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:

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 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.

2014 in review

The WordPress.com stats helper monkeys prepared a 2014 annual report for this blog.

Here’s an excerpt:

The Louvre Museum has 8.5 million visitors per year. This blog was viewed about 83,000 times in 2014. If it were an exhibit at the Louvre Museum, it would take about 4 days for that many people to see it.

Click here to see the complete report.

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:

2014 US Senate Midterm Elections Predictions

Using methods from stochastic calculus, brownian motion, and statistical mechanics, we have developed algorithms to predict the outcome of the 2014 US Senate Midterm elections. You can find our results below. Note, the raw data was obtained from http://elections.huffingtonpost.com/pollster, a great service provided by Huffington Post. We used MATLAB to implement the algorithms and create the output. These algorithms were completed under ISK Analytics Inc. and the data extraction and research was done by Hargun Singh Kohli

These graphs show the probability of each candidate winning the November, 2014 elections.
These graphs show the probability of each candidate winning the November, 2014 elections.

 

The graphs above were generated by our stochastic calculus algorithms, in which we generate 100,000 random walks to obtain the predictions above. We show below the output of these random walks on election day. For brevity and clarity, we have shown the results of the first 100 random walks, but the pattern is clear.

The results of our random walk experiments based on our stochastic calculus algorithms. These results show the candidate's popular vote percentage on election day, November 4, 2014.
The results of our random walk experiments based on our stochastic calculus algorithms. These results show the candidate’s popular vote percentage on election day, November 4, 2014.

The output summary generated by our algorithm is as follows:

Arkansas
Cotton:62.77 % chance of winning.
Pryor:37.23 % chance of winning.
Cotton final poll:45.4389 +/-13.7051 %
Pryor final poll:40.1777 +/-11.3596 %
Colorado
Udall:82.87 % chance of winning.
Gardner:17.13 % chance of winning.
Udall final poll:49.1646 +/-7.0376 %
Gardner final poll:41.1147 +/-5.8643 %
Iowa
Ernst:38.5 % chance of winning.
Braley:61.5 % chance of winning.
Ernst final poll:39.1375 +/-15.7919 %
Braley final poll:44.9138 +/-7.4095 %
Kentucky
McConnell:65.93 % chance of winning.
Grimes:34.07 % chance of winning.
McConnell final poll:47.4181 +/-8.8916 %
Grimes final poll:42.9658 +/-9.5813 %
Louisiana
Cassidy:19.29 % chance of winning.
Landrieu:80.71 % chance of winning.
Cassidy final poll:41.9593 +/-7.9842 %
Landrieu final poll:50.4055 +/-8.2332 %
Montana
Daines:94.93 % chance of winning.
Walsh:5.07 % chance of winning.
Daines final poll:53.3766 +/-9.0295 %
Walsh final poll:35.322 +/-3.7087 %
New Hampshire
Shaheen:78.07 % chance of winning.
Brown:21.93 % chance of winning.
Shaheen final poll:47.391 +/-12.3806 %
Brown final poll:34.9852 +/-10.5021 %
North Carolina
Hagan:74.2 % chance of winning.
Tillis:25.8 % chance of winning.
Hagan final poll:48.4451 +/-11.8512 %
Tillis final poll:39.8438 +/-9.723 %
Oregon
Merkley:77.01 % chance of winning.
Wehby:22.99 % chance of winning.
Merkley final poll:48.5639 +/-13.0143 %
Wehby final poll:36.7674 +/-11.6739 %
South Dakota
Rounds:88.4 % chance of winning.
Weiland:11.6 % chance of winning.
Rounds final poll:53.0504 +/-11.9886 %
Weiland final poll:37.8299 +/-7.6665 %
Virginia
Warner:95.65 % chance of winning.
Gillespie:4.35 % chance of winning.
Warner final poll:51.0216 +/-9.7838 %
Gillespie final poll:24.1766 +/-9.2446 %
West Virginia
Capito:74.88 % chance of winning.
Tennant:25.12 % chance of winning.
Capito final poll:47.727 +/-8.291 %
Tennant final poll:40.2505 +/-8.0285 %