Thomas W. Miller [Thomas W. Miller] - Sports Analytics and Data Science: Winning the Game with Methods and Models

This book is different from other sports analytics books because it views sports analytics in the broader context of data science. Data scientists speak the language of businessaccounting, finance, marketing, and management. They know about information technology, including data structures, algorithms, and object-oriented programming. They understand statistical modeling, machine learning, mathematical programming, and simulation methods. These are the things that data scientists do:

Information search and selection. We begin by reviewing the research literature in the field, learning what others have done in the past. Then we search for relevant data sources and select sources for analysis and modeling.

Preparing text and data. Text is unstructured or partially structured data that must be prepared for analysis. We extract features from text. We define measures. Quantitative data are often messy or missing. They may require transformation prior to analysis. Data preparation consumes much of a data scientists time.

Looking at data. We do exploratory data analysis, data visualization for the purpose of discovery. We look for groups in data. We find outliers. We identify common dimensions, patterns, and trends.

Predicting how much. We are often asked to predict how many units or dollars of product will be sold, the price of financial securities or real estate. Regression techniques are useful for making these predictions.

Predicting yes or no. Many business problems are classification problems. We use classification methods to predict whether or not a person will buy a product, default on a loan, or access a web page.

Testing it out. We examine models with diagnostic graphics. We see how well a model developed on one data set works on other data sets. We employ a training-and-test regimen with data partitioning, cross-validation, or bootstrap methods.

Playing what-if. We manipulate key variables to see what happens to our predictions. We play what-if games in simulated marketplaces. We employ sensitivity or stress testing of mathematical programming models. We see how values of input variables affect outcomes, payoffs, and predictions. We assess uncertainty about forecasts.

Explaining it all. Data and models help us understand the world. We turn what we have learned into an explanation that others can understand. We present project results in a clear and concise manner.

Prediction is distinct from explanation. We may not know why models work, but we need to know when they work and when to show others how they work. We identify the most critical components of models and focus on the things that make a difference.

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Data scientists are methodological eclectics, drawing from many scientific disciplines and translating the results of empirical research into words and pictures that management can understand. These presentations benefit from well-constructed data visualizations. In communicating with management, data scientists need to go beyond formulas, numbers, definitions of terms, and the magic of algorithms. Data scientists convert the results of predictive models into simple, straightforward language that others can understand.

Data scientists are knowledge workers par excellence. They are communicators playing a critical role in todays data-intensive world. Data scientists turn data into models and models into plans for action.

The approach we have taken in this and other books in the Modeling Techniques series has been to employ both classical and Bayesian methods. And sometimes we dispense with traditional statistics entirely and rely on machine learning algorithms.

Within the statistical literature, Seymour Geisser introduced an approach best described as Bayesian predictive inference (). In emphasizing the success of predictions in data science, we are in agreement with Geisser. But our approach is purely empirical and in no way dependent on classical or Bayesian thinking. We do what works, following a simple premise:

The value of a model lies in the quality of its predictions.

We learn from statistics that we should quantify our uncertainty. On the one hand, we have confidence intervals, point estimates with associated standard errors, significance tests, and p-valuesthat is the classical way. On the other hand, we have posterior probability distributions, probability intervals, prediction intervals, Bayes factors, and subjective (perhaps diffuse) priorsthe path of Bayesian statistics.

The role of data science in business has been discussed by many ().

Doing data science means implementing flexible, scalable, extensible systems for data preparation, analysis, visualization, and modeling. We are empowered by the growth of open source. Whatever the modeling technique or application, there is likely a relevant package, module, or library that someone has written or is thinking of writing. Doing data science with open-source tools is discussed in Conway and White ().

This appendix provides an overview of data science methods, citing relevant sources for further reading. Topics include mathematical programming, classical and Bayesian statistics, regression and classification, machine learning, data visualization, text analytics, and time series analysis. The final section shows how data science relates to other disciplines.

A.1 Mathematical Programming

We use the term to refer to problems that involve constrained optimization. The word programming in this context means planning, as in resource planning. It does not mean computer programming, although we certainly use computer programs to solve constrained optimization problems. We specify constrained optimization in what is known as standard form. The objective or goal is to maximize the quantity z, which is a sum of n non-negative decision variables xj:

There is one and only one objective in this standard form, and the equation is linear in the parameters cj. In standard form, we maximize the objective. But it is easy enough to set minimization as the objective by maximizing the negative of z. Many problems involve minimizing costs, which explains why we use the letter c for the fixed parameters in the objective function. Using standard form, we write less-than-or-equal-to inequality constraints on the decision variables. The form of the m constraint inequalities is linear with fixed parameters aij and bi.

problem. We sometimes solve integer programming problems by pretending that the decision variables are continuous and using linear programming. This provides what is known as relaxation of linear programming. Most mathematical programming problems involve many constraints. A knapsack or backpack problem is a special type of integer programming problem involving only one constraint.