Sep 15 2009

Mathletics Part III: Basketball

Like any other self-respecting basketball geek, the first part of Wayne Winston‘s new book Mathletics I read was Part III: Basketball.

Before diving into what I think about this part of the book, I think it’s important to spell out the intent of the book. Although it has math in the title, this book isn’t filled with a bunch of scary math.

Instead, this book is intended to introduce the reader to various models that are used to analyze sports, with the idea that some of these models are actually being used in practice by team management to aid in the decision making process. This means you’re not going to see a lot of discussion as to the theoretical underpinnings of the models. You’ll instead see practical implementation of the models.

So even though there is math in this book, it’s built from the ground up as the book progresses. If you have some prior experience with elementary statistics and regression then you should have no problems skipping ahead to the basketball part of the book.

Here are the chapters of the basketball part of Mathletics:

  • Basketball Statistics 101
  • Linear Weights for Evaluating NBA Players
  • Adjusted +/- Player Ratings
  • NBA Lineup Analysis
  • Analyzing Team and Individual Matchups
  • NBA Players’ Salaries and the Draft
  • Are NBA Officials Prejudiced?
  • Are College Basketball Games Fixed?
  • Did Tim Donaghy Fix NBA Games?
  • End-Game Basketball Strategy

I don’t want to give away all of Wayne’s hard work, but I do want to give you a sense of what you’ll find in these chapters of the book.

The first chapter, Basketball Statistics 101, introduces the reader to Dean Oliver‘s four factors of basketball success. Wayne also uses a regression to show how these factors relate to wins, in a similar fashion to this regression by Ed Küpfer, except that Ed looked at win percentage instead of total season wins. The only issue I have with Wayne’s regression is that it seems like there should be a way to transform the data to make the coefficients easier to interpret. This is mere speculation on my part, though. You can still interpret them without too much effort, and he shows you how to do so with a minimal amount of math.

I think it’s worth noting that if you haven’t done so already, it’s after finishing this chapter where you might want to read the paper A Starting Point for Analyzing Basketball Statistics.

The next chapters, Linear Weights for Evaluating NBA Players and Adjusted +/- Player Ratings, cover evaluating individual players. The reader is first introduced to the linear weight ratings of NBA Efficiency Rating, Player Efficiency Rating (PER), and Win Scores/Wins Produced. Because they’re based on the box score, we know that these ratings do not capture the entire game, and I like how Wayne details inadequacies with these models by showing how these metrics reward bad players for doing stuff they shouldn’t do.

After taking a tour of these measures, the Adjusted +/- Player Ratings chapter covers one way of estimating player value that attempts to equally weight a player’s offensive and defensive abilities using play-by-play data instead of the box score. I believe that Dan Rosenbaum‘s adjusted +/- article was the first public attempt to re-create what Wayne outlines in this chapter.

One thing that has always confused me about the various published adjusted +/- ratings is the use of minutes versus possessions as a measure of time in the model formulation. I’ll let you read the book to see exactly what Wayne does, but a lingering question I have is: “Why would I want to use minutes instead of possessions?” Speaking of exactly what Wayne does, at the end of the chapter he shows you how to use Excel Solver to find adjusted +/- ratings (you may also be interested in how Eli Witus‘ fit a similar model with Excel here and here, and you can find a wealth of ratings at Basketball Value).

The next two chapters, NBA Lineup Analysis and Analyzing Team and Individual Matchups, cover topics I’m very interested in. Adjusted +/- ratings are useful, but ultimately I want to know how players perform together and how they perform against other player combinations. These chapters give some insight into how Wayne does this for the Mavs (speaking of which, my sense is that these two chapters only cover a combined 9 pages because of these obligations).

These chapters give us a general idea of how these ratings are calculated, but we don’t exactly get a handy Excel tutorial to guide us through the process. One thing I don’t like about the lineup analysis chapter is the use of the standard error of the mean (at least as it’s used in the book) as a crutch to determine if one lineup is better than another. I think it’s more complicated than that. I don’t have a rigorous rebuttal to this, so I’ll simply say that it feels dirty to me. I usually like dirty, I just don’t like it in the world of math. I think this is certainly something worth studying, and I hope it turns out to be a case of me trying to make things more complicated than they have to be, which I tend to often do.

I like the examples given in the matchups chapter, and it makes me want to study the finer points of this type of analysis. Wayne gives an interesting example from the 2006 NBA playoffs to illustrate the point, and I would like to know how this holds on a larger level. He can’t give away the toolbox, but he has at least given motivation for things to look at.

The final chapters in this part of the book cover topics outside the realm of quantifying team strength and player value. The NBA Players’ Salaries and the Draft chapter explores a model for determining if the NBA draft is efficient. I’ve never studied this kinda thing, so the results were interesting to see.

In the next chapters, Are NBA Officials Prejudiced? and Did Tim Donaghy Fix NBA Games?, Wayne shows how we might try to analyze these topics, and what conclusions we’d want to arrive at based on the analysis.

The final chapter of the basketball part of Mathletics is End-Game Basketball Strategy, where we want to know what shot to take when down by 2, and if we should foul when we’re up by 3. This is a topic that intrigues me, especially after reading the paper Optimal End-Game Strategy in Basketball, where I felt the restrictions on the model were perhaps too simplistic, which is again a case of me maybe making things more complicated than they have to be. I’m not alone, though, as Wayne notes he is working on a simulation model to help solve this problem, which is something that makes a lot of sense. The good news is Wayne presents some general results and performs a sensitivy analysis on the model, which gives you an idea as to what conclusions you would draw for various inputs to the model.


I have a hunger for information, so of course Mathletics was simply a large dinner that will only hold me over for so long.

That said, I think that the book does a great job of accomplishing its goal: introducing the reader to real world models used in analyzing sports. This of course assumes Wayne has done as good a job with the other parts of the book as he’s done with the basketball part, but I don’t think that’s too much of a stretch.

To read more of Wayne’s work related to the book, see his blog at, and you can follow Wayne on Twitter @winston3453.

9 Comments on this post


  1. Is One Lineup Better Than Another? wrote:

    […] part of Wayne Winston’s new book Mathletics that I didn’t really like was the way he compared raw lineup data to determine if one lineup […]

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  1. edkupfer said:

    Thanks for the review. I’ll be picking it up as soon as it’s available here.

    September 15th, 2009 at 2:48 pm
  2. David said:

    The CREZ basketball software system has the ability to calculate Dean Oliver’s statistics. All you need to do is input existing box scores or calculate live stats yourself.

    Everything is self-contained in the product.

    Note: the whole product can be demo’d for 30 days. After 30 days, the CREZscorer system remains for free which allows you to enter rosters, score games, webcast stats, and print reports.


    September 16th, 2009 at 1:16 pm
  3. David said:

    Oh – note that Dean Oliver has a testimonial on the CREZ site.


    September 16th, 2009 at 1:18 pm
  4. Tim Varner said:

    Good stuff, Ryan. I think I’ve identified my next purchase.

    September 16th, 2009 at 1:38 pm

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