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.

PlayerWOWYRError
Robertson..Oscar.7.51.5
Abdul.Jabbar6.92.3
Russell..Bill.6.42.0
West..Jerry.6.11.2
Cunningham5.91.5
Thurmond5.81.7
Johnson..Marques.5.33.3
Schayes..Dolph.5.32.0
Ray..Cliff.5.32.7
Lanier5.21.2
Chamberlain5.11.3
McMillian..Jim.5.11.4
DeBusschere4.71.9
Arizin4.71.9
Free4.62.0
Hayes..Elvin.4.42.0
Frazier4.34.1
McGinnis4.21.9
Cheeks4.06.5
Jones..Bobby.3.93.1
Smith..Bingo.3.82.9
Gilmore3.72.9
Murphy..Calvin.3.72.1
Silas..Paul.3.51.1
Barry..Rick.3.51.2
Johnson..John.3.41.9
Sloan3.21.7
Barnett..Dick.3.21.3
Greer3.12.8
Porter..Kevin.3.11.2
Marin3.11.1
Erving3.13.0
Dukes3.02.2
Cousy2.91.5
Hazzard2.91.5
McGlocklin2.92.2
Howell2.81.5
Issel2.65.0
Beaty2.61.7
Gola2.61.5
Johnson..Dennis.2.67.2
Mullins2.52.4
Hagan2.52.3
Boozer..Bob.2.41.1
Unseld2.41.3
Pettit2.42.7
Drew..John.2.31.9
White..Jo.Jo.2.31.9
Hollins..Lionel.2.21.2
Jones..Sam.2.12.0
Heinsohn2.11.4
Bellamy2.11.2
Smith..Phil.2.02.2
Baylor2.01.1
Brown..Fred.2.02.1
Havlicek2.01.5
Adams..Alvan.2.02.0
Bing1.91.1
Chaney1.91.7
Haywood..Spencer.1.81.4
Sharman1.82.0
Smith..Randy.1.71.9
Kerr..Red.1.61.6
Yardley1.62.0
Sears1.61.8
Ford..Chris.1.61.5
Bradley..Bill.1.63.5
Van.Arsdale..Dick.1.51.4
Roundfield1.52.2
Newlin1.41.8
Collins..Doug.1.21.7
Johnson..Gus.1.11.2
Martin..Slater.1.11.7
Chones1.11.3
Westphal1.02.1
Carr..Austin.1.01.5
Bridges0.91.5
Cowens0.91.5
Loughery0.91.5
Embry0.82.6
Van.Arsdale..Tom.0.71.2
Braun0.72.1
Shue0.61.9
Nelson..Don.0.61.1
Monroe..Earl.0.61.5
Maravich0.61.3
Attles0.52.1
Snyder..Dick.0.51.3
Love..Bob.0.52.9
Meschery0.42.6
Dandridge0.41.7
Scott..Ray.0.41.1
Shelton0.42.6
Sobers0.31.7
Chenier0.31.8
Bridgeman0.22.0
Hairston0.21.1
Bantom0.11.4
Hudson..Lou.0.01.5
Van.Lier0.01.4
Ramsey-0.11.3
Washington..Jim.-0.12.1
Erickson-0.11.2
Rowe-0.21.8
Twyman-0.22.9
Winters-0.22.8
Heard-0.31.0
Ellis..Leroy.-0.31.2
Lovellette-0.52.0
Naulls-0.51.6
Wilkens-0.51.4
Russell..Cazzie.-0.51.3
Clark..Archie.-0.61.3
Goodrich-0.91.5
Malone..Moses.-0.92.3
Reed..Willis.-0.91.4
Walker..Chet.-1.02.3
Wilkes-1.04.0
Komives-1.11.6
Guerin-1.31.4
McAdoo-1.31.5
Miles..Eddie.-1.42.0
Robinson..Truck.-1.41.1
Maxwell..Cedric.-1.53.6
Russell..Campy.-1.51.7
Jones..Wali.-1.62.3
Johnson..Mickey.-1.61.9
Costello-1.81.8
Lucas..Mo.-1.91.9
Green..Johnny.-2.41.5
Ohl-3.21.3
Barnett..Jim.-3.21.6
Rodgers..Guy.-3.51.7
Tomjanovich-3.52.0
LaRusso-3.81.5
Johnson..George.-3.92.6
Sanders..Tom.-4.42.5
Lucas..Jerry.-4.51.4
Jones..Caldwell.-6.12.2
Carter..Fred.-6.42.2
Wicks-7.32.6
Gervin-9.38.7

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

Lineups

  • ~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.

 

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. 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 on this page.

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. 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 will 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 would 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.