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, 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:

Creation

  • 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).

Fouling

  • 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.

Defense

  • 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. 

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.

 

How 2016 NBA Teams Differentiated Themselves on Offense

Dean Oliver’s Four Factors uses box score data to determine how teams are successful in key elemental areas. Instead of looking at box stats like turnovers and rebounding, what if we used different types of plays to determine a team’s offensive strengths? Synergy tracks a number of play types, but not all have a large impact on the game. Based on the 2016 data on nba.com, the following were the most common play types this year:

  • 25% were pick-n-roll plays
  • 20% were spot-ups
  • 15% were in transition

Naturally, teams differentiate themselves from the pack based on the plays they run the most; The Lakers led the league in isolation plays, but their efficiency was below-average on those plays, so they lost lots of ground on the average offense. The five categories from Synergy with the largest degree of differentiation were:*

  1. Pick-n-Roll (PnR)
  2. Spot Up
  3. Transition
  4. Post Up
  5. Off Screen

Below is a visual of how every team in the NBA this year fared in these five factors.

2016 Differentiation by Play Type

The y-axis represents the per-game differentiation based on efficiency of a given play type (relative to league average). For instance, if a team ran 820 post ups (10 per game) and averaged 0.10 points per play more than league average, they would generate an extra point per game.

Not surprisingly, the most differentiating play type during the 2016 season was a Golden State spot-up shot. Of the 203 players with at least 100 spot-ups, Steph Curry was 2nd in efficiency at 1.49 points per play and splash brother Klay Thompson 15th at 1.18 points per play. (League average was 0.97 points per spot-up.) Let’s simplify the above visual and just focus on the final eight teams left in this year’s playoff field:

2016 Differentiation Final 8

Now it’s easier to see how the remaining teams stack up. The Warriors don’t really have a post-up game, but so what? They excel at everything else and created the most differentiation of any team in the league in three major categories (PnR, Spot Up and Off Screen.) On the other hand, the Spurs were dominant in the post and excellent in their own right at spot-up plays, but they don’t do damage in transition. (San Antonio also led the league in “put backs” by a large degree, generating over a point of separation alone in that category.) The East’s best team, Cleveland, was above-average at everything.

*Isolation plays would be the 6th major play type. However, no team in 2016 created a point of positive or negative differentiation from isolation plays, which accounted for 8% of all plays tracked during the season.