Probability & Statistics Archives - Practically Predictable

Elo Ratings for NBA Teams

In this post, we will learn about the Elo rating system. This system was originally developed to rate chess players, and has become a very popular tool to analyze many sports. We will look at how to apply the system to basketball to rate NBA teams. My goal is to show you the key assumptions and math behind Elo ratings, and how to implement the system in Python. We will use Elo ratings in upcoming posts to examine NBA playoff match ups.

My other goal is to point out some of the limitations of Elo ratings. In future posts, we will examine ways to address these limitations, and look at alternative ratings systems that try to do a better job.
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Probability of Winning a Tennis Game

In this post, we will look at a simple probability model for winning a tennis game. This model is far too simple to be accurate in predicting real tennis matches, but it will be the starting point for building more useful models. It is also a good introduction to some of the more advanced counting techniques used to analyze probability.
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Analyzing the Board Game Risk

I enjoy playing the game Risk with my family. The game provides a nice balance of strategy and chance. The pace of play is good and the rules are easy to remember.

In Risk, you win the game by attacking and conquering your opponents’ territories with your armies. Since the game uses up to 5 dice to determine the outcome of each attack, chance is an unavoidable part of the game. The main tool players have to control chance is to position their armies wisely, and attack when the odds are in their favor.

This post shows you how to use the probability tools from this site to analyze the odds in Risk, so you can make better decisions and hopefully improve your chances of winning.
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Coin Flips and Multiplying Probabilities

In this post, we will look at coin flips to see how to analyze outcomes which depend on more than one source of randomness. These are called joint events and have joint probability distributions. We will see how you combine the probabilities of simpler events to create joint probabilities by multiplication.
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Probability Distributions and Dice Rolls

This post builds on the previous post on probability modeling in Python. In this post, we will discuss the concept of probability distribution and how to represent it in Python.
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Probability Modeling: Getting Started

This post introduces a framework to represent the mathematical concept of probability in Python. We’ll develop tools over a series of posts that we can use to analyze games of chance and some popular board games. We will also show how to apply these ideas to uncertainty in sports.
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