## So, What’s Wrong with the Knicks?

As I write this post, the Knicks are currently 12th in the Eastern conference with a record of 22-32. A plethora of people are offering the opinions on what is wrong with the Knicks, and of course, most of it being from ESPN and the New York media, most of it is incorrect/useless, here are some examples:

A while ago, I wrote this paper based on statistical learning that shows the common characteristics for NBA playoff teams. Basically, I obtained the following important result:

This classification tree shows along with arguments in the paper, that while the most important factor in teams making the playoffs tends to be the opponent number of assists per game, there are paths to the playoffs where teams are not necessarily strong in this area. Specifically, for the Knicks, as of today, we see that:

opp. Assists / game : 22.4 > 20. 75, STL / game: 7. 2 < 8.0061, TOV / game : 14.1 < 14.1585, DRB / game: 33.8 > 29.9024, opp. TOV / game: 13.0 < 13.1585.

So, one sees that what is keeping the Knicks out of the playoffs is specifically pressure defense, in that, they are not forcing enough turnovers per game. Ironically, they are very close to the threshold, but, it is not enough.

A probability density approximation of the Knicks’ Opp. TOV/G is as follows:

This PDF has the approximate functional form:

P(oTOV) =

Therefore, by computing:

$\int_{A}^{\infty} P(oTOV) d(oTOV)$,

=

,

where Erfc is the complementary error function, and is given by:

$erfc(z) = \frac{2}{\sqrt{\pi}} \int_{z}^{\infty} e^{-t^2} dt$

Given that the threshold for playoff-bound teams is more than 13.1585 opp. TOV/game, setting A = 13 above, we obtain: 0.435. This means that the Knicks have roughly a 43.5% chance of forcing more than 13 TOV in any single game. Similarly, setting A = 14, one obtains: 0.3177. This means that the Knicks have roughly a 31.77% chance of forcing more than 14 TOV in any single game, and so forth.

Therefore, one concludes that while the Knicks problems are defensive-oriented, it is specifically related to pressure defense and forcing turnovers.

By: Dr. Ikjyot Singh Kohli, About the Author

## The Most Optimal Strategy for the Knicks

In a previous article, I showed how one could use data in combination with advanced probability techniques to determine the optimal shot / court positions for LeBron James. I decided to use this algorithm on the Knicks’ starting 5, and obtained the following joint probability density contour plots:

One sees that the Knicks offensive strategy is optimal if and only if players gets shots as close to the basket as possible. If this is the case, the players have a high probability of making shots even if defenders are playing them tightly. This means that the Knicks would be served best by driving in the paint, posting up, and Porzingis NOT attempting a multitude of three point shots.

By the way, a lot of people are convinced nowadays that someone like Porzingis attempting 3’s is a sign of a good offense, as it is an optimal way to space the floor. I am not convinced of this. Spacing the floor geometrically translates to a multi-objective nonlinear optimization problem. In particular, let $(x_i, y_i)$ represent the (x-y)-coordinates of a player on the floor. Spreading the floor means one must maximize (simultaneously) each element of the following distance metric:

subject to $-14 \leq x_i \leq 14, 0 \leq y_i \leq 23.75$. While a player attempting 3-point shots may be one way to solve this problem, I am not convinced that it is a unique solution to this optimization problem. In fact, I am convinced that there are a multiple of solutions to this optimization problem.

This solution is slightly simpler if one realizes that the metric above is symmetric, so that there are only 11 independent components.

## How close were The Knicks to making the Playoffs?

It is another New York Knicks season where fans have to wait until next year to see if the Knicks will make the playoffs or not.

Yesterday, there was a lot buzz around the idea that Phil Jackson may want to keep Kurt Rambis on as head coach, and as usual, there were numerous people that were very vocal in their criticism.

However, in actuality, the Knicks were much closer to the playoffs than people realize. A previous post of mine described in detail using data science methodologies the criteria a team must meet to have a high probability of making the playoffs.

Using the decision tree generated in that post, I evaluated the Knicks playoffs chances this season based on possible playoff criteria scenarios, and found the following:

One sees that a big problem was the Knicks margin of victory, which was too negative. However, even in this case, there are possibilities that existed that would have allowed the Knicks to make the playoffs. For example, a slight increase in the Knicks’ opponent’s field goal attempts or a very slight decrease in the Knicks’ field goal attempts per game would have greatly impacted their playoff chances.

These metrics can easily be adjusted for the upcoming season which will likely require a more organized execution of the triangle offense and discipline on both ends of the floor. They really are almost there!

## What Do NBA Playoff Teams Have in Common?

I’ve been interested for some time on figuring out an analytical way to determine what characterizes an NBA team as a playoff team. Looking at the previous six seasons, I pulled together almost 65 different statistics that characterize how a team plays, and then performed a classification tree analysis. I found the following result:

For the above tree, the misclassification error rate was 2.73%. Also, MOV stands for margin of victory, o3PA is the number of opponent three-point attempts per game, DRtg, is defensive rating, which is the number of points a team allows per 100 possessions, and so on. The data itself was taken from Basketball-Reference.com.

We see that the following patterns emerge among NBA playoff teams over the past number of seasons.

1. MOV > 2.695
2. MOV < -0.54, MOV > -1.825, Opponent 3PA > 16.0732, Defensive Rating < 106.05
3. MOV < -0.54, MOV > -1.825, Opponent 3PA > 16.0732, Defensive Rating > 106.05, FGA < 80.2195
4. MOV < 2.695, Opponent FGA < 82.0671, MOV < 0.295, Opponent FT > 16.7866
5. MOV < 2.695, Opponent FGA < 82.0671, MOV > 0.295
6. MOV < 2.695, Opponent FGA > 82.0671,  Opponent DRB > 29.7683, FGA < 83.128
7. MOV < 2.695, Opponent FGA > 82.0671,  Opponent DRB > 29.7683, FGA < 83.128, MOV < 2.17