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:

Sikhs in the Army

There has been much noise in recent days of Sikhs wanting to enlist in the U.S. Army and being unable to do so because they insist on following their religious mandates of uncut hair, an untrimmed beard, and covering their hair with a turban. The recent news stories are summarized here:

As usual, a myriad of folks have come out chiding the Sikh person for not conforming by disobeying his religion and removing his hair and beard. Such comments have been supported with questions that have typically come up whenever similar stories have come in the media of how Sikhs are expected to wear gas masks, how can they perform in combat operations without a helmet, etc… The point is that all of these issues are in fact, non-issues and are completely unfounded. There is much literature on Sikhs’ performance in the various wars throughout history and their success in said wars with turbans and beards, so I will not pursue that discussion here. However, I would like to take this opportunity to point out a level of hypocrisy  which people who oppose Sikhs in the military on the aforementioned grounds seem to have a penchant for. Here are just a few examples of countless numbers of White, American soldiers fighting in US conflicts with beards and in some cases, long hair. Why weren’t the same questions and objections raised in their cases?

7a7dce77b24c4e2aa032c295da1d8574 a878778a988ead3e85a1dd6db86b3cb1 jeb_stuart b73da4b73d8ac784e1c44855931c065e images tumblr_lngxnsjmt51qjgeygo1_500 tumblr_mg9p27NYgO1rhfkooo1_1280.png 10471851_1429317854007032_1504366875_a lumberjack_commandos Special-Forces_Hamid_Karzai 5702a68d67a498eb8a9d623bc183841c 4de9f6c939baf7e037b4bbacb7ec2488

Here are just some examples of Sikhs fighting and giving their lives in World War II for the Allied forces. As you can see, there are no technical issues of turbans and beard arising in these cases:

sikh-wars-04 p02btwht Soldier British-Indian-soldiers-examine-a-captured-german-tank tumblr_ln4cj46UwA1qlcc4to1_500 v0_master TwoWorldWarsandtheSikhs_clip_image004 ss-wwII SikhSoldiers10 Indian_sikh_soldiers_in_Italian_campaign 4-sikh_soldiers_manning_a_tank_in_libiya_world_war_two._0 TwoWorldWarsandtheSikhs_clip_image012

Winston Churchill had this to say about Sikhs as well:

“…..It is a matter of regret that due to the obsession of the present times people are distorting the superior religious and social values, but those who wish to preserve them with respect, we should appreciate them as well as help them. Sikhs do need our help for such a cause and we should give it happily. Those who know the Sikh history, know England’s relationship with the Sikhs and are aware of the achievements of the Sikhs, they should persistently support the idea of relaxation to Sikhs to ride a motorbike with their turbans on, because it is their religious privilege.”

Churchill, further added:

“…British people are highly indebted and obliged to Sikhs for a long time. I know that within this century we needed their help twice and they did help us very well. As a result of their timely help, we are today able to live with honour, dignity, and independence. In the war, they fought and died for us, wearing the turbans. At that time we were not adamant that they should wear safety helmets because we knew that they are not going to wear them anyways and we would be deprived of their help. At that time due to our miserable and poor situation, we did not force it on them to wear safety helmets, why should we force it now? Rather, we should now respect their traditions and by granting this legitimate concession, win their applaud.”

So, we should all strive to be a bit more educated in this regard. These exemptions have been granted to White, American soldiers in the past, and even if not in a formal sense, there is an eerie silence coming from the same critics of Sikhs wanting to join the military when non-Sikhs have also not conformed to these rules as the above pictures clearly demonstrate.

A Universe from Nothing

Many people have obviously been reading Lawrence Krauss’ infamous book: “A Universe from Nothing: Why There is something Rather Than Nothing”

Krauss and many other physicists continuously engage in this type of low-level philosophy with the ironic goal of diminishing the value of philosophy using “science”.

This paper dissects all the arguments in Krauss’ book and shows from a mathematical standpoint that like others who make similar arguments, they are not grounded in actual physics and are extremely flawed. One therefore concludes, that such arguments are not based in science, but in bad philosophy.

The paper: A Universe from Nothing

A teaser: This is what “nothing” actually looks like, well one depiction of it anyways:
IMG_0117But this is not nothing, it is something, where did this structure come from? Krauss actually ignores the question entirely in his book, which is very strange.

The famed cosmologist George Ellis also has discussed Krauss’ book in one of his talks, here is the link for that:

A video making some of the arguments in the above paper easier to understand can be found here: