Normalizing Ratings, Calculating Probabilities, and Converting to Decimal Odds

Normalizing ratings allows us to bring disparate data types onto a common scale, making it easier to compare and analyze them. This tutorial will provide an in-depth guide on normalising a set of ratings, transforming these into probabilities, and then representing these probabilities as decimal odds. This methodology has broad applications, including sports analytics, machine learning, and predictive modelling.

For this guide, we’ll work with the following ratings: 74, 71, 77, 69, 82, 58, 60, 67, 66, 56.

Step 1: Normalizing Ratings

What We’re Doing

In this step, we aim to adjust the ratings to fit into a specific range, typically 0 to 1. This makes comparing ratings that originally might have been on different scales easier.

The Formula

To normalize ratings, we use the Min-Max Scaling formula, which is:

Normalized Value = (x – Min) / (Max – Min)

Here, x is the original rating, Min is the smallest rating in the set, and Max is the largest.

How to Do It

1. Find Min and Max: First, identify your data set’s smallest and largest ratings. For our example, Min is 56, and Max is 82.
2. Apply the Formula: For each rating, subtract the Min and divide by the range (Max – Min). Example for the first rating, 74: Normalized Value = (74 – 56) / (82 – 56) = 18 / 26 = 0.6923
3. Handle Zeros: If any rating normalizes to 0, you might want to substitute it with a small constant (like 0.01) to ensure that it remains in the calculations for subsequent steps.

Step 2: Convert to Probabilities

What We’re Doing

Here, we convert the normalized ratings into probabilities. The idea is to express each rating as a fraction of the total, providing a probabilistic perspective.

The Formula

The formula to convert normalized ratings into probabilities is:

Probability (p) = Normalized Rating / Sum of all normalized ratings

How to Do It

1. Sum the Normalized Ratings: Add up all the normalized ratings. This total will be your denominator for the next step. For us, this sum is 4.6253.
2. Divide Each by the Sum: Divide each normalised rating by this sum. For the first normalized rating of 0.6923 : Probability = 0.6923 / 4.6253 = 0.1498

Step 3: Convert to Decimal Odds

What We’re Doing

In this step, we’ll convert probabilities into decimal odds. These odds can be interpreted as the potential bet return, including the stake.

The Formula

The formula to convert probabilities into decimal odds is:

Decimal Odds = 1 / Probability

How to Do It

Take the reciprocal of each probability to get the corresponding decimal odds.

For the first probability of 0.1498:

Decimal Odds = 1 / 0.1498 = 6.68

Final Table

After performing these calculations, you can compile all this information into a table, ideally sorted by Decimal Odds for easy reference:

By following these steps, you’ll have normalized a set of raw ratings and transformed these normalized values into both probabilities and decimal odds. This gives you a powerful toolset for analyzing and interpreting the original ratings.