I wrote an extensive application using NLP and TensorFlow/Keras in Python that looks at all of the current and upcoming Hollywood releases for 2020 and tracks the online Twitter sentiment for each of them. The model output was then displayed in a PowerBI dashboard. In essence, we are predicting the classification probability .

You can access the dashboard by clicking on the screenshot below:

We have also included a new feature that gives a daily popularity score for movies. An algorithm was designed to rank movies according to daily positive sentiment. This can be found on Page 2 of the dashboard link.

You can select different titles by clicking the dropdown list. The left-side graph shows you the sentiment distribution of all of the tweet data corresponding to a film. The right-side graph calculates the median tweet sentiment for a given day for the selected film. (Right now, we go back 30 days from the present day). It is intended that this dashboard will be refreshed every day.

Abstract: It is shown that the standard/common definition of team offensive rating/offensive efficiency implies that a team’s offensive rating increases as its opponent’s offensive rebounds increase, which, in principle, should not be the case.

Over the past number of years, the advanced metric known as Offensive Rating has become the standard way of measuring a basketball team’s offensive efficiency. Broadly speaking, it is defined as points scored per 100 possessions. Specifically, for teams, it is defined as (See: https://www.basketball-reference.com/about/ratings.html and https://www.nbastuffer.com/analytics101/possession/ AND https://fansided.com/2015/12/21/nylon-calculus-101-possessions/):

There is a significant issue with this definition as I now demonstrate. Let us compute the partial derivative of this expression with respect to OppORB, we easily obtain:

As the denominator is always positive, we would like to examine the numerator. The numerator is always negative due to physical constraints (i.e., can’t have negative points or rebounds!) and if OppFG < OppFGA, which makes intuitive sense. It is only positive if OppFG > OppFGA, which logically cannot happen. Therefore, this numerator is always negative (except for the rare case when OppFG = OppFGA of course), which means that the entire partial derivative is positive.

This means that a team’s offensive rating / offensive efficiency increases as it’s opponent’s offensive rebounds increase. Intuitively, this shouldn’t be the case. If your opponent has a high number of offensive rebounds, this should give you less possessions, and put pressure on you to score, thus resulting in less points overall. The problem is that the more general definition of offensive efficiency is 100*(Points Scored)/(Possessions), which is obviously maximized when possessions is minimized. The problem of course, is that the more detailed definition of possessions implies that this minimization of possessions occurs at the cost of maximizing opponent offensive rebounds, which intuitively should not be the case.

Here is an embedded dashboard that shows a number of statistical insights for NBA teams, their opponents, and individual players as well. You can compare multiple teams and players. Navigate through the different pages by clicking through the scrolling arrow below. (The data is based on the most recent season “per-game” numbers.)

(If you cannot see the dashboard embedded below for whatever reason, click here to be taken directly to the dashboard in a separate page.)

The Golden State Warriors have posed quite the conundrum for opposing teams. They are quick, have a spectacular ability to move the ball, and play suffocating defense. Given their play in the playoffs thus far, all of these points have been exemplified even more to the point where it seems that they are unbeatable.

I wanted to take somewhat of a simplified approach and see if opposing teams are missing something. That is, is their some weakness in their play that opposing teams can exploit, a “weakness in Helm’s deep”?

The most obvious place to start from a data science point-of-view seemed to me to look at every single shot the Warriors took as a team this season in each game and compile a grand ensemble shot chart. Using the data from Basketball-reference.com and some data scraping scripts I wrote in R, I obtained the following:
Certainly, on the surface, it seems that there is no discernible pattern between made shots and missed shots. This is where the machine learning comes in!

From here, I now extracted the x and y coordinates of each shot and recorded a response variable of “made” or “missed” in a table, such that the coordinates were now predictor variables and the shot classification (made/missed) was the response variable. Altogether, we had 7104 observations. Splitting this dataset up into a 70% training dataset and a 30% test data set, I tried the following algorithms, recording the % of correctly classified observations:

Algorithm

% of Correctly Predicted Observations

Logistic Regression

56.43

Gradient Boosted Decision Trees

62.62

Random Forests

58.54

Neural Networks with Entropy Fitting

62.47

Naive Bayes Classification with Kernel Density Estimation

57.32

One sees that that gradient boosted decision trees had the best performance correctly classifying 62.62% of the test observations. Given how noisy the data is, this is not bad, and much better than expected. I should also mention that these numbers were obtained after tuning these models using cross-validation for optimal parameters.

Using the gradient boosted decision tree model, we made a set of predictions for a vast number of (x,y)-coordinates for basketball court. We obtained the following contour plot:

Overlaying this on top of the basketball court diagram, we got:

The contour plot levels denote the probabilities that the GSW will make a shot from a given (x,y) location on the court. As a sanity check, the lowest probabilities seem to be close to the 1/2-court line and beyond the three-point line. The highest probabilities are surprisingly along very specific areas on the court: very close the basket, the line from the basket to the left corner, extending up slightly, and a very narrow line extending from the basket to the right corner. Interestingly, the probabilities are low on the right side of the basket, specifically:

A map showing the probabilities more explicitly is as follows (although, upon uploading it, I realized it is a bit harder to read, I will re-upload a clearer version soon!)

In conclusion, it seems that, at least according to a first look at the data, the Warriors do indeed have several “weak spots” in their offense that opponents should certainly look to exploit by designing defensive schemes that force them to take shots in the aforementioned low-probability zones. As for future improvements, I think it would be interesting to add as predictor variables things like geographic location, crowd sizes, team opponent strengths, etc… I will look into making these improvements in the near future.

I have now made a significant update to my applied machine learning paper on predicting patterns among NBA playoff and championship teams, which can be accessed here: arXiv Link .

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 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 . 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.

Where is Lebron James most effective on the court?

Based on 2015-2016 data, we obtained from NBA.com the following data which tracks Lebron’s FG% based on defender distance:

From Basketball-Reference.com, we then obtained data of Lebron’s FG% based on his shot distance from the basket:

Based on this data, we generated tens of thousands of sample data points to perform a Monte Carlo simulation to obtain relevant probability density functions. We found that the joint PDF was a very lengthy expression(!):

Graphically, this was:

A contour plot of the joint PDF was computed to be:

From this information, we can compute where/when LeBron has the highest probability of making a shot. Numerically, we found that the maximum probability occurs when Lebron’s defender is 0.829988 feet away, while Lebron is 1.59378 feet away from the basket. What is interesting is that this analysis shows that defending Lebron tightly doesn’t seem to be an effective strategy if his shot distance is within 5 feet of the basket. It is only an effective strategy further than 5 feet away from the basket. Therefore, opposing teams have the best chance at stopping Lebron from scoring by playing him tightly and forcing him as far away from the basket as possible.