Calculated Bets
Computers, Gambling, and Mathematical Modeling to Win
by Steven Skiena
Cambridge University Press, 2001, 232 pgs., with notes and index

The book The Predictors is an account of the early days of Prediction Company in Santa Fe, New Mexico. Prediction Company was founded by two physicists who did some early work on chaos theory. The company was founded to build predictive financial models that would drive trading in various markets (e.g., futures and stocks). After reading The Predictors I was was fascinated by the idea that market models could be used to predict stock prices, at least to a degree better than chance. The Predictors was carefully reviewed by the staff of Prediction Company to make sure that very little useful information was provided on the techniques Prediction Company used to build models. The book left me with the belief that the Prediction Company's financial models where mysterious things, the result of brilliance and deep insight (after journeying to the Emerald City I had the same surprises that Dorothy did). Steven Skiena's book Calculated Bets came out two years after The Predictors was published. If I had read Calculated Bets I would have had some idea of how predictive models can be built and tested.

Prof. Skiena teaches at the State University of New York at Stony Brook. He is also the author of The Algorithm Design Manual. From reading his books he seems like a wonderful teacher and I wish I had a professor like him when I attended college. Prof. Skiena give the impression that he has fun in his research work and it seems like he might transmit that feeling of fun to his students. He writes

Tenure give you the freedom to work on whatever you want. You have to teach your classes, and you have to do your committee work, but otherwise what you do with your time is pretty much up to you. If I wanted to devote a little effort to an interesting mathematical modeling problem, well, nobody was going to stop me.

The "interesting mathematical modeling problem", which is recounted in Calculated Bets, is the construction of a predictive computer model for the game of jai alai. In the early chapters of Calculated Bets we learn that

Jai alai is a sport of Basque origin in which opposing players or teams alternate hurling a ball against the wall and catching it until one of them finally misses and loses the point. The throwing and catching are done with an enlarged basket or cesta.

Like horse racing, Jai alai is a game that the spectators and those "off track" can bet on (via the telephone). Jai alai betting is pari-mutuel (which Prof. Skiena explains). Prof. Skiena's objective is to build a predictive model that will make money betting on jai alai.

The idea of predicting the future has a magical aura. At a core level most of us know that in many ways the future is unknowable and unpredictable. Who will win the next presidential election? Where will the Standard and Poor index of the stock market close a year from now? We know that so many unexpected events may take place that this kind of long term prediction is difficult or impossible. But we predict minor short term events all the time. As I write this review the temperature outside is over 90 degrees Fahrenheit. I can predict with a high degree of accuracy that tomorrow will have a temperature range between 75 and 110. If I had detailed intra-day weather information from the National Weather Service, a weather model and a supercomputer I could predict tomorrows exact temperature within a much narrower range of error.

Weather prediction and market prediction deal with complex systems which cannot be completely quantified. In contrast, what can be known about the game of jai alai can, in theory, be known. Prediction in jai alai is an easier to understand problem and provides a good introduction to predicting more complex systems.

Calculated Bets assumes very little background in mathematics, computer science or jai alai. The early chapters of the book cover the history and the rules of jai alai. Prof. Skiena's family vacationed in Florida, where there are jai alai frontons (the arenas where jai alai is played). His descriptions of these outings and the small bets he and his brothers made using Pepe's Green Card (a jai alai tip sheet, sold at the fronton) are amusing and charming. After covering the basics of jai alai so that the reader can understand the jai alai model, Calculated Bets introduces the basics of modeling, including Monte Carlo simulation, curve fitting and the problems of model testing, including over-fitting.

Calculated Bets is written at an advanced Scientific American readership level. There are a few equations, but the book can be read without understanding them. This makes the book readable by jai alai fans and computer scientists. For the computer scientist interested in modeling building the lack of technical detail can be frustrating. In writing for a general readership, many of the details of model building are glossed over. For example, the model was "back tested" against historical jai alai data. But Prof. Skiena does not emphasize the techniques he may have applied to verify the accuracy of his model and avoid over fitting. In calculating the coefficients for the curve he used to model player (or team) performance, Prof. Skiena writes "Through trial-and-error experiments, we determined that [an alpha of approximately] 0.4 seemed to do the best job of predicting the winners of jai alai games, and that is what we generally will use from here on out." While this is more than enough information for the casual reader, the model builder wants to know how exactly the trial-and-error experiments were performed.

Calculated Bets is a charming book and it provides a good introduction to model building. Many people who work on financial models that are used to drive real trading systems feel that those who know how to build good models are trading them, not writing about them. Perhaps this is the reason that I have seen few books on building financial models, although there are a number of books on specialized topics like time series modeling and prediction. There is also a growing literature in statistics on advanced validity and testing techniques (bootstrapping, for example). So while Calculated Bets provides an decent starting point, there is no defined path that I know of for those who want to implement predictive models.


I've listed a few references below on modeling financial time series and market data. Even more difficult than building a model is finding the predictors to encorporate into the model. Finance journal articles can provide a starting point. However, in the end, predictor discovery is experimental. One technique that can be used in an attempt to uncover predictors is data mining of financial data. This is, by itself a complex topic. As Prof. Skiena points out in a brief digression on the book The Bible Code, over-fitting a data set can lead to erroneous conclusions.

Ian Kaplan
July 2003
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