## The “Interference” of Phil Jackson

By: Dr. Ikjyot Singh Kohli

So, I came across this article today by Matt Moore on CBSSports, who basically once again has taken to the web to bash the Triangle Offense. Of course, much of what he claims (like much of the Knicks media) is flat-out wrong based on very primitive and simplistic analysis, and I will point it out below. Further, much of this article seems to motivated by several comments Carmelo Anthony made recently expressing his dismay at Jeff Hornacek moving away from the “high-paced” offense that the Knicks were running before the All-Star break:

“I think everybody was trying to figure everything out, what was going to work, what wasn’t going to work,’’ Anthony said in the locker room at the former Delta Center. “Early in the season, we were winning games, went on a little winning streak we had. We were playing a certain way. We went away from that, started playing another way. Everybody was trying to figure out: Should we go back to the way we were playing, or try to do something different?’’

Anthony suggested he liked the Hornacek way.

“I thought earlier we were playing faster and more free-flow throughout the course of the game,’’ Anthony said. “We kind of slowed down, started settling it down. Not as fast. The pace slowed down for us — something we had to make an adjustment on the fly with limited practice time, in the course of a game. Once you get into the season, it’s hard to readjust a whole system.’’

First, it is well-known that the Knicks have been implementing more of the triangle offense since All-Star break. All-Star Weekend was Feb 17-19, 2017. The Knicks record before All-Star weekend was amusingly 23-34, which is 11 games below .500 and is nowhere mentioned in any of these articles, and is also not mentioned (realized?) by Carmelo.

Anyhow, the question is as follows. If Hornacek was allowed to continue is non-triangle ways of pushing the ball/higher pace (What Carmelo claims he liked), would the Knicks have made the playoffs? Probably not. I claim this to be the case based on a detailed machine-learning-based analysis of playoff-eligible teams that has been available for sometime now. In fact, what is perhaps of most importance from this paper is the following classification tree that determines whether a team is playoff-eligible or not:

So, these are the relevant factors in determining whether or not a team in a given season makes the playoffs. (Please see the paper linked above for details on the justification of these results.)

Looking at these predictor variables for the Knicks up to the All-Star break.

1. Opponent Assists/Game: 22.44
2. Steals/Game: 7.26
3. TOV/Game: 13.53
4. DRB/Game: 33.65
5. Opp.TOV/Game: 12.46

Since Opp.TOV/Game = 12.46 < 13.16, the Knicks would actually be predicted to miss the NBA Playoffs. In fact, if current trends were allowed to continue, the so-called “Hornacek trends”, one can compute the probability of the Knicks making the playoffs:

From this probability density function, we can calculate that the probability of the Knicks making the playoffs was 36.84%. The classification tree also predicted that the Knicks would miss the playoffs. So, what is being missed by Carmelo, Matt Moore, and the like is the complete lack of pressure defense, hence, the insufficient amount of opponent TOV/G. So, it is completely incorrect to claim that the Knicks were somehow “Destined for glory” under Hornacek’s way of doing this. This is exacerbated by the fact that the Knicks’ opponent AST/G pre-All-Star break was already pretty high at 22.44.

The question now is how have the Knicks been doing since Phil Jackson’s supposed interference and since supposedly implementing the triangle in a more complete sense? (On a side note, I still don’t think you can partially implement the triangle, I think it needs a proper off-season implementation as it is a complete system).

Interestingly enough, the Knicks opponent assists per game (which, according to the machine learning analysis is the most relevant factor in determining whether a team makes the playoffs) from All-Star weekend to the present-day is an impressive 20.642/Game. By the classification tree above, this actually puts the Knicks safely in playoff territory, in the sense of being classified as a playoff team, but it is too little, too late.

The defense has actually improved significantly with respect to the key relevant statistic of opponent AST/G. (Note that, as will be shown in a future article, DRTG and ORTG are largely useless statistics in determining a team’s playoff eligibility, another point completely missed in Moore’s article) since the Knicks have started to implement the triangle more completely.

The problem is that it is obviously too little, too late at this point. I would argue based on this analysis, that Phil Jackson should have actually interfered earlier in the season. In fact, if the Knicks keep their opponent Assists/game below 20.75/game next season (which is now very likely, if current trends continue), the Knicks would be predicted to make the playoffs by the above machine learning analysis.

Finally, I will just make this point. It is interesting to look at Phil Jackson teams that were not filled/packed with dominant players. As the saying goes, unfortunately, “Phil Jackson’s success had nothing to do with the triangle, but, because he had Shaq/Kobe, Jordan/Pippen, etc… ”

Well, let’s first look at the 1994-1995 Chicago Bulls, a team that did not have Michael Jordan, but ran the triangle offense completely. Per the relevant statistics above:

1. Opp. AST/G = 20.9
2. STL/G = 9.7
3. AST/G = 24.0
4. Opp. TOV/G = 18.1

These are remarkable defensive numbers, which supports Phil’s idea, that the triangle offense leads to good defense.

## 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

## 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

## Breaking Down the Knicks’ Season

Like many of my fellow Knicks fans, I am in an absolute state of shock and disappointment as the Knicks are currently 5-29 to start the new year! Many analysts from the standard outlets, ESPN, Yahoo! sports, etc… have given their share of reasons why the Knicks are playing the way they are. Being a mathematical physicist and data scientist, I decided to see if one could deduce any useful information from how the Knicks have been playing to see what is the true reason why they are losing all of these games. Here is what I found. Based on the data available at Basketball-Reference.com,  I designed an algorithm in R to go through each game, and fit regression trees (Here is a link to more on regression trees if you are unfamiliar with the concept) and found the following:

1. The number of points the Knicks score per game:

From this regression tree, we see that if the Knicks for example make less than 33.5 FG’s in a game, and have a 3-Point shooting percentage of less than 0.309, they will be expected to score no more than 79 points in a game. On the other hand, if they make more than 38.5 FG’s in a game, and also attempt more than 19 free throws in a game, they can be expected to score more than 111 points in a game.

2. The number of points the Knicks’ opponents score per game:

From this regression tree, note that first “Tm” denotes how many points the Knicks score in a game. We see that for example, if the Knicks have less than 28 defensive rebounds in a game, also score less than 98 points in a game, and have fewer than 4-5 blocks in a game, their opponents will slightly outscore them, and win the game. In fact, if the Knicks manage to get less than 28-29 defensive rebounds per game, and score less than 98 points in a game, they will be expected to lose every game they play! Now, let’s say, the Knicks do manage to get more than 28 defensive rebounds in a game, if they still only manage to score less than 89 points in a game, they are still almost guaranteed to lose as well.

Although, many analysts have probably pointed these things out, the conclusion one draws from these regression tree analyses, is that the Knicks have a significant problem with defensive rebounding, as that seems to be the number one factor in them not winning games. Further, they also have a significant problem with how many points they score per game, which is a direct result of this Knicks team still not running their offense correctly.

Would Tyson Chandler have made a difference? As the above analyses show, no single factor determines whether the Knicks win games or not. It is reasonable to assume that if Tyson Chandler was on the team, then, the Knicks would get more than 28-29 defensive rebounds in a game. But, according to the above analyses, and the right of the previous regression team, if they still as a team would attempt more than 78-79 field goals, they would still be expected to lose every game. The question then remains would Tyson Chandler’s presence increase the Knicks’ offensive efficiency? In principle, according to his career FG% stats, I would say yes. According to Basketball-Reference.com, Tyson Chandler had a FG% of 0.638 while in New York, and for his career has a FG% of 0.588, which is quite high for NBA standards. It is quite reasonable to assume therefore, that the Knicks would have considerably less FGA’s (certainly less than 78-79) in a game, and their opponents would be held to around 91.0 points per game. One would conclude that from a statistical perspective, trading away Tyson Chandler was perhaps a mistake and had an overall negative impact on the team’s performance both defensively and offensively.