Add ELO Rating calculator for each team based on the plays

[mramachandran]

The Elo rating system is widely used in various sports, including soccer, to rank players or teams based on their performance relative to their opponents. In soccer, Elo ratings are commonly used to assess the relative strength of teams and predict match outcomes. The system works by assigning a numerical rating to each team, with higher ratings indicating stronger teams.

Here's a brief overview of how the Elo rating system works in soccer:

1. Initial Ratings: At the beginning, each team is assigned an initial rating. This rating could be based on historical performance, such as previous seasons' results or international rankings.

2. Calculating Expected Outcome: Before a match, the Elo system calculates the expected outcome for each team based on their ratings. The formula considers the difference in ratings between the two teams and produces probabilities for win, loss, or draw.

3. Updating Ratings: After the match, the ratings of the teams are updated based on the actual outcome compared to the expected outcome. If a team performs better than expected (e.g., wins against a stronger opponent), their rating will increase. Conversely, if a team performs worse than expected (e.g., loses to a weaker opponent), their rating will decrease. The magnitude of the rating change depends on factors such as the difference in ratings between the teams and the importance of the match.

4. Repeating the Process: This process is repeated for every match played, continuously updating the ratings of teams based on their performance over time.

There are various implementations and variations of the Elo rating system used in soccer, with different organizations and analysts employing slightly different formulas and parameters. However, the basic principles remain the same.

Elo ratings can be used for various purposes in soccer, including ranking teams, predicting match outcomes, and determining seedings for tournaments. They provide a quantitative measure of team strength that can be useful for analysis and comparison.

[mramachandran]

In that way, if you give an ELO rating between two teams, you can easily calculate the probability of the teams winning or losing

[mramachandran]

To calculate Elo ratings for two teams based on 10 different features, you first need to define how each feature contributes to the teams' relative strengths. Then, you can use these features to estimate the expected outcome of a match and update the Elo ratings accordingly. Here's a general outline of the process:

1. Define Features: Identify 10 different features that you believe are relevant to determining the relative strengths of the two teams. These could include statistics like win-loss ratio, average points scored, player rankings, team experience, etc.

2. Normalize Features: Normalize each feature to ensure they are on a comparable scale. For example, you might scale all features to have a mean of 0 and a standard deviation of 1.

3. Assign Initial Elo Ratings: Assign initial Elo ratings to each team. This could be a simple average or based on prior performance if available.

4. Calculate Expected Outcome: Use the normalized features and the teams' Elo ratings to calculate the expected outcome of a match. You can use a logistic regression model or another appropriate method to estimate the probability of each team winning.

5. Update Elo Ratings: After the match, update the Elo ratings based on the actual outcome and the expected outcome. If a team performs better than expected, their Elo rating should increase, and vice versa.

6. Repeat: Continuously repeat steps 4 and 5 for each match played, updating the Elo ratings based on the actual outcomes and recalculating the expected outcomes using the updated ratings.

Here's a simplified example of how you might calculate the expected outcome using logistic regression:

Let's say you have 10 features (F1, F2, ..., F10) and the corresponding coefficients (B1, B2, ..., B10) from your logistic regression model. The Elo ratings of Team A and Team B are Elo_A and Elo_B, respectively.

The expected outcome (E_A) for Team A winning can be calculated as:

[ E_A = \frac{1}{1 + e^{-(B_0 + B_1F1 + B_2F2 + ... + B{10}*F{10} + K*(Elo_B - Elo_A))}} ]

And the expected outcome (E_B) for Team B winning can be calculated as:

[ E_B = \frac{1}{1 + e^{-(B_0 + B_1F1 + B_2F2 + ... + B{10}*F{10} + K*(Elo_A - Elo_B))}} ]

Where K is a constant that determines the sensitivity of the Elo ratings to the outcome of the match.

After the match, if Team A wins, you would update the Elo ratings as follows:

[ Elo_A' = Elo_A + K(1 - E_A) ] [ Elo_B' = Elo_B + K(0 - E_B) ]

And if Team B wins:

[ Elo_A' = Elo_A + K(0 - E_A) ] [ Elo_B' = Elo_B + K(1 - E_B) ]

Repeat this process for each match, updating the Elo ratings based on the actual outcomes, and you'll gradually refine the ratings based on the teams' performances across the 10 different features. Adjustments to the model may be necessary over time to improve its accuracy and predictive power.