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The process of creating a scoring system using Python for a multiplication competition would involve the following steps:

1. Define the rules of the competition, such as the number of questions, the time limit, and the difficulty level.

2. Create a list of multiplication questions that will be presented to the contestants. Each question should have a corresponding answer.

3. Define a scoring system that will be used to determine the winner of the competition. This could be based on the number of correct answers, the time taken to answer the questions, or a combination of both.

4. Write a Python script that will randomly select questions from the list and present them to the contestants. The script should also record the answers given by each contestant and calculate their score.

5. At the end of the competition, the Python script should display the final scores and announce the winner.

6. You can also add features like a leaderboard if you are hosting multiple competitions and an option to record a player's performance.

Overall, the process of creating a scoring system using Python for a multiplication competition involves defining the rules, creating a list of questions and answers, defining a scoring system, writing a Python script to implement the scoring system, and presenting the final scores to the contestants.