Measuring the NBA MVP Race and Solomon Hill

In two days, we will find out who is the NBA MVP: James Harden, Kawhi Leonard, and Russell Westbrook. Each player has their pros and cons, and have been heavily debated over the past month since the finalists have been listed. Despite Leonard leading the Spurs into the second best record in the league (61-21) for a second season in a row; Leonard is viewed as the third horse in a two-horse race. Most debates have centered about Harden and Westbrook. Harden led the league in assists and finished second in points per game. Westbrook, similarly, finished first in points per game and second in assists. Westbrook finished the season with a triple-double, the first since Oscar Robertson in 1962 (Cincinnati Royals), leading the Thunder to 47 wins. Harden finished 151 rebounds shy of a season average triple-double; 1.86 rebounds per game shy. The basic stat sheets show that Harden and Westbrook are effectively identical players.

Looking at other types of analytics, such as Hollinger’s player efficiency rating (PER) and ESPN’s weighted stat line, Westbrook edges out Harden for the MVP awards. However, discussions lead to these types of arguments: Harden beats Westbrook head to head and has more wins (Bleacher Report), Vegas Odds favor Westbrook (Forbes), or Harden’s lack of defensive prowess vs. Westbrook’s questionable shot selection (CBS Sports).

Problems with some of the advanced analytics such as Hollinger’s PER and ESPN’s combined analytic is that it does not take into account of the player’s indirect contributions. For instance, strong defensive players are frequently rated low. Assumptions are commonly made such as players off the basketball have no effect on the play. Bleacher Report breaks down a couple common advanced analytics/metrics; showing their glaring issues.  To give an example, in a sample of thirty random Stephen Curry steals from the 2015-2016 season, eleven were off-ball steals. That is, roughly a third of his steals were jumping passing lanes. Of the nineteen on-ball steals, five were as gamble steals; attacking an offensive player from behind on a double team. Another seven were post strip steals on shot attempts. This means seven steals were one-on-one steals. That said, while Steph Curry is credited for thirty steal, most come about due to coordinated defense with a teammate. The most common teammate was Klay Thompson; which, if you’ve been following this blog (or my Twitter account), I’ve been high on Klay Thompson’s defensive pressure. The second most common teammate? Shaun Livingston.

Supersized “Plus-Minus”

Instead of taking raw numbers, if we supersized the plus-minus stat-line and then applied a manifold projection. What on Earth does this mean? Let’s break it down. Instead of looking at plus-minus, let’s look at plus-minus plus actions. We’ve been running this analytic since 2010; publishing results since 2013. Typically, the league MVP will be within the top 10; usually in the top 5. Only once an MVP has not been in the top 10: Derrick Rose (2009). Last year, the MVP (Steph Curry) was eighth. Note that Klay Thompson was at the top of the list. An example of the analytic is given in detail in that post.

What this plus-minus will capture  are those steals that are ignited by defenders that do not record the steal. It also identifies when baskets are not scored and how those events occur. Steals, misses, and defensive rebounds are extra minus values for offensive players. This metric also incorporates effective field goal (eFG) percentage as the weighted field goals are captured by defensive rebounds and including points. The eFG is smeared a little as offensive rebounds erase missed field goal attempts.

For the 2016-17 NBA season, 170,282 actionable possessions occurred over the 1,230 NBA games; approximately 70 actionable possessions per team. These possessions eliminate end of quarters, technical fouls, dead ball situations. Over this season, 486 NBA players participated in at least one actionable possession. This means we include Danuel House (one minute played for Washington; three possessions) and Jarnell Stokes (3.5 minutes played for Denver; five actionable possessions – two dribble out clock possessions not included).

Using these possessions, we look at the 486 players in each play and fit a response curve to the multiple (if they exist) responses. This in turn becomes a local-linear embedding that identifies the statistical manifold that best fits the resulting super-plus-minus values. The resulting weights are whitened (covariance scaled) across all players and then weighted against the proportion of actionable possessions for each player. This means if a player gets big time stats in garbage time, then the big time stats are crushed to near-nothing.

So Who Are the Top Players?

The top player this year is Steph Curry with a score of 3.397. Second in the league? Klay Thompson with 2.884. Once again, we find that the Golden State back-court duo is the toughest duo (offense and defense combined) in the league. And yet once again, John Wall and Bradley Beal of Washington are the second toughest back-court in the league; coming in at fourth and eighth, respectively.

So let’s take a look at the Top 25 NBA players this year:

  1. Stephen Curry (Golden State) – 3.3974
  2. Klay Thompson (Golden State) – 2.8837
  3. Paul George (Indiana) – 2.7205
  4. John Wall (Washington) – 2.7080
  5. Jae Crowder (Boston) – 2.6422
  6. James Harden (Houston) – 2.5038
  7. Harrison Barnes (Dallas) – 2.4385
  8. Bradley Beal (Washington) – 2.2952
  9. Solomon Hill (New Orleans) – 2.2419
  10. LeBron James (Cleveland) – 2.2354
  11. Courtney Lee (New York) – 2.2081
  12. Kentavious Caldwell-Pope (Detroit) – 2.1307
  13. Giannis Antetokounmpo (Milwaukee) – 2.0946
  14. Kemba Walker (Charlotte) – 2.0440
  15. Russell Westbrook (Oklahoma City) – 2.0343
  16. Aaron Gordon (Orlando) – 2.0003
  17. Gordon Hayward (Utah) – 1.9816
  18. Seth Curry (Dallas) – 1.9421
  19. Joe Ingles (Utah) – 1.8292
  20. Ryan Anderson (Houston) – 1.7836
  21. Luc Mbah a Moute (Los Angeles Clippers) – 1.7459
  22. Tony Snell (Milwaukee) – 1.6908
  23. Markieff Morris (Washington) – 1.6816
  24. Jimmy Butler (Chicago) – 1.6783
  25. Karl-Anthony Towns (Minnesota) – 1.6783

As a small note, I will mention fellow Madisonian Wesley Matthews (Dallas) as the 26th player with a score of 1.6685. Matthews is from James Madison Memorial high school currently playing in the Roy Boone Summer League in Madison.

So Who Is MVP?

The argument for MVP typically morphs into a debate between “who is the best player in the league / who would you build a team around” vs. “If that player was removed from their team, how bad would they be?” Voters historically vote in the latter direction; as indicated by the fact that LeBron James is not MVP every year. (Feel free to argue that statement!)

This year, we are reduced to James Harden, Kawhi Leonard, and Russell Westbrook. If we select the best player based on all-around game play; then James Harden is the MVP. However, if we look at most importance to their team, then Russell Westbrook is the MVP. For their team contributions: Kawhi Leonard has a t-Statistic of 2.22, James Harden has a t-Statistics of 2.28, and Russell Westbrook has a t-Statistics of 2.71. Combine this with Westbrook’s triple-double record, there should be little doubt that Russell Westbrook will be MVP this year.

That said, if Westbrook is indeed the MVP, he will be the lowest rated player in history to win MVP. This is primarily due to the work-load required by Westbrook to have the Thunder a fighting chance in every game. We see that he is head-and-shoulders the top player on Oklahoma City; and his presence is key to Thunder winning games. Therefore, with a 47-35 record and copious amounts of playing time, Westbrook’s gaudy numbers are going to be shrunken down due to having a few more losses than another player, like Harden. But let’s magnify this by using another player…

Solomon Hill…?

On a similar note, Solomon Hill… he of 7.0 PPG, 29.7 MPG, 3.8 RPG, and 1.8 APG… has the highest differential for New Orleans. Hill has the third highest salary on the New Orleans payroll but has produced one of the worst offensive stat lines for his salary; therefore having the 23rd best (fourth worst) PER on the team (ESPN). But why is he rated so high? His defensive presence and ability to space the floor when Anthony Davis is on the court. That, and having a strong center in Davis that provides offense and defense helps his cause.

Hill played in 6584 actionable possessions this past season. 3567 on defense and 3017 on offense. Let’s compare Hill to his teammate, Anthony Davis. Davis played in 7502 actionable possessions, a total of 918 more possessions than Hill. Davis played a similar ratio to Hill with 4084 defensive possessions against 3418 possessions. Taking a moment to plot the results of every actionable possession, we find that Hill does indeed out-perform Davis.


Distribution of Solomon Hill’s Super +/- for both offense and defense (blue, red respectively). Compared to Anthony Davis’ (respective dashed lines).

We see that Hill’s distribution on defense matches Anthony Davis’, but his offensive performance actually helps his team overall.

If we take this one step further, let’s look at all Anthony Davis-less Solomon Hill possessions; as well as all Solomon Hill-less Anthony Davis possessions and see if anything changes. In this case, Solomon Hill plays 1382 actionable possessions without Anthony Davis. Similarly, Anthony Davis plays 2300 actionable possessions without Solomon Hill. Taking a look at the distributions, we find that Anthony Davis actually improves Solomon Hill’s offense


Distribution of Super +/- for both Solomon Hill (solid) and Anthony Davis (dashed) in situations where one is playing without the other.

Seeing the activity for Solomon Hill when Davis is off the court, we lose the bulge sitting at 1 to 3. This shows that Davis improves offensive performance from Solomon Hill. Let’s dig a little deeper in understanding this result. Looking at Davis’ results, nothing changes when Hill is either added or taken away from Davis. However, adding Hill improves Hill’s offense. This suggests then that Hill plays better in the presence of Davis; and not specifically that Davis improves Hill’s game.

What the curious case of Solomon Hill teaches us is this: these super +/- numbers are only indicative of the personnel relationships during a game. The numbers do not suggest that the best players have the higher numbers; but rather suggest that the players that affect the game have higher numbers. If only then those high number players also have stat-stuffing capabilities, then that player is the “best” player on the team. Hence this metric will commonly tease out the top players for each team, with respect to game impact. However, it may magnify players for more mediocre teams; as their star players will suffer nearly as many negative possessions as positive possessions. This is clearly shown in the Hill-Davis breakdown for a 34-48 New Orleans team.

Who’s Most Important on Each Team?

Finally, let’s jot down the top three players for each squad; broken down by rankings: Team (Record; Average Super +/-).

  1. Golden State Warriors (67-15; 0.7218)
    1. Stephen Curry – 3.3974
    2. Klay Thompson – 2.8837
    3. Draymond Green – 1.6645
  2. Boston Celtics (53-29; 0.7060)
    1. Jae Crowder – 2.6422
    2. Marcus Smart – 1.6677
    3. Amir Johnson – 1.3839
  3. Washington Wizards (49-33; 0.7056)
    1. John Wall – 2.7080
    2. Bradley Beal – 2.2952
    3. Markieff Morris – 1.6816
  4. Houston Rockets (55-27; 0.6713)
    1. James Harden – 2.5038
    2. Ryan Anderson – 1.7836
    3. Corey Brewer – 1.3135
  5. Indiana Pacers (42-40; 0.6704)
    1. Paul George – 2.7205
    2. C.J. Miles – 1.6655
    3. Thaddeus Young – 1.6070
  6. Charlotte Hornets (36-46; 0.6044)
    1. Kemba Walker – 2.0440
    2. Nicolas Batum – 1.5089
    3. Marco Belinelli – 1.4458
  7. Toronto Raptors (51-31; 0.5942)
    1. Terrence Ross – 1.5560
    2. Jonas Valanciunas – 1.1064
    3. Patrick Patterson – 1.1000
  8. Utah Jazz (51-31; 0.5529)
    1. Gordon Hayward – 1.9816
    2. Joe Ingles – 1.8292
    3. Joe Johnson – 1.0578
  9. New York Knicks (31-51; 0.5518)
    1. Courtney Lee – 2.2081
    2. Carmelo Anthony – 1.5669
    3. Derrick Rose – 1.3944
  10. Milwaukee Bucks (42-40; 0.5512)
    1. Giannis Antetokounmpo – 2.0946
    2. Tony Snell – 1.6908
    3. Malcolm Brogdon – 1.0890
  11. Minnesota Timberwolves (31-51; 0.5511)
    1. Karl-Anthony Towns – 1.6735
    2. Ricky Rubio – 1.3978
    3. Andrew Wiggins – 1.2451
  12. Miami Heat (41-41; 0.5409)
    1. Tyler Johnson – 1.4824
    2. Hassan Whiteside – 1.0750
    3. James Johnson – 0.8174
  13. Dallas Mavericks (33-49; 0.5371)
    1. Harrison Barnes – 2.4385
    2. Seth Curry – 1.9421
    3. Wesley Matthews – 1.6685
  14. Los Angeles Clippers (51-31; 0.5363)
    1. Luc Mbah a Moute – 1.7459
    2. DeAndre Jordan – 1.4698
    3. JJ Redick – 0.9605
  15. Portland Trailblazers (41-41; 0.5281)
    1. C.J. McCollum – 1.6010
    2. Damian Lillard – 1.4202
    3. Maurice Harkless – 1.2843
  16. Chicago Bulls (41-41; 0.5043)
    1. Jimmy Butler – 1.6783
    2. Dwyane Wade – 0.8476
    3. Taj Gibson – 0.8309
  17. Oklahoma City Thunder (47-35; 0.4892)
    1. Russell Westbrook – 2.0343
    2. Ersan Illyasova – 1.2025
    3. Steven Adams – 1.0426
  18. Brooklyn Nets (20-62; 0.4794)
    1. Isaiah Whitehead – 1.1270
    2. Randy Foye – 1.0266
    3. Chris LeVert – 0.9884
  19. San Antonio Spurs (61-21; 0.4757)
    1. Kawhi Leonard – 1.5006
    2. Pau Gasol – 1.1372
    3. LaMarcus Aldridge – 1.1338
  20. Memphis Grizzlies (43-39; 0.4418)
    1. Mike Conley – 1.6364
    2. Marc Gasol – 1.2323
    3. Tony Allen – 1.0515
  21. Denver Nuggets (40-42; 0.4197)
    1. Nikola Jokic – 1.5798
    2. Jameer Nelson – 1.1782
    3. Will Barton – 1.0541
  22. Sacramento Kings (32-50; 0.4193)
    1. DeMarcus Cousins – 1.4693
    2. Garrett Temple – 1.1426
    3. Matt Barnes – 1.0362
  23. Orlando Magic (29-53; 0.4063)
    1. Aaron Gordon – 2.0001
    2. Elfrid Payton – 1.1618
    3. Serge Ibaka – 0.9803
  24. Cleveland Cavaliers (51-31; 0.4015)
    1. LeBron James – 2.2354
    2. Kyrie Irving – 1.3842
    3. Kevin Love – 0.8288
  25. New Orleans Pelicans (34-48; 0.3838)
    1. Solomon Hill – 2.2419
    2. Jrue Holiday – 1.3509
    3. Anthony Davis – 1.0138
  26. Detroit Pistons (37-45; 0.3518)
    1. Kentavious Caldwell-Pope – 2.1307
    2. Ish Smith – 1.2248
    3. Marcus Morris – 1.1042
  27. Phoenix Suns (24-58; 0.3129)
    1. P.J. Tucker – 1.2122
    2. Eric Bledsoe – 1.2105
    3. Devin Booker – 0.8601
  28. Philadelphia 76ers (28-54; 0.3108)
    1. T.J. McConnell – 1.0169
    2. Nik Stauskas – 0.7724
    3. Jerami Grant – 0.7169
  29. Atlanta Hawks (43-39; 0.2571)
    1. Dennis Schroeder – 0.9575
    2. Paul Millsap – 0.7569
    3. Tim Hardaway Jr. – 0.7213
  30. Los Angeles Lakers (26-56; 0.2530)
    1. Larry Nance Jr. – 1.1928
    2. Brandon Ingram – 1.0376
    3. Lou Williams – 0.9232

Some last notes on these numbers. We see that the the Atlanta Hawks are dead last. This is primarily due to the disappearance of Dwight Howard this season. There are 76 of the 486 players that are “negative” players. Dwight Howard is one of these 76 players, ranking 472nd out of 486.

Similarly, the Cavaliers get pulled down dramatically due to Tristan Thompson’s 478th ranking. This is primarily due to teams figuring out ways to score against the Cavaliers when Thompson is on the court.

The Spurs rate low in part due to their large roster. The Spurs had ten players play in at least one-third of possessions. Compare this to the Rockets (8), Raptors (7), and Warriors (5); and we see why the Spurs take a drop; particularly with Dewayne Dedmon and David Lee getting large loads of time.

So who do you think will win the MVP?


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