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.

On the Importance of Solar Eclipses

As has been well documented over recent days, there has been great excitement over the recent activity of full and partial solar eclipses, with students, astronomy enthusiasts, etc… all over showing great enthusiasm. However, a vast majority seem to be completely unaware as to why these solar eclipses are so important. Their most important purpose is that one can directly confirm as Eddington did in 1919 the validity of Einstein’s theory of General Relativity. When the sun is eclipsed, one can directly observe starlight from behind the sun being bent as should happen according to Einstein’s theory, namely that light bends according to the curvature of spacetime. I document here a brief calculation that demonstrates this:

We will assume that the spacetime under consideration is spherically symmetric and static, and so by Birkhoff’s theorem, outside the spherically symmetric body, the solution to Einstein’s equations is the well-known Schwarzschild metric:

eq1 To determine an equation for the path that light should follow in this spacetime, one writes the associated Lagrangian of geodesics as:

Applying the Euler-Lagrange equations and exploiting the fact that the spacetime is spherically symmetric and static, one obtains the orbit equation for light as:


More on this calculation can be found in my handwritten notes by clicking the image below: 

For the Sun, the deflection angle turns out to be approximately


That is, the curvature of spacetime induced by the Sun causes starlight from behind the sun to be “bent”/deflected by 1.75”. This is precisely what Eddington’s team observed in their 1919 expedition. This test was what finally confirmed Einstein’s theory of General Relativity, and is the true reason why solar eclipses are so important!