According to statistics, the probability of winning the team on the field is 0.453. This is the average value calculated for all participants, and the probability of winning on the field, for the two teams selected randomly. Let's denote the probability with the letter P. We want to find out what is the connection between the first goal scored and the victory in the game.
To understand further calculations we need to remember what conditional probability and the Formula of Full Probability are. The conditional probability P (A|B) denotes the probability that event A will occur if we know that event B took place. For us, this means the probability of victory of the team that plays on its field, in the event that it scored the first goal. Accordingly, P (A|C) the probability that the hosts will win, despite the fact that the first goal was scored by the guests. P(A|D) is absurd, and so the probability is 0.
P (house win) = P (A)
P (first team to score) = P (B)
P (away team scores first) = P (C)
P (no team scores first) = P (D)
P (home win|first goal scored by home team) = P (A|B)
P (home win|first goal scored by guests) = P (A|C)
P (home win|first goal not scored) = P (A|D)
P (first goal scored by the hosts|home win) = P (B|A)
For mutually exclusive conditions, such as a win, loss, or draw in a football match, the Full
Probability Formula would be:
P (A)=P (B)×P (A|B)+P (C)×P (A|C)+P (D)×P (A|D)
Let's substitute the statistics of the NPL championship into this formula.
P (A) = 0.453
P (B) = 0.543
P (C) = 0.39
P (D) = 0.076
P(A|B) = 0.718
P(A|C) = 0.178
P(A|D) = 0
Notice how the odds of winning or losing change depending on which team scored the first goal. The absolute probability of winning on the home field is 0.453 for 2 teams from a random sample.
However, as soon as we take into account the first goal scored, the values begin to deviate sharply from the average. The first goal scored gives a significant advantage to the hosts, the chances of winning grow to 0.718, if they, on the contrary, concede a goal first, the probability of victory decreases to 0.178.
0.453 = (0.534)(0.718) + (0.39)(0.178) + (0.076)(0)
There is also an inverse conditional dependence P(B|A) - the probability that the first goal was scored by the winning team, which acts on its field. In no case should these two events be confused: P (A / B) and P (B|A).
P(A|B) = 0.718
P(B|A) = 0.847
Thus, in 71.8% of cases, when the hosts scored the first goal, their team won. Also, in 84.7% of the matches won, the hosts scored the first goal.
Now let's calculate the same probabilities for the RFL for the last two completed seasons: 2014-2015 and 2015-2016.
P (A) = 0.425;
P (B) = 0.5104;
P(A|B) = 0.7102;
P(B|A) = 0.8529;
As you can see, the values are very close to those that were obtained for the NPS, and most likely we are dealing with a pattern.
How can this knowledge help us in betting on football? You can expect that in live, the coefficient of 1 for the team playing on its own field, after the first goal scored, will decrease by one and a half times on average. For example, if in Saturday's game teams "Manchester city-Tottenham" after the first goal of the hosts rate 1 will change from 2 to 1.6, then such a rate will be gross, since in reality the rate should fall to 1.33.
It should be taken into account that there are no average teams or very few of them and in order to achieve accuracy it is necessary to study the statistics of the first goal for a particular team and compare it with the average of all teams. One thing is for sure-the first goal scored significantly increases the chances of winning!
To understand further calculations we need to remember what conditional probability and the Formula of Full Probability are. The conditional probability P (A|B) denotes the probability that event A will occur if we know that event B took place. For us, this means the probability of victory of the team that plays on its field, in the event that it scored the first goal. Accordingly, P (A|C) the probability that the hosts will win, despite the fact that the first goal was scored by the guests. P(A|D) is absurd, and so the probability is 0.
P (house win) = P (A)
P (first team to score) = P (B)
P (away team scores first) = P (C)
P (no team scores first) = P (D)
P (home win|first goal scored by home team) = P (A|B)
P (home win|first goal scored by guests) = P (A|C)
P (home win|first goal not scored) = P (A|D)
P (first goal scored by the hosts|home win) = P (B|A)
For mutually exclusive conditions, such as a win, loss, or draw in a football match, the Full
Probability Formula would be:
P (A)=P (B)×P (A|B)+P (C)×P (A|C)+P (D)×P (A|D)
Let's substitute the statistics of the NPL championship into this formula.
P (A) = 0.453
P (B) = 0.543
P (C) = 0.39
P (D) = 0.076
P(A|B) = 0.718
P(A|C) = 0.178
P(A|D) = 0
Notice how the odds of winning or losing change depending on which team scored the first goal. The absolute probability of winning on the home field is 0.453 for 2 teams from a random sample.
However, as soon as we take into account the first goal scored, the values begin to deviate sharply from the average. The first goal scored gives a significant advantage to the hosts, the chances of winning grow to 0.718, if they, on the contrary, concede a goal first, the probability of victory decreases to 0.178.
0.453 = (0.534)(0.718) + (0.39)(0.178) + (0.076)(0)
There is also an inverse conditional dependence P(B|A) - the probability that the first goal was scored by the winning team, which acts on its field. In no case should these two events be confused: P (A / B) and P (B|A).
P(A|B) = 0.718
P(B|A) = 0.847
Thus, in 71.8% of cases, when the hosts scored the first goal, their team won. Also, in 84.7% of the matches won, the hosts scored the first goal.
Now let's calculate the same probabilities for the RFL for the last two completed seasons: 2014-2015 and 2015-2016.
P (A) = 0.425;
P (B) = 0.5104;
P(A|B) = 0.7102;
P(B|A) = 0.8529;
As you can see, the values are very close to those that were obtained for the NPS, and most likely we are dealing with a pattern.
How can this knowledge help us in betting on football? You can expect that in live, the coefficient of 1 for the team playing on its own field, after the first goal scored, will decrease by one and a half times on average. For example, if in Saturday's game teams "Manchester city-Tottenham" after the first goal of the hosts rate 1 will change from 2 to 1.6, then such a rate will be gross, since in reality the rate should fall to 1.33.
It should be taken into account that there are no average teams or very few of them and in order to achieve accuracy it is necessary to study the statistics of the first goal for a particular team and compare it with the average of all teams. One thing is for sure-the first goal scored significantly increases the chances of winning!
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