Data Analytics and The Raptors 2015 Loss

          Based on several internal statistical models that my colleagues and I developed, we all have concluded that the Raptors losing the way they did in the first round was somewhat of a statistical anomaly. Through an extensive analysis, I present evidence below that shows it was due to several coaching breakdowns in strategy that lead to the Raptors’ collapse. 

Optimal preparedness would have been to prepare and utilize an extensive analysis of the Washington Wizards’ style of play. Using advanced machine learning techniques, we generated two results, first based on tree boosting, and the other based on classification trees that found the weak points in the Wizards’ system that would have greatly helped the Raptors in this series. 

First, one should be interested in the most important commonalities and characteristics in the Wizards’ play. This result is as follows:

One can immediately see that out of several factors, the two most important factors in determining whether the Wizards will win or lose a game is their team FG% and the number of points their opponent score in a game. From this analysis, we obtain that to beat the Wizards, the Raptors should have focused on particularly strong interior defense, and in particular, stopping penetration. From an offensive point of view, the Raptors should have played a strong and slow half-court game focused on getting close-to-the-basket, high-percentage shots, instead of “high-octane” running up and down the court as they seemed to do very frequently. 

Going deeper in this analysis, one also has as a result the following classification tree:

In this tree, “W” and “L” denote whether the Wizards will win or lose a game, “FG.” denotes the Wizards’ FG%,  “OFG.%” denotes the Raptors’ field goal percentage, and “OPTS” denotes the number of points in a game the Raptors should score. One sees that for the Wizards to lose games, the coaching strategy should have been designed to ensure that the Wizards would shoot below 45.25%, while the Raptors should have shot at least 40.3% each game. Complementary to the above analysis, one notes that since three point shots are not fundamental to the Wizards’ offense, to accomplish this, the Raptors should have had strong half-court defensive schemes (including traps and trapping zones), combined with slow-paced, interior offensive schemes. 

In conclusion, it is important to note that these analytical results and ideas were available well in advance of the NBA playoffs, and the Raptors would have tremendously benefited from using these ideas. I would also like to point out that I have only offered a preview of the results I obtained. I have also developed several results pertaining to optimal offensive and defensive schemes that would not only change the way the Raptors play, but would make them significantly better.


NBA Scores Predictions – April 11, 2015

I am testing out a new algorithm that I have been developing over the past few months that attempts to predict the outcome of sports games, in particular, NBA games. I am taking it out for a “Test Run” today. Here is what I predict:


Probabilities in principle are not too difficult to predict assuming you have the correct algorithm! What is more challenging is trying to predict the scores. Here is my prediction for the individual game outcomes:

Team 1

Team 2

Point Difference








































Note: p1 and p2 denote probabilities of each team winning.

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, 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!


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,  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:

knicksplot1From 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:

knicksplot2From 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, 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.

Some of Lemaitre’s Contributions


Many have no doubt heard of Lemaitre’s important contributions to cosmology theory. In this brief post, I provide links to Lemaitre’s original papers:

1. Lemaitre proposing that the universe is expanding: Full paper available here for free

2. Lemaitre proposing that the universe had a beginning, the original Big Bang model: Full paper requires subscription to Nature

Cosmology Lectures on the Web

Here are some links  to some excellent cosmology lectures on YouTube. The videos actually teach you cosmology, as you would see it in a university/college setting. They do require some knowledge of General Relativity, but one in principle, can get away by knowing what a metric tensor is, Christoffel symbols are, and the various Riemann and Ricci tensor definitions. A good book for learning all of this is by Stephani, which is aimed at an introductory level. These lectures are by the world-renowned cosmologist George F.R. Ellis, who is now Professor Emeritus at The University of Cape Town.

Here are some lectures on Cosmology and Philosophy and their importance to one another, these are not at a technical level: