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Curve Ball: Baseball, Statistics, and the Role of Chance in the Game

Jim Albert and Jay Bennett
Publication Date: 
Number of Pages: 
[Reviewed by
J. Kevin Colligan
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When I was six (and until I was about 40!), I thought baseball was life, and life was baseball. Of course, I was right, but I didn't realize how right I was until I later saw the connection between baseball and mathematics. Curve Ball takes this connection to a deeper, statistical level.

I've heard some colleagues who are familiar with this book say it's unclear who the target audience is. There may be a grain of truth there, but it seems to me that that goal of the book is to expand the horizons of sports statisticians to include statistical modeling and not just statistics gathering. The authors correctly point out that even though statistics and baseball are storied partners — think of all the times you've heard announcers give a pinch hitter's batting average against a particular reliever or a team's success rate at driving in a run with two outs and a runner on third — it is still rare that we hear anyone hold court about the proper way to measure an individual's contribution to team success in anything other than qualitative terms.

Curve Ball tries to fill this gap with sound, fact-based reasoning, and succeeds.

This book treats a wide variety of topics, including:

  • comparing measures of batting ability;
  • the impact of situation on performance;
  • streaks;
  • measuring a player's clutch performance; and
  • did the best team win the World Series.

(The last of those is a personal favorite, and one for which I have a completely unbiased answer: No, of course not. Otherwise the Cardinals would win every year.)

I particularly enjoyed the middle three chapters, which were devoted to nonstandard ways to measure offensive performance and the value of a hitter to a team. I don't believe it will ruin anyone's read to quote two conclusions therefrom:

  1. If ...player evaluations are normalized with respect to the number of opportunities the player had to produce offensively, the number of outs is a better measure than at-bats or plate appearances for this purpose.
  2. The standard measures used by Major League Baseball and the media were the worst evaluators of offensive performance among those reviewed.

With the exception of the fact that some of the models build on previous ones, this book has the appealing quality that you can start reading at almost any chapter and enjoy and understand the journey. And for those of us who are not statisticians by training, we can also learn some statistics. However, remember the goal here isn't to teach statistics, it's to acquaint the reader with the tools and frame of mind needed to compare statistical models. This is similar to the two tasks of learning to use a calculator, and learning how and when to use a calculator. I'm firmly in the camp that says it's our job to teach the latter skills.

This book's one real shortcoming is the lack of an index. There are so many performance models given — many of which are tweaks to previous ones — that I found myself frequently searching the book looking for previous definitions. Even a glossary would have been helpful for those like me with short (or at least limited!) memories. At the core, however, baseball is about belief, not proof. Recall Yogi Berra's immortal comment: "Ninety percent of the game is half mental."

Curve Ball is a fascinating source book for both baseball and statistical applications thereof. It's a good read, and good mathematics. Nonetheless, use the information there sparingly: as we all know, baseball is more about religion than mathematics!

J. Kevin Colligan ( is a past governor of the Maryland-DC-Virginia section of the MAA. He enjoys but does not have enough time for golf, running, go, and the piano. He loves New Orleans jazz, science fiction, and chili, and is always encouraging his New Orleans born and bred wife to cook more Creole dishes.

Introduction * Simple Models * Situational Effects * How Do We Evaluate Players * Clutch Hitting * Streakiness * Does The Best Team Win? * Predicting Results * Wrap-Up