st0v / 2024-olympics

Win percentage of athletes sent vs medals won per country.

Objective: Compare a countries success at the olympics in a normalized fashion.

To compare a country's success at the Olympics in a normalized fashion, you can use several methods that account for various factors such as population size, economic resources, and historical performance. Here are some effective approaches:

Medals per Capita:

Calculate the total number of medals (gold, silver, bronze) won by a country and divide it by the country's population. This gives a per capita measure of Olympic success. Formula: $( \text{Medals per Capita} = \frac{\text{Total Medals}}{\text{Population}} )$

Medals per GDP:

This method normalizes medal counts by the country's economic resources. Divide the total number of medals by the country's Gross Domestic Product (GDP). Formula: $( \text{Medals per GDP} = \frac{\text{Total Medals}}{\text{GDP}} )$

Medals per Athlete:

This approach considers the number of athletes sent to the Olympics. Divide the total number of medals by the number of athletes representing the country. Formula: $( \text{Medals per Athlete} = \frac{\text{Total Medals}}{\text{Number of Athletes}} )$

Weighted Medal Count:

Assign different weights to medals (e.g., gold = 4 points, silver = 2 points, bronze = 1 point) to reflect the varying significance of each medal type. Then, normalize this score by population or GDP. Formula: $( \text{Weighted Score} = (4 \times \text{Gold}) + (2 \times \text{Silver}) + (1 \times \text{Bronze}) )$

Historical Performance Index:

Create an index that considers historical performance over multiple Olympic Games, adjusting for factors like population growth and changes in the number of participating countries. This could involve a more complex statistical model that accounts for trends over time.

Success Rate:

Calculate the success rate by dividing the number of medals by the total number of events in which the country participated. This gives insight into how competitive the country is across different sports. Formula: $( \text{Success Rate} = \frac{\text{Total Medals}}{\text{Total Events}} )$

Z-Scores:

Calculate the Z-score for each country based on their medal counts relative to the mean and standard deviation of all participating countries. This standardizes the data and allows for comparison across different scales. Formula: $( Z = \frac{(X - \mu)}{\sigma} )$ where $( X )$ is the country's medal count, $( \mu )$ is the mean medal count, and $( \sigma )$ is the standard deviation.

By using one or a combination of these methods, you can create a more normalized and fair comparison of Olympic success among different countries. Each method has its strengths and weaknesses, so the choice may depend on the specific context and the factors you wish to emphasize.