This post represents a **real-world example** of **Binomial** and **Beta probability distribution** from the sports field. In this post, you will learn about how the run scored by a Cricket player could be modeled using Binomial and Beta distribution. Ever wanted to predict the probability of **Virat Kohli **scoring a half-century in a particular match. This post will present a perspective on the same by using **beta distribution to model the probability of runs that can be scored** in a match. If you are a data scientist trying to understand beta and binomial distribution with a real-world example, this post will turn out to be helpful.

First and foremost, let’s identify the random variable that we would like to study. In this post, lets set the **random variable** as the **half-century (runs equal to or more than 50) scored by a player in a match**.

X = Half-century (runs equal to or more than 50) scored by a player in a match

First and foremost, let’s identify the random variable that we would like to study. In this post, lets set the random variable as the **half-century (runs equal to or more than 50) scored by a player in a match**. If the player scores a half-century, the random variable takes the value of SUCCESS (X = 1). If the player does not score a half-century, the random variable takes the value of failure (X = 0).

### Representing Runs Scored as Binomial Distribution

Taking the last 30 matches in the consideration, there will be **N** number of successes (half-century scored) and **(30-N)** number of failures. This can be modeled using **Binomial Distribution** (a series of successes and failures).

### Representing Probability of Runs as Beta Distribution

Let’s say we would like to predict the likelihood of whether the player will score a half-century in the upcoming cricket match. This problem could be modeled using Beta Distribution as the likelihood of the player scoring half-century could take value anywhere in the range of [0, 1]. Note the fact that we are predicting **prior** expectations.

Given our current problem, the best way to represent these prior expectations is with the Beta distribution. We are roughly expecting whether the player will score half-century even before the player has played the first ball of the match. Let’s say that it is expected that the probability that the player will score half-century will be most likely around .27, but that it could reasonably range from .21 to .35. The following plot will represent the beta distribution.

### References

Intuition behind Beta Distribution

- Generative Modeling in Machine Learning: Examples - March 19, 2023
- Data Analytics Training Program (Beginners) - March 18, 2023
- Histogram Plots using Matplotlib & Pandas: Python - March 18, 2023

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