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# The Poisson distribution: forecasting account when betting on football

## The Poisson distribution: forecasting account when betting on football

Beginners in the betting, it is difficult to navigate in the mechanism of determining rates a bookie who looks like factors (mainly decimal). Take the example of betting on football Russian Premier League:

Dividing a unit on decimal numbers, the bettor will receive the likelihood that a bookie victory of the first team – Amkar 1/6,25=0,16х100%= 16%, whereas the victory of Zenit is estimated to 62.5% (1/1.60), draw 26%.

To make the decision to take or not to take the odds, the bettor should compare the probability of outcomes the bookie with their own, preferably based on mathematical calculations, not instinct.

Elihu Feustel professional bettor, author of books on the subject of sports betting offers the use of formulas of the Poisson distribution describing the probability of a random event that depends on a set of individual events.

In relation to football, the victory of one team or a draw are in the form of a random variable, depending on the number of goals scored during the playing season. Formula Poisson distribution as follows:

The Poisson distribution helps to determine the outcome of the meeting (in this case football) if win, lose or draw to represent in a finite number of unlikely events. The calculation is based on the basis of the matches of the season, given the scored and conceded goals to identify the series of meetings, both victories and defeats. First, we calculate the probability of goals for each team in the projected game, limited to four banks.

The formula for the Poisson distribution, for sports betting comes down to the tablemu mind:

The task of the bettor to determine λ is the average number of goals scored in the games of the season, for each of the two teams, the outcome of the game where bets are placed.

A simple way of calculation – the number of goals divided by the number of games, but even non-football people know how important guest and home matches. Therefore, λ "guest" and λ "home" we consider it separately:

Amkar played 6 games this season, scoring away, not catching the eye gets home, therefore we consider only λ guest = 1/6= 0,16 (formula 1).

Referring to the statistics of the team, find out how many scored average goals per match and how many goals conceded in home games and road games:

`TabStop λ = 0, λпрсрдом = 0,5; subtleties λ = 0.3, the λпргост =1,5.`

With this information, the bat calculates the probability of attack attack λ= 0,16 (the ratio of all games to the "guest" goals" x subtleties λ = 0,16*0,3=0,048 (Formula 2).

`protection λ = 0 because, as goals scored at home. (Formula 3).`

Similar calculations hold for the team of Zenit:

First consider the average number of goals scored at home, on the road, divided by the total number of games:

` guest λ = 4/6 = 0,66; (Formula 4);`

` homemade λ = 11/6 = 1,83 (Формула5).`

`TabStop λ= 3.7 V λпрсрдω=0.7 and protection indicators is excellent, Zenit scored well and missed less home – take data directly from the corresponding columns of statistics.`

`subtleties λ= 1,3 λпргост=0,3 – these data are also "taking from the table of statistics, Zenit scored away worse but the defense held.`

`assault λ= λ guest * subtleties λ = 0,66*1,3= 0,858; (Formula 6).`

`protection λ= λ home* λпрсрдом = 1,83*07=1,218 (Formula 7).`

From the properties of Poisson distribution – mean value λ is defined as the product of mathematical expectations for each discrete case. The bettor should calculate the total probability with respect to the predicted outcome of the meeting of the two teams.

In the formula include:

`Amkar λ = λгостевая_Амкар (formula 1)* λ zaditen (Formula 7)* λ napadeniya (Формула2) = 0,16*1,218 *0,048= 0,0009;`

`Zenit λ = λгостевая_Зенит (Formula 4)* λ zaditor (none)* λ napadenie (Formula 6) = 0,66* 0,858=0,566.`

Construct a table of probabilities from 0 to 4 goals in the upcoming match, using a calculator. Substituting instead of X numbers of goals for each outcome λ of the team:

We find the average probability of a draw outcome, multiplying the probabilities of goals between them, folded them and then dividing. It is equal to 6% vs 26%, a specific bookie (1/ratio draw from the line of beech). The likely victory of Amkar will receive by calculating the average of all the probabilities from the table – it will be in 0.104, compared to 16% of the betting calculations.

Similarly, we calculate the probability of a victory of Zenit, having 48.17%. Comparing with the calculated cafam beech on Zenit win (1/1,6), equal to 62.5% are aware that it is overpriced and you can bet. The match cannot end with a draw, to win Zenit Amkar have no chance, and the win of Zenit, because valuing ratio, you can earn.

In conclusion, we note that the highest probability in the table at the Zenith, the column – 1 goal. The outcome ended with such a score, Amkar pulled one Bank.