Applied Efficiency: A New NBA Scoring Efficiency Stat


by Baltej Parmar

Comparing players is the stock in trade of fandom. Whatever your team, everyone wants to know which player is better than his peers. Statistics allow us to compare various aspects of player performance – perhaps most notably efficiency. “Russell Westbrook has a career FG% of .434, while Stephen Curry has a FG% of .476. The difference isn’t much.” Are we sure that a difference of .042 is not much, though? The scale of statistics can make it difficult to use them responsibly in comparisons. In the example above, Curry makes 42 shots more than Westbrook out of 1,000. Since a player doesn’t take 1,000 shots in a game, it is not directly obvious how much more likely Curry’s team is to win a game based on the difference in FG%. What if we had a better way to measure how much a player’s shooting impacts the score on a game-by-game basis? That’s why I’m introducing Applied Efficiency, a new NBA stat which does just that.

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Who is Really the Best Defensive Center in the League?


As with the previous posts in this series which detailed the best defenders at each position, I start with the question “Who are the best defensive centers in the league?” In order to address the question properly when evaluating centers, however, it is necessary to answer a prior question. What is a center’s defensive role in the modern NBA? During some prior eras, the center could remain near the basket either defending a fellow behemoth on the low block or walling off the path of opposing drives. Rule changes constricted the scope of zone defense. Then, the 3-point shooting revolution caught even big men in its tantalizing web. For the first time in basketball history, forces conspired to pull centers away from the basket for good.

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Failure to Launch


by Alan Moghaddam

The Houston Rockets are at a point of critical failure – or rather, they have reached a crux with more than one point of critical failure.

The Rockets’ record stands at 13-7 roughly a quarter of the way into the regular season. It has finally been long enough to shake off the “it’s too early to comment” crowd, and we can finally make some valid statement about this team long-term. To all appearances, things are not looking particularly spectacular for a team that entered the season with championship expectations.

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What is TPA?


by Alan Moghaddam

Chances are if you’re into sports you’ve seen the famed charts from @NBA_Math that feature overlapping pictures of NBA players in a conventional Cartesian plot with a line plotted on it (y=-x). Anything above the line is good, anything below is bad, and average values will tend to walk the line. The graph is a visual attempt to quantify some mystery statistic known as TPA.

This is a standard TPA graph from @NBA_Math

What is TPA?

This is something of a loaded question; the acronym TPA stands for “Total Points Added”. The basic idea behind it is that a player adds points on offense and defense. You then total these subsections to get TPA.

Unfortuantely, the definition above is rather incomplete. We now need to understand Offensive Points Added (OPA) and Defensive Points Saved (DPS), the components which make up TPA. The two subcategories are much more complex than TPA alone.

To get OPA and DPS, we need to use “Box Plus/Minus,” an all-in-one statistic created by Daniel Myers and hosted at basketball-reference.com. I promise we are almost at the bottom of the well here in terms of stat definitions. Box Plus/Minus is a relativistic stat that gauges a player’s impact on team performance when s/he is on the court. S/he again will have an impact on both defense and offense, so accordingly Box Plus/Minus can break down into two stats: Offensive Box Plus/Minus (OPBM) and Defensive Box Plus/Minus (DPBM). We can already see that TPA has the same structure as Box Plus Minus; both purport to measure a player’s impact on both ends of the floor. What is the difference between the two?

Equation 1. Calculation of TPA as a function of Defensive Points Saved and Offensive Points Awarded
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A Prediction Model for Sports Match Results – Part 2



As outlined in the first post, this installment of the series will be about the model’s estimates and predictions. I will also touch on how to compare predictions between models. For all that to work, I will have to introduce a few mathematical definitions. In a similar way to the first post, I will give both an intuitive explanation of every concept and a mathematical explanation.

The Estimates section will begin with an explanation of how the model fits the data (with a few graphs to show the process of finding the estimates for last season’s NBA), followed by a brief introduction on Bayesian inference. Next, the Model Comparisons section will define the predictive likelihood of a model, and how to calculate it. I will also discuss a few different ways to compare predictions. Finally, in the Discussion section, I will offer critiques of the work presented in this post.

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The Best Defensive Power Forwards in the NBA


Small ball is no longer the wave of the future – it’s the wave of the present. The 80’s and 90’s featured brawny, bruising power forwards who could soak up punishment in the post, clean the glass, and protect the paint as weak side shot blockers. In a game dominated by giants, power forwards were the centers’ sidekicks. Even the beginning of the 21st century saw the San Antonio Spurs’ “Twin Towers” follow the same frontcourt structure that had held sway throughout the league’s existence.

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A Prediction Model for Sports Match Results


by André Vizzoni


In this post, I will introduce a prediction model that was the product of a research project that spanned four years (winning a few awards) and was the final project for my degree in Statistics. For those interested in the final project, here it is – though I warn everyone in advance that it is in Portuguese. The objective of this post, then, is to translate the most central parts of that project to English while, at the same time, talking about applications of the model to basketball data, since the original project used soccer data.

First, I will give an intuitive explanation of the model, with no equations or mathematical concepts introduced. Next will come the methodology section, where there will be a lot more maths and formal definitions. As such, people who are interested only on the intuitive definitions might wish to skip the methodology section). The idea behind this structuring of the post is for it to be understandable, both by laypeople and by people well versed in statistics. Finally, in the discussion section there will be a few summary comments, as well as a preview of things to come on this site.

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The Best Defensive Small Forwards in the NBA


In the last installment of this series, we evaluated the best defensive shooting guards. We noted that the shooting guard group is crucial in the modern NBA due to the advantages gained by employing versatile defenders capable of stopping opponents of different sizes and skill sets. The same rationale applies for the players in the “small forward” bin using basketball-reference.com’s play-by-play position designations. When compared with the previous group, the main difference is that the small forwards are larger. (perhaps we should start calling them “big wings”?)

Wings, whether they are categorized as “shooting guards” or “small forwards,” exhibit greater spread in the defensive load they carry than other position groups do.

While the median values are relatively consistent across positions, wings have a wider distribution than other positions. Raw defensive load for wings can range from very high (>15 ppg) to very low (<6 ppg). Other positions, especially interior defenders, have much more compressed distributions.

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Who Are the Best Defensive Shooting Guards in the League?


The NBA changes as rapidly as the seasons, and the league is heading toward a greater and greater reliance on versatile perimeter players. The prevalence of 3-pointers, combined with the emergence of bigger primary ball handlers replacing some of the smaller “point guards” of previous eras, has resulted in a single mandate for NBA defenses: to find defenders who are big enough and quick enough to guard anyone.

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Who are the Best Defensive Point Guards in the NBA?


Rankings are among the most popular exercises for most NBA fans, and also among the least efficient ways to evaluate data. The enduring appeal of rankings and lists owes to their relationship, however tangential, with the big questions: Who is the best? Which player is better? How much better or worse would a team be if they replaced this player with that one? Every fan, analyst, scout, coach, and executive needs to be able to answer these questions.

The problem with rankings is not the questions they address, but the biases implicit in ordinal numbering. Our brains are trained to think that the difference between 12 and 17 is the same as the difference between 18 and 23, and that all these values are on a different order of magnitude from single digit numbers. When we transfer these assumptions to rankings of the “Top 50 Players in the NBA” or something similar, we start with false presuppositions. There is not an identical difference in value between each pair of contiguous players on any player ranking. Even a hypothetically perfect, pie-in-the-sky ranking that ranked players in the exactly correct order would still need something besides the ranking to indicate the players’ true value relative to their peers. Our habit of using ordinal numbers to rank players blinds us to the shape of the data.

As a result, both league insiders and outsiders spend an inordinate amount of time debating questions such as “Is Kevin Durant the second-best player in the league or the eighth-best?” “Is Paul George a top 5 player, a top 10 player, or a top 15 player?” What really matters is how much a player contributes to wins by helping put points on the board (on offense) and keep points off the board (on defense). If the 6th ranked player in the league and the 16th ranked player are nearly identical in terms of their contribution to team success, it makes little sense to lay so much weight on their difference in the rankings.

What a valuable ranking system can tell us is how much value a player generates, relative to the rest of the population. In answering the question posed in the title of this article, I will attempt to provide enough context for the reader to be able to comprehend the shape of the data. As such, let’s start with refining the question itself:

Who are the best defensive point guards in the league?

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