### Tutorial on Calculating Single Event Probabilities in Sports Betting

#### Introduction

Calculating single event probabilities in sports betting involves determining the likelihood of a specific outcome occurring in a sports event. Understanding the math behind calculating these probabilities is crucial for informed betting decisions. It’s important to note that this tutorial assumes a statistically significant sample size. Do not worry about what that means, yet. For now just think of it like “we have enough data to assume that the event wasn’t a fluke.”

#### Basics of Probability Calculation

Probability is expressed as a number between 0 and 1, where 0 indicates an impossible event and 1 indicates a certain event. The probability of an event is calculated as:

#### 1. Baseball Example: Hitting a Home Run

Suppose a batter has hit 50 homeruns in 400 at bats (really good hitter). The probability (P) of him hitting a home run in any single at-bat is:

This means there’s a 12.5% chance of the player hitting a home run in a given at-bat. Simple enough?

#### 2. Basketball Example: Making a Free Throw

Imagine a basketball player with a free throw percentage of 80% on 300 free throws attempted (large sample size). The probability of making a single free throw is:

There’s an 80% chance of him making a free throw.

#### 3. American Football Example: Completing a Pass

If a quarterback has completed 300 out of 500 pass attempts, the probability of completing the next pass is:

This suggests a 60% chance of completing a pass.

#### 4. Baseball Example: Striking Out a Batter

A pitcher has struck out 100 batters so far this season out of 400 total batters faced. The probability of striking out the next batter is:

There is a 25% chance of striking out any batter, not taking into account a batter’s skill level. The fact that we’re not taking into account batter skill level is an inherent flaw with just using general probabilities for sports betting. We’ll dive into this later, but it’s where machine learning comes into play.

#### 5. Basketball Example: Hitting a 3-Pointer

If Steph Curry has made 70 out of 200 attempts, the probability of him making a 3 pointer is:

This indicates a 35% chance of him making a 3 pointer.

These are all very simple, intuitive calculations but it’s important to drill the fundamentals before moving on to more complex topics. Below is a brief outline of how machine learning can be far superior to using simple calculations like the ones above. But it’s important to always start simple, and gradually get more complex. As with anything, there is often a tradeoff between simplicity and interpretability.

#### Using Machine Learning for Probabilities

Machine learning can enhance the accuracy of sports betting probabilities by analyzing vast amounts of data, including player performance, team dynamics, weather conditions, and more. These models can identify patterns and trends not immediately apparent through traditional statistical methods. However, the probabilities generated by machine learning models are often more complex and harder to understand due to the intricate algorithms and multifaceted data involved. They provide a more nuanced and dynamic understanding of the probabilities but require a deeper understanding of machine learning techniques to fully appreciate their insights.