Walton had the biggest observable impact of qualifying players (i.e. players who were injured or traded) on any team ever, his presence improving the Blazers by more than eight points per game.

In researching Thinking BasketballI examined hundreds of these WOWY runs. For those familiar with it, I also cleaned up the data, adding controls and incorporating postseason games for over 1,500 instances since the inception of the shot clock in 1954-55. And if we combine those instances for players — only focusing on what I’ve liberally called their “prime” — we can see who left a large impact when in and out of the lineup for an entire career.

Below are the top 10 prime WOWY scores of all-time, with a minimum sample of 20 games missed:

Top 10 WOWY Scores All Time

Indeed, the best combined numbers are from players often found in all-time top-10 or top-20 lists. You can see all the results in this spreadsheet of over 200 qualifying players.

The two outliers — Robertson and West — make most top-20 or top-15 lists. (ESPN had them at 11 and 13, respectively, in their recent top-100 rankings.) While Oscar is largely revered, most people don’t know that his impact was quantifiably enormous, dragging an otherwise inept team in Cincinnati to respectability, then later catapulting Kareem’s Bucks into the upper stratosphere.

Meanwhile, when West was healthy, many of his teams were elite, only overshadowed in history by the dynastic Celtics. Amazingly, West’s teams performed better with him in all 12 lineups that he missed time. Oscar did the same for 11 consecutive lineups. (Note that about one third of WOWY scores on that list are negative.)

538’s Benjamin Morris ran a limited version of this years ago to argue for the greatness of Dennis Rodman, although he only used a minimum of 15-game injury blocks. Rodman’s good, but he clocks in at 16th here. And yes, Kobe (26th) beats Jordan (32nd), but MJ’s number comes largely from 1986 when he broke his foot and missed most of the season. (His 22 missed games from 92, 93 and 95 respectively would elevate him to 25th on the list.)

While this is all valuable data, it’s still limited. It doesn’t help answer our original question for players who don’t miss much time, like Chamberlain and Russell (and even Jordan). We’ll address that issue in Part II of this series on historical impact. For now, I’ll leave you with a WOWY primer below…

What’s WOWY?

It stands for “With or Without You,” and compares the performance of a roster with a given player and without that given player over the course of an entire game. It is an attempt to isolate a player’s impact on that given roster.

I almost always control for players who played at least 25 minutes per game (noted in the control column of this spreadsheet). This typically yields five to seven-man rotations for most teams, depending on how they distribute the minutes. There are some instances where I’ll control for the entire starting 5, even if someone is below the 25-minute mark. Similarly, there are situations that call for including two players at around 23 to 24 minutes per game because there is no clear-cut fifth man on a team.

How is WOWY different from On/Off?

On/Off captures changes within a game. WOWY captures changes from game-to-game. One strength of WOWY is that multi-collinearity is not a problem; in other words, player values cannot be confounded by moving in and out of the game together. In that sense, it is an incredibly pure representation of a player’s value to a given roster, troubled by issues like sample size (major issue), team growth (minor issue), opponent unhealthy lineups (minor) and valuable bench cohorts (minor).

(Note that some lineups have synergistic effects where the whole is greater than the sum of the parts, and removing any player from that equation can disrupt the synergy.)

What’s a WOWY Score?

It’s an attempt to quantify how impressive a given WOWY run is. It takes into account sample size, the distribution of SRS scores in a given era and the quality of the player’s team.

What is “95% +/-?”

It is a confidence interval, based on the SRS-variance of a typical NBA team. For example, from 1977-1978 the Blazers were a -1.2 team in 26 controlled games without Bill Walton. A 95% +/- value of “3.5” means that 95% of the time, the actual full-season SRS of such a team will fall within 3.5 points of that value, or somewhere between -4.7 and +2.3 SRS. (Note: More consistent teams will be slightly penalized by this and more inconsistent teams with benefit from it.)

What is SIO?

It stands for “simple in/out,” and is a basic curving of impact based on the quality of a team. It means that taking a -10 team to -5 is given less value than taking a +5 team to +10.

When combining runs for a “prime score,” why is SIO different than WOWY score?

Uneven samples can provide extremely warped results due to some basic math illusions. Take Michael Jordan, who missed the majority of his games in 1986. His team’s “out” totals will then largely reflect the 1986 Bulls (who were below .500), but his “in” totals will be weighted heavily by the Bulls dynastic teams. So, even if his team performed the same with or without him, his out sample largely be from a -3 SRS team, while his in sample would be teams closer to 9 SRS.

WOWY score was designed to correct this problem — for multiple seasons, it takes the impact (SIO) from a given sample and weighs it accordingly. For instance, if a player makes a team 10 points better in a five-game sample, and then two points better in a 20-game sample, his weighted impact is 3.6 points (because 80% of the sample is from the two-point change).

The actual in and out values are included for posterity, but unless a player played on relatively consistent teams, the numbers won’t reflect the actual impact the player had on his lineups.

Why are there multiple entries for the sample player-season?

The controls are different. Players might miss games from one lineup and then, following a team trade, might play with and without a different lineup.

From the Vault: Are Role Players Worse on the Road

This post was originally published on June 3, 2012. 

On the ESPN pregame show before Game 4 of the Eastern Conference Finals between Boston and Miami, there was a long discussion about why peripheral players tend to struggle more on the road than at home. Which, of course, begs the question…do peripheral players really struggle more on the road than at home?

If we break down player importance by minutes played, we can stratify everyone in the NBA into six categories, ranging from guys who play under 15 minutes per game to those who play more than 35. This is what the results look like for free throw shooting:

Free Throw% Away Home Diff Away % of Home
Players Over 35 mpg .763 .757 -.006 100.8%
30-35 .796 .795 -.001 100.1%
25-30 .774 .768 -.005 100.7%
20-25 .712 .722 .011 98.5%
15-20 .707 .689 -.018 102.6%
Under 15 .677 .675 -.002 100.3%

This confirms another myth-buster we learned at the Sloan MIT Sports Conference this year: teams shoot free throws better on the road, not at home. Players over 35 minutes per game see a small improvement on the road, with home-cooking only reserved for players in the 20 to 25 minute bracket. Those players see a 1.1% decrease in free throw shooting on the road.

Obviously, free throw shooting isn’t a category that tells us much. Instead, let’s look at overall box score statistics that ballpark play based on the basic box stats. First, Game Score (similar to PER) and then Expected Value run only on the box score stats. Finally, points per game and True Shooting% are included.

Game Score Away Home Diff Away % of Home
Players Over 35 mpg 14.6 15.7 1.1 93.2%
30-35 11.1 12.0 0.9 92.5%
25-30 7.7 8.7 0.9 89.4%
20-25 5.9 6.1 0.2 96.8%
15-20 4.0 4.0 0.0 99.8%
Under 15 2.2 2.4 0.2 90.9%
Box EV Away Home Diff Away % of Home
Players Over 35 mpg 4.5 5.4 0.8 84.3%
30-35 3.8 4.4 0.6 87.4%
25-30 2.9 3.4 0.5 84.0%
20-25 2.3 2.5 0.2 92.6%
15-20 1.5 1.5 -0.3 102.2%
Under 15 0.6 0.7 0.1 85.9%
Points Per Game Away Home Diff Away % of Home
Players Over 35 mpg 18.95 19.62 0.7 96.6%
30-35 14.75 15.36 0.6 96.0%
25-30 10.79 11.17 0.4 96.6%
20-25 7.81 7.81 0.0 100.0%
15-20 5.43 5.31 -0.1 102.2%
Under 15 3.18 3.33 0.2 95.5%
True Shooting% Away Home Diff Away % of Home
Players Over 35 mpg .535 .556 .021 96.2%
30-35 .534 .554 .020 96.4%
25-30 .522 .534 .013 97.6%
20-25 .520 .519 -.001 100.2%
15-20 .506 .506 .000 100.0%
Under 15 .471 .485 .013 97.2%

Based on these measurements, lower minute players are actually more consistent on the road than they are away from home. Consider:

  • 25-30 minute players decrease the most on the road by Game Score and Box-based EV
  • 25-30 minute player see no decline in points per game and TS%
  • Under 15 minute players see a Road decline comparable to high minute players in points and efficiency

Otherwise, the players with the biggest drop-off in road performance are the high-minute players! Whether it’s composite box metrics or scoring and shooting, the biggest difference between road and home is typically seen in the key players. In the composite metrics especially, the high-minute players see a significantly larger decline on the road than the low-minute players do.

Keep in mind this is not a definitive study, but a broad examination. We could change the criteria to examine “only All-Stars” or “only All-Stars in the playoffs,” and it’s possible the results look different. But it’s important to note, that in general, it is not the role players who decline more on the road, but the stars.

The Best “Healthy” Offenses of All-Time

In the last post, we looked at the best point-differentials of all-time posted by teams that were “healthy” (when all 25-minute per game players were in action, minimum 41 games played together). But what about isolating the offensive side of the ball?

Since box scores aren’t readily available before 1984, we are limited to teams from the last 32 seasons. But that’s fine — 99 of the top 100 most efficient teams in NBA history played in 1984 or later. (The 1982 Nuggets are the exception.)

Before analyzing the list, a quick disclaimer to keep in mind: Offensive rating is not a perfect representation of offensive quality. Teams can choose offensive-centric lineups at the expense of defense for a net boost, such as crashing the offensive boards instead of retreating in transition defense. Below are the top offenses, relative to the defenses faced, based on these healthy lineup standards:

Healthy Offense Relative ORtg

The 2006 Suns played the second half of the season without Kurt Thomas after running out of big men. As a result, they played one of the most lopsided lineups in NBA history, starting Boris Diaw at center and three wings alongside Steve Nash. They had one big man (Brian Grant) off the bench. While they feasted on defenses, they were defensively compromised and posted an abysmal +6.6 defensive rating during these games. Given that, I wouldn’t rush to crown them the GOAT offense. Some of the Dallas teams on the list also suffer from this kind of lineup tradeoff, slotting Dirk Nowitzki at center next to an offensively-leaning forward.

Offensive rebounding has declined drastically over the last two decades as teams have sacrificed crashing the glass in order to defend transition. Some teams still crash the glass hard, but sometimes individuals are just great offensive rebounders. Dennis Rodman is the ultimate example example of this — he’ll jump a team two tiers by himself. For example, in 37 games without Rodman, the ’96 and ’97 Bulls — with Longley, Kukoc, Jordan and Pippen playing — saw a 5.1% drop in their offensive rebounding rate, which is about the difference between the best offensive rebounding team in the league and an average one.

So let’s expand the list to include components that help place a team’s offensive rating in perspective, such as offensive rebounding rate and turnover percentage. Let’s also include the raw offensive rating and true shooting percentage (TS%) of the team:

Healthy Offense Expanded

First, the 2004 Kings number is shocking because they did it without Chris Webber; they smoked the league with Brad Miller starting in place of him, a phenomenon I discuss in Thinking Basketball.

The ’96 Magic and ’16 Warriors certainly jump out as candidates for the best offenses ever. If you’re eyes thought you’d never seen anything like Golden State this year, you were right; the Warriors shooting efficiency yielded an unheard of 1.19 points per scoring attempt. The ’96 Magic were amazing too, but aided by a shortened 3-point line.

There’s a dark horse in there: The 2016 Cavs, the team that beat the Warriors. Injuries have masked an all-time level offense, led by LeBron JamesKyrie Irving and even Kevin Love. They are not in the upper stratosphere of shooting efficiency, but are a low-turnover offense (11.5%) that benefits from player-specific offensive rebounding by Tristian Thompson.

But how good is an offense that can only take advantage of a fundamentally poor defense? While most offenses perform better against weaker defenses, Cleveland has no correlation between an opponent’s defensive strength and its own offensive production. A linear regression predicts that the Cavs offense will actually perform better against elite defenses than almost every team on this list, including Golden State. Given the small samples, I wouldn’t put too much stock in this, but it is worth noting nonetheless.

Of course, there’s an elephant in the room. Where will Kevin Durant, Steph Curry and the 2017 Warriors place on this list?



From the Vault: Observations from a season of Stat-Tracking

This post was originally published on April 13, 2011. It is a summary of findings after one year of stat-tracking basketball games in attempt to extend the box score. SportsVU now captures similar data. 

If one spends enough time watching NBA games with a DVR, trends start to jump out. Unfortunately, there’s no way the human brain can accurately catalog all that information. Perhaps Data from Star Trek should be assigned to finding trends in basketball games. In the meantime, here are some statistical observations from roughly 23,000 possessions of stat-tracking in 2011:


  • 16% of all field goals came off of an Opportunity Created (OC).
  • 46% of 3-pointers came off of an OC.
  • The average player shot 40% on 3-point shots off of an OC.
  • The Spurs led the league in OC’s (23.5 per 100 possessions), with the Hawks second at 23.4.
  • The Jazz needed the most help on defense — which means their opponents create the most opportunities (23.7 OC per 100).
    • The Jazz had the lowest Defensive Rating in the sample by far (118.7).


  • The Lakers committed the fewest shooting fouls in the league (16.5 free throws/100).
  • Someone takes an offensive foul every 88 possessions…or a little more than once per game.
  • Phoenix takes more offensive fouls than any other team – 2.2 per 100 possessions.


  • In guarded situations, the most successful teams are the best defensive teams: The four leaders in guarded field goal percentage are in the top-5 in defensive rating (and Milwaukee’s sample was too small):
    1. Miami (36.6%)
    2. Chicago (36.6%)
    3. Boston (36.9%)
    4. LA Lakers (37.7%)
  • The Lakers make the most defensive errors…but give up the fewest points per error (1.50 points/error), a credit to Andrew Bynum and Pau Gasol protecting the paint.
  • Every 172 possessions there is a forced turnover not counted as a steal (eg slapped off a leg out of bounds. That means the NBA doesn’t track about 1700 “steals” during the season.
  • Teams shoot the worst in unguarded situations against the Lakers (56.6% eFG%), which suggests that LA does well closing out shots and fighting through screens…or they’re just lucky.

Top “Healthy” Teams in NBA History

Who are the best teams in NBA history? We often answer this question by looking at a team’s entire body of work, lumping in the good, the bad and the injured. Most teams have key players miss games and some even trade for key players, changing the chemistry of a given lineup. So who were the best teams when all of the key actors were on stage?

Below I’ve indexed the top “healthy” teams — when all 25-minute per game players were in action for a game — since the shot clock (1955) by SRS (adjusted margin of victory). Using this criteria, 51 teams have posted at least an 8.0 SRS when healthy.  Just 29 teams have eclipsed the 9.0 mark. (10 of those teams failed to win a title — well inline with what is predicted by the variability of a 7-game series.) The best are below, playoffs included:

Top Healthy Offenses

Disclaimers: SRS, while a better predictor of results than win percentage, is not a de facto team-ranker. First, it’s subject to the usual variance seen in the NBA (detailed in Chapter 4 of Thinking Basketball), so it’s not a perfect representation of team strength. Second, some teams are more resilient in makeup — they are better equipped at handling a variety of opponents while still remaining efficient, boosting their odds of winning from series to series. Finally, SRS is a measure of within-season dominance, so it cannot allow for perfect comparisons across seasons. A 10 SRS in 1986 is probably more impressive than one in 1972.

With that said, it is by far the single best metric for evaluating the performance of a team against its competition. The teams listed above were manhandling opponents, which is why many went on to win a title.

While this year’s Warriors were the most dominant single-season team ever, their SRS is influenced by a league that was incredibly top-heavy. Four of the top-40 healthy teams ever played in 2016 (Golden State, San Antonio, Oklahoma City and Cleveland), which is either an unlikely coincidence, or a reflection of inflated numbers from a lopsided league.

The other top four seasons are from expansion eras, when teams could pick up an additional point or two by facing expansion squads a few times a year and padding their numbers with blowouts. All of those teams are in the conversation for “greatest ever,” but their statistical dominance here should be slightly curved.

As mentioned, we see the usual suspects: Jordan’s first three-peat Bulls. Jordan’s second three-peat Bulls. Kareem’s Bucks and the early 70’s Lakers. This is all line with in-depth analysis of the greatest teams ever.

So who are the most impressive teams of all-time that you probably didn’t know about:

  1. 2014 Spurs. When healthy, they posted an amazing 11.8 SRS. That team is basketball’s Sistine Chapel and Gregg Popovich its Michelangelo.
  2. 2004 Pistons. Absolutely impregnable after the Rasheed Wallace trade in ways that reminded everyone it was time for a rule change.
  3. 2008-09 Lakers and Celtics. These teams were fantastic in an incredibly competitive league. The Celtics were +8.8 and +9.3 when healthy, and the Lakers +9.7 and +9.0 once Pau Gasol joined. Kevin Garnett’s injury robbed us of possibly the NBA’s greatest trilogy.
  4. 1996 Magic. Yes, they were worthy of a documentary.

Amazingly, of the top 40 healthy teams of all-time, seven are Pop’s Spurs teams. Five are Jordan’s Bulls. Four are Laker teams with Kobe Bryant.

Remember this list the next time you construct an all-time list or you look ahead to the 2016 season.

Edit: This post was updated to include the postseason totals for the 2016 Warriors, and 96-97 Bulls. 

From the Vault: Exploring the Spacing Effect

This post was originally published on November 26, 2011. It examines a concept mentioned in my new book, Thinking Basketball

One of the more dominant themes of this summer’s Online Hoops Summit of Nerdness was the “Spacing Effect” that good shooters provide for an offense. By being a threat to score from all over the floor, shooters pull out defenders who could otherwise help on penetration or flood the paint for defense and rebounding. For example, in the last post we combed over five years of raw on/off data — how well a team performed with a player in the lineup versus when he was on the bench — and some of the biggest impacts were made by great shooters.

Of the 21 players who added at least six points of efficiency to a 107 offense (teams averaging 107 points or more per 100 possessions without the player), seven are on the all-time top-100 list of 3-point percentage leaders (minimum 500 attempts). 17 of the 21 (81%) used the 3-point shot regularly, with only Brad Miller (2004), Shaquille O’Neal (2005), Kevin Garnett (2008) and Tyson Chandler (2008) operating primarily inside the arc. The average 3-point percentage from that group was a whopping 38.2%. (League average 35.7% over that time.)

Below are the 21 player seasons, with their 3-point percentage:

Player Year Net Change Ortg On Court Ortg Off Court Season 3 pt %
Josh Howard 2004 6 117.6 111.6 .303
Radmanovic 2008 8.6 119.5 110.9 .406
Williams 2008 6.1 116 109.9 .395
Nowitzki 2004 6.2 115.6 109.4 .341
Bryant 2008 6.5 115.4 108.9 .361
Lewis 2005 7.3 116 108.7 .400
Joe Johnson 2005 8.4 117 108.6 .478
Josh Howard 2007 6.5 114.9 108.4 .385
Allen 2005 7 115.2 108.2 .376
Marion 2007 8.6 116.8 108.2 .317
Radmanovic 2005 11.7 119.8 108.1 .389
Chandler 2008 6.9 114.5 107.6
O’Neal 2005 7.6 114.9 107.3
Christie 2004 6.7 114 107.3 .345
Finley 2005 6.8 114 107.2 .407
Posey 2006 6.2 113.4 107.2 .403
B. Miller 2004 7.5 114.6 107.1
Billups 2008 8 115.1 107.1 .401
Terry 2006 8.5 115.5 107 .411
Garnett 2008 8 115 107

Also from that five-year chunk of data, there were 55 instances of players boasting an on/off of 9.0 or better on offense (minimum 1000 minutes played). Again, this means their teams offense scored at least nine more points per 100 possessions with them on the court that year. Only ten of those seasons saw a player attempt less than one 3-point shot per game. We see the same results: the other 45 (82% of the group) averaged 38.4% from behind the arc.

Of particular interest are the shooting specialists. Who we classify as one-dimensional shooters is somewhat subjective, but it’s a mighty coincidence that Vladimir Radmanovic appears on the above list twice, with two different teams. And that Peja Stojakovic does the same, in two different situations, in his two best 3-point shooting seasons (43.3% in 2004, 44.1% in 2008). And that Damon Jones seemed to help Miami so much in 2005 with a career-best 43.2% from downtown. And that Fred Hoiberg led the league in 3-point percentage in 2005 at a staggering 48.3% and booted Minnesota’s offense while on the court.

Of course, making so many 3′s is also part of the reason these players are helping so much, but perhaps not quite as much as one would think. In Hoiberg’s case, he attempted 4.1 3′s every 36 minutes, which means the difference between 48.3% and league average was roughly 1.6 points per 36 minutes, or about 2.3 points/100 at Minnesota’s 2005 pace. Radmanovic launched 5.7 3′s every 36 minutes in 2008, and if he converted at league average the Lakers would have scored about 1.8 fewer points in his games.

So while greater accuracy translates directly to more points, something else is happening here indirectly. It’s possible these shooters are repeatedly the beneficiary of coming in and out of the lineup with their team’s superstars. Although that seems unlikely, we can look at long-term adjusted plus-minus (APM) data and see the same pattern.

In Joe Ilardi’s 2003-2009 APM model, the best offensive players in the league are names we’d expect: Steve NashLeBron JamesKobe BryantChris Paul and Dwyane Wade. It’s also littered with resident shooters, like Antawn Jamison (“stretch” power forward) at No. 7, Michael Redd (12th), Ray Allen (13th), Jason Terry (19th), Anthony Morrow (21st), Peja Stojakovic (22nd), Rashard Lewis (23rd), Danilo Gallinari (26th), Anthony Parker (40th), Mike Bibby (45th) and Sasha Vujacic (48th). Below are how the top-50 3-pooint shooters (500 attempts) by percentage scored in Ilardi’s APM study:

Player 3P% Off APM
Jason Kapono .454 -1.36
Steve Nash .439 8.84
Anthony Parker .424 2.55
Ben Gordon .415 2.37
Raja Bell .414 -1.22
Daniel Gibson .412 1.40
Bobby Simmons .410 -0.61
Brent Barry .409 0.32
Matt Bonner .409 1.00
Peja Stojakovic .409 4.15
Bruce Bowen .408 -4.99
Wally Szczerbiak .406 1.08
Leandro Barbosa .404 0.51
Kyle Korver .404 -0.20
Eddie House .403 -1.88
Mike Miller .402 1.21
Chauncey Billups .401 5.32
Matt Carroll .400 0.39
Troy Murphy .398 0.41
Roger Mason .395 -0.58
Brian Cook .394 -2.41
Danny Granger .393 1.40
James Jones .393 1.80
Ray Allen .392 5.33
Steve Blake .392 -0.08
Luther Head .392 -1.21
Shane Battier .391 0.33
Rashard Lewis .390 3.91
Michael Finley .389 -1.58
Kevin Martin .389 1.10
Jameer Nelson .389 0.14
Hedo Turkoglu .389 1.89
Jason Terry .387 4.41
Mo Williams .386 1.39
Tyronn Lue .384 -0.47
Jose Calderon .383 0.71
Vladimir Radmanovic .381 1.84
Michael Redd .381 5.46
Kirk Hinrich .380 -0.88
Mike Bibby .379 2.31
Joe Johnson .379 1.40
Dirk Nowitzki .379 4.71
Mike James .378 -0.80
Delonte West .378 -0.39
Andrea Bargnani .377 -1.24
Maurice Evans .377 0.26
Mehmet Okur .377 -0.48
Sasha Vujacic .377 2.24
Manu Ginobili .376 4.94
J.R. Smith .376 1.98
Derek Fisher .375 -1.60

The average Offensive APM in the entire study was -0.45. The average Offensive APM of the top-50 3-point shooters on the list is +1.08. 32 of the 50 were positive-impact players. The glaring outlier, Bruce Bowen, can be explained away quite nicely. We’re using the 3-point shot to approximate outside shooting ability (or the threat of outside shooting), and Bowen isn’t a very good outside shooter. Using available data, he took about one deep jumper a game from 2007-2009 converting at 38%. He shot 57.5% from the free throw line during the period, the worst of anyone of the list by nearly 8%.

We could further define “good outside shooters” by looking at floor data on shooting from 16-23 feet if we wanted to. Although, despite the presence of someone like Bowen, 3-point shooting is sufficient for now to demonstrate the presence of the Spacing Effect.

Thinking Basketball Now Available on Amazon

Excited to announce that my new book, Thinking Basketball, is now available on Amazon in paperback.

The book is largely a culmination of the ideas on this blog over the years, using our own cognition to explore misconceptions about the NBA. It’s built on the concepts that have been presented on this blog (some of which I’ll try and re-upload this summer), as well as new research that was developed specifically for the book.

It would not exist without you, the reader, supporting this blog over the years and constantly participating to improve the ideas shared in this space. Thanks for reading and I hope you enjoy it!

Some core topics:

  • Averaging 50 points per game is rarely better than averaging 20
  • Why “Chokers” aren’t always chokers
  • How winning warps our memories, and thus our narratives about players and teams
  • The value of clutch play and closers
  • Building championship teams and the value of one-on-one play

Half-Court Math: Hack-a-Whoever, Isolation and Long 2’s

In my upcoming book, Thinking Basketball, I allude to certain instances where “low efficiency” isolation offense provides value for teams. Most of us compare a player’s efficiency to the overall team or league average, but that’s not quite how the math works, because the average half-court possession is worth less than the average overall possession.

In 2016, the typical NBA possession was worth about 1.06 points. That’s a sample that includes half-court possessions against a set defense, but also scoring attempts from:

  • transition
  • loose-ball fouls
  • intentional fouls
  • technical fouls

Transition is by far the largest subset of that group, accounting for 15% of possessions for teams, per Synergy Sports play-tracking estimations. Not surprisingly, transition chances, when the defense is not set, are worth far more than half-court chances. As are all of the free-throw shooting possessions that occur outside of the half-court offense.

Strip away those premium opportunities from transition and miscellaneous free throws and the 2016 league averaged 95 points per 100 half-court possessions. (All teams were between 7 and 14 points worse in the half-court than their overall efficiency.) Golden State, the best half-court offense in the league this year, tallied an offensive rating around 105, far off its overall number of 115 that analysts are used to seeing.

Transition vs Half Court Efficiency

This has major implications for the math behind “Hack-A-Whoever.” If the defense is set, then, all things being equal, fouling someone who shoots over 50% from the free throw line is doing them a favor. One might think that a 53% free throw shooter (1.06 points per attempt) at the line is below league average on offense because of the overall offensive efficiency. But it’s actually well above league average against a set, half-court defense. (Other factors, like offensive rebounding and allowing the free-throw shooters team to set-up on defense complicate the equation.)

Said another way — fouling a 53% free throw shooter is similar to giving up a 53% 2-point attempt…which is woeful half-court defense.

There could be other viable reasons to “Hack-A-Whoever,” such as breaking up an opponent’s rhythm or psychologically disrupting the fouled player. (These would be good strategic reasons to keep the rule, in my opinion.) But assuming he was a 50-60% foul shooter, coaches would still be making a short-term tradeoff, exchanging an inefficient defensive possession for other strategic gains.

This also has ramifications for isolation scorers and long 2-point shots. Isolation matchups that create around a point per possession in the half court — or “only” 50% true shooting — are indeed excellent possessions. If defenses don’t react accordingly, they will be burned by such efficiency in the half-court. As an example, San Antonio registered about 103 points per 100 half-court possessions this year, and combined it with a below-average transition attack to still finish with an offensive rating of 110, fourth-best in the league.

The same goes for the dreaded mid-range or long 2-pointer — giving these shots to excellent shooters from that range (around 50% conversion) is a subpar defensive strategy. And even a 35% 3-point shooter (1.05 points per shot) yields elite half-court offense.

So, when we talk about the Expected Value of certain strategies, mixing transition possessions together with half-court ones will warp the numbers. Sometimes, seemingly below-average efficiency is actually quite good.