Ranking NBA Players

The 2015-2016 NBA season is dawning upon us, and as usual, ESPN has been doing their usual #NBArank, where they are ranking players based on the following non-rigorous methodology:

We asked, “Which player will be better in 2015-16?” To decide, voters had to consider both the quality and quantity of each player’s contributions to his team’s ability to win games. More than 100 voters weighed in on nearly 30,000 pairs of players.

Of course, while I suspect this type of thing has to be just for fun , it has generated a great deal of controversy with many arguments ensuing between fans. For example, Kobe Bryant being ranked 93rd overall in the NBA this year gained a fair deal of criticism from Stephen A. Smith on ESPN First Take.

In general, at least to me, it does not make any sense to rank players from different positions that bring different strengths to a team sport such as basketball. That is, what does it really mean for Tim Duncan to be better than Russell Westbrook (or vice-versa), or Kevin Love to be better than Mike Conley (or vice-versa), etc…

From a mathematical/data science perspective, the only sensible thing to do is to take all the players in the league, and apply a clustering algorithm such as K-means clustering to group players of similar talents and contributions into groups. This is not a trivial thing to do, but it is the sort of thing that data scientists do all the time! For this analysis, I went to Basketball-Reference.com, and pulled out last season’s (2014-2015) per game averages of every player in the league, looking at 25 statistical factors from FGA, FG% to STL, BLK, and TOV. One can see that this is a 25-dimensional problem.

Our goal then is to consider the problem where denoting $C_{1}, ... C_{K}$ as sets containing the observations in each cluster, we want to solve the optimization problem:

$\mbox{minimize}_{C_{1},...C_{k}} \left\{\sum_{k=1}^{K} W(C_{k})\right\}$,

where $W$ is our distance measure. We use the squared Euclidean distance to define the within-cluster variation, and then solve:

The first thing to do is to decide how many clusters we want to use in our solution. This is done by looking at the within sum of squares (WSS) plot:

First, we will use 3 clusters in our K-means solution. In this case, the between sum of squares versus total sum of squares ratio was 77.0%, indicating a good “fit”). We use three clusters to begin with, because based on visual inspection, the data clusters very nicely into 3 clusters. The plots obtained were as follows:

The three clusters of players can be found in the following PDF File. Note that the blue circles represent Cluster 1, the red circles represent Cluster 2, and the green circles represent Cluster 3.

Next, we dramatically increase the number of clusters to 20 in our K-means solution.

Performing the K-means clustering, we obtain the following sets of scatter plots. (Note that, it is a bit difficult to display a 25×25 plot on here, so I have split them into a series of plots. Note also, that the between sum of squares versus total sum of squares ratio was 94.8 %, indicating a good “fit”):

The cluster behaviour can be seen more clearly in three dimensions. We now display some examples:

The 20 groups of players we obtained can be seen in the PDF file linked below:

nbastatsnewclusters

The legend for the clusters obtained was:

Two sample group clusters from our analysis are displayed below in the table. It is interesting that the analysis/algorithm provided that Carmelo Anthony and Kobe Bryant  belong in one group/cluster while LaMarcus Aldridge, Lebron James, and Dwyane Wade belong in another cluster.

 Group 16 Group 19 Arron.Afflalo.1 Steven.Adams Carmelo.Anthony LaMarcus.Aldridge Patrick.Beverley Bradley.Beal Chris.Bosh Andrew.Bogut Kobe.Bryant Jimmy.Butler Jose.Calderon DeMarre.Carroll Michael.Carter.Williams.1 Michael.Carter.Williams Darren.Collison Mike.Conley Goran.Dragic.1 DeMarcus.Cousins Langston.Galloway Anthony.Davis Kevin.Garnett DeMar.DeRozan Kevin.Garnett.1 Mike.Dunleavy Jeff.Green.2 Rudy.Gay George.Hill Eric.Gordon Jrue.Holiday Blake.Griffin Dwight.Howard Tobias.Harris Brandon.Jennings Nene.Hilario Enes.Kanter.1 Jordan.Hill Michael.Kidd.Gilchrist Serge.Ibaka Brandon.Knight.1 LeBron.James Kevin.Martin Al.Jefferson Timofey.Mozgov.2 Wesley.Johnson Rajon.Rondo.2 Brandon.Knight Derrick.Rose Kawhi.Leonard J.R..Smith.2 Robin.Lopez Jared.Sullinger Kyle.Lowry Thaddeus.Young.1 Wesley.Matthews Luc.Mbah.a.Moute Khris.Middleton Greg.Monroe Donatas.Motiejunas Joakim.Noah Victor.Oladipo Tony.Parker Chandler.Parsons Zach.Randolph Andre.Roberson Rajon.Rondo P.J..Tucker Dwyane.Wade Kemba.Walker David.West Russell.Westbrook Deron.Williams

If we use more clusters, players will obviously be placed into smaller groups. The following clustering results can be seen in the linked PDF files.

1. 50 Clusters – (between_SS / total_SS =  97.4 %) – PDF File
2. 70 Clusters – (between_SS / total_SS =  97.8 %) – PDF File
3. 100 Clusters – (between_SS / total_SS =  98.3 %) – PDF File
4. 200 Clusters (extreme case) – (between_SS / total_SS =  99.1 %) – PDF File

I did not include the visualizations for these computations because they are quite difficult to visualize.

Looking at the 100 Clusters file, we see two interesting results:

• In Cluster 16, we have: Carmelo Anthony, Chris Bosh, Kobe Bryant and Kevin Martin
• In Cluster 74, we have: LaMarcus Aldridge, Anthony Davis, Rudy Gay, Blake Griffin, LeBron James and Russell Westbrook

CONCLUSIONS:

We therefore see that is does not make much mathematical/statistical sense to compare and two pairs of players. In my opinion, the only logical thing to do when ranking players is to decide on rankings within clusters. So, based on the above analysis, it makes sense to ask for example whether Carmelo is a better player than Kobe or whether Lebron is a better player than Westbrook, etc… But, based on last season’s statistics, it doesn’t make much sense to ask whether Kobe is a better player than Westbrook, because they have been clustered differently. I think ESPN could benefit tremendously by using a rigorous approach to these sorts of things which spark many conversations because many people take them seriously.

The Effect of Kobe Bryant on The Lakers’ Play

Much has been said about the effect that Kobe has had on the Lakers this season. Byron Scott has been limiting his minutes at times, and at times has played him almost the entire game. There have been times this season where analysts and fans of the Lakers have claimed that the team actually plays better without Kobe. We decided to look at these ideas from a statistical perspective.

We looked at a whole bunch of data of Kobe’s play this season (courtesy of Basketball-Reference.com), and compared his individual play to whether the Lakers win games or not. This is what we found.

In this first classification tree, note that ‘Y’ denotes when the Lakers are expected to win, and ‘N’ denotes when they are expected to lose. What we found is any time that Kobe shoots at least 44.95%, the Lakers can be expected to win. If he shoots less than this percentage, then the only way the Lakers can win with Kobe still in the game is if he has less than 3 personal fouls, shoots less than 36.65% from the 3PFG% line and attempts more than 6-7 shots in the game.

From a statistical perspective, the Lakers can win many more games if Byron Scott optimizes the Lakers offense to get Kobe the ball in high-percentage shooting areas of the floor, i.e., closer to the basket than further away from it. Certainly, from a statistical perspective, Byron Scott’s way of allowing Kobe to play “freestyle” basketball is hurting the Lakers’ chances at winning games.

The second classification tree analysis that we did was to look at the whole debate over how many minutes is optimal for Kobe to play. What we found was that if Kobe plays less than 31 minutes in a game, the Lakers can expect to lose that game, while he is on the roster. If he plays more than 31 minutes, and has more than 7-8 assists, the Lakers can expect to win. The only other possibility for the Lakers to win games in this context is if he plays more than 31 minutes, has less than 7-8 assists, makes more than 6-7 of his shots, and plays less than 34-35 minutes a game.

Our previous analysis showed that the Lakers have the best chance of winning consistently when Kobe shoots a high percentage. This analysis shows that it is optimal for him to play between 31-35 minutes a game if he has less than 7 assists, but anytime he has more than 7 assists in a game, the Lakers can be expected to win. Therefore, from an offensive strategy perspective, the Lakers need to play more team-oriented basketball centered around Kobe. In hindsight, which is supported statistically, Kobe and the Lakers would be much better off in a post-oriented offense that promotes distributing the ball, high-percentage shots, and a slow pace. All of these three seem to be completely opposite to how Byron Scott has managed this team this year, and we feel that is why the Lakers have the record that they do!