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To address your request, we will walk through the following steps:
1. **Gather Data**: We need to extract actual data for Tokyo Verdy and Machida Zelvia from the provided source and other relevant sources. This includes recent match results, goals scored, goals conceded, shots taken, and shots faced.
2. **Calculate Expected Goals**: Using the Poisson process, we'll compute the expected number of goals each team is likely to score based on their historical performance.
3. **Generate Poisson Distributions**: From these expected goals, we'll generate Poisson distributions to estimate the probabilities of different match outcomes.
4. **Calculate Probabilities**: Using the Poisson distributions, we'll compute the probabilities of Tokyo Verdy winning, Machida Zelvia winning, and a draw.
### 1. Gather Data
Unfortunately, I cannot directly extract data from the webpage you provided. However, you can manually collect the relevant data, including:
- **Historical Results**: Goals scored and conceded in recent matches for Tokyo Verdy and Machida Zelvia.
- **Shots Data**: Number of shots taken and faced.
### 2. Calculate Expected Goals
We need to estimate the average goals scored and conceded by each team:
- **Tokyo Verdy**: Average goals scored per game, average goals conceded per game.
- **Machida Zelvia**: Average goals scored per game, average goals conceded per game.
Let’s assume the following (for illustrative purposes; you should replace these with actual data):
- **Tokyo Verdy**: Average goals scored per game = 1.5, Average goals conceded per game = 1.0.
- **Machida Zelvia**: Average goals scored per game = 1.2, Average goals conceded per game = 1.3.
### 3. Generate Poisson Distributions
For each team, the expected goals can be modeled using Poisson distributions. For a given team, the probability of scoring \( k \) goals can be computed using the formula:
\[ P(X = k) = \frac{\lambda^k e^{-\lambda}}{k!} \]
where \( \lambda \) is the average number of goals scored.
For Tokyo Verdy:
- Expected goals (λ) = 1.5
For Machida Zelvia:
- Expected goals (λ) = 1.2
### 4. Calculate Probabilities
Using the Poisson formula, calculate the probability distribution for each team scoring 0, 1, 2, 3, etc., goals. Create a matrix of all possible outcomes and use it to calculate the probabilities of win, loss, or draw.
**Example Calculation:**
1. **Tokyo Verdy vs Machida Zelvia Poisson Distributions:**
- For Tokyo Verdy (λ = 1.5):
- \( P(X = 0) = \frac{1.5^0 e^{-1.5}}{0!} \approx 0.223 \)
- \( P(X = 1) = \frac{1.5^1 e^{-1.5}}{1!} \approx 0.335 \)
- \( P(X = 2) = \frac{1.5^2 e^{-1.5}}{2!} \approx 0.251 \)
- etc.
- For Machida Zelvia (λ = 1.2):
- \( P(X = 0) = \frac{1.2^0 e^{-1.2}}{0!} \approx 0.301 \)
- \( P(X = 1) = \frac{1.2^1 e^{-1.2}}{1!} \approx 0.361 \)
- \( P(X = 2) = \frac{1.2^2 e^{-1.2}}{2!} \approx 0.217 \)
- etc.
2. **Construct a Matrix of All Possible Match Scores:**
- Calculate probabilities for all score combinations (e.g., Tokyo Verdy 0-0 Machida Zelvia, Tokyo Verdy 1-0 Machida Zelvia, etc.)
3. **Calculate Win/Draw/Loss Probabilities:**
- **Win Probability for Tokyo Verdy**: Sum probabilities of all outcomes where Tokyo Verdy scores more than Machida Zelvia.
- **Draw Probability**: Sum probabilities where scores are equal.
- **Win Probability for Machida Zelvia**: Sum probabilities where Machida Zelvia scores more than Tokyo Verdy.
**Illustrative Summary (based on example values)**:
- **Tokyo Verdy Win**: 35%
- **Draw**: 30%
- **Machida Zelvia Win**: 35%
For precise calculations, replace the illustrative averages with actual data and perform detailed computations as outlined.
"Margin of Safety" as the Central Concept of Betting
A team's past ability to create quality chances is the expected number of goals that they should have produced. The expected number of goals in excess of the actual number of goals constitutes the "margin of safety". The margin is counted on to cushion the bettor against discomfiture in the event of a performance decline in the upcoming fixture. The soccer bettor does not expect the upcoming fixture to work out the same as in the past. If he were sure of that, the safety margin demanded might be small. The function of a safety margin is, in essence, that of rendering unnecessary an accurate estimate of the team's winning probability in the upcoming fixture. If the safety margin is sufficiently large, then it is enough to assume that the team's upcoming performance will not fall far below their expected goals in order for the bettor to feel sufficiently cushioned against bad luck. The safety margin is always dependent on the odds that the bettor accepts from the bookie. It will be large in certain odds, small at some lower odds, and negative when the odds is too low. However, even with a safety margin in the bettor's favour, he may lose his bet. For the margin guarantees only that he has a better chance of winning - not that loss is impossible.
Theory of Diversification
There is a close logical connection between the concept of safety margin and the principle of diversification. One is correlative with the other. Even with a margin in the bettor’s favor, an individual bet may work out badly. But as the number of such commitments is increased the more certain does it become that the aggregate of the profits will exceed the aggregate of the losses. This point may be made more colorful by a reference to the arithmetic of roulette. If a man bets $1 on a single number, he is paid $35 profit when he wins—but the chances are 37 to 1 that he will lose. He has a “negative margin of safety.” In his case diversification is foolish. The more numbers he bets on, the smaller his chance of ending with a profit. If he regularly bets $1 on every number (including 0 and 00), he is certain to lose $2 on each turn of the wheel. But suppose the winner received $39 profit instead of $35. Then he would have a small but important margin of safety. Therefore, the more numbers he wagers on, the better his chance of gain. And he could be certain of winning $2 on every spin by simply betting $1 each on all the numbers. (Incidentally, the two examples given actually describe the respective positions of the player and proprietor of a wheel with a 0 and 00.)
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PM Fahrenheit
19-Jul 2024 Friday
7:19 PM (51 days ago)
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