### 1. **Poisson Distribution**

The Poisson distribution is often used to model the number of goals scored in a soccer match. The formula is:

$P(x;λ)=x!λ⋅e $

Where:

- $P(x;λ)$ is the probability of $x$ goals being scored.
- $λ$ is the average number of goals scored (expected goals).
- $x$ is the number of goals.

You can use this formula to estimate the likelihood of various outcomes based on historical data.

### 2. **Expected Goals (xG)**

Expected Goals (xG) is a metric that estimates the quality of scoring chances and the likelihood of a goal being scored. The formula is:

$xG=∑_{i=}Chance Probability_{i}$

Where:

- $Chance Probability_{i}$ is the probability of scoring from each chance $i$.
- $n$ is the number of scoring chances.

You calculate the xG for each team to estimate their potential to score in a match.

### 3. **Kelly Criterion**

The Kelly Criterion is a formula used for bankroll management to determine the optimal bet size:

$f_{∗}=bp⋅(b+)− $

Where:

- $f_{∗}$ is the fraction of your bankroll to bet.
- $p$ is the probability of winning.
- $b$ is the odds received (decimal odds – 1).

The Kelly Criterion helps in maximizing your bankroll growth while minimizing the risk of bankruptcy.

### 4. **Value Bet Formula**

To find value bets, you compare the probability of an outcome with the odds offered:

$Value=(Probability×Odds)−1$

Where:

- Probability is your estimated chance of the outcome occurring.
- Odds are the decimal odds offered by the bookmaker.

A positive value indicates a potentially profitable bet.

### 5. **Betting Exchange Market**

In betting exchanges, you can use the following formula to calculate the implied probability from odds:

$Implied Probability=Odds1 $

Where:

- Odds are the decimal odds of the outcome.

You can use this to compare with your estimated probability and find value in the market.

### 6. **Statistical Regression Models**

Advanced bettors use regression models to predict outcomes. One common model is:

$Goals Scored=β_{0}+β_{1}⋅Team Strength+β_{2}⋅Opponent Strength+ϵ$

Where:

- $β_{0}$ is the intercept.
- $β_{1}$ and $β_{2}$ are coefficients.
- $Team Strength$ and $Opponent Strength$ are variables representing team capabilities.
- $ϵ$ is the error term.

This model helps in predicting goals based on team and opponent strengths.

### 7. **Head-to-Head (H2H) Analysis**

While not a formula, H2H analysis involves examining past matchups between two teams to identify patterns or tendencies. Key metrics include:

- Win/loss ratio in H2H matches.
- Average goals scored/conceded in H2H encounters.
- Performance in recent H2H games.

Using these formulas and techniques can help in making more informed soccer betting decisions.