Poisson distribution in sports betting

This mathematical model was developed in the 19th century by the French mathematician and physicist Poisson. According to a special algorithm, it can be used to calculate the probabilities of outcomes and predict the outcome of matches.

This method allows you to determine the strength of the offense and defense of clubs, based on which the probabilities of scoring one and the other team. This mathematical model allows you to determine the most likely score of the match. Let’s talk about the Poisson distribution and give examples.

The essence of the Poisson distribution

According to the methodology, based on the statistics of the league and the playing teams before the match, the outcome of their future game is predicted. On the basis of league statistics, in which the teams in question play (total number of home and away goals), as well as home and away goals of these teams, the strength of the opposing offensive and defensive lines is calculated. After that, it is necessary to determine the individual total of each team. After obtaining these values using the online calculator you can calculate the percentage probability of 0, 1, 2, 3, 4, 5 or more goals of each team in the match.

You may also be interested: Expected goals

Use in betting

Poisson’s model is most widely used in sports with low performance: mostly soccer, but also hockey, futsal and some other disciplines with an average match total of 3–7.

Poisson’s mathematical model allows you to calculate a number of match parameters at once:

• Individual totals of playing teams;
• The most probable score of the match (based on the obtained probabilities, you can bet on 2–3 final scores of the game);
• Total score of the match;
• Draw a line on sports event.

Calculation of probability of the match score

Let’s analyze the Poisson distribution based on determining the most probable score of the match “Bayern — Eintracht” 2019/2020 season. For the calculations we need data on goals scored and conceded and Bayern’s games at home in the current season (after 26 rounds), as well as similar figures of Eintracht away and the average of these parameters. You also need to know the number of meetings played and the number of goals scored at home and away.

Next, we calculate the strength of the attack and defense of Bayern and Eintracht according to the following algorithm:

• We find the strength of Bayern’s attack. To do this, divide its average number of goals at home by the average number of home goals in the league: 2.92 / 1.72 = 1.7;
• The same for “Eintracht”. Dividing the average total of “Eintracht” away goals by the average total of away goals in the league: 0.916 / 1.52 = 0.6;
• We find the strength of Bayern’s defensive structures. To do this, divide the average number of goals conceded by them at home by the average number of goals scored in the league away: 0.846 / 1.52 = 0.557;
• Same for Eintracht. Dividing their conceded away goals by the average total of goals in home Bundesliga matches: 2.08 / 1.72 = 1.21;
• Next, we calculate the likely individual goal total for each team;
• For Bayern Munich multiply the previously calculated strength of the Munich attack, Eintracht defense and the average number of home goals in the league: 1.7 * 1.21 * 1.72 = 3.54;
• The same parameter for “Eintracht”: multiply the attacking power of “Eintracht”, the strength of “Bayern” defense and the average total of guest goals in the APL: 0.6*0.557*1.52 = 0.51.

According to the calculation, the match should end with a score of 3.54–0.51 in favor of “Bayern”.

Probability of goals for each team

Next, you need to enter all the necessary data into the online Poisson calculator, it will give the probability of goals scored in the game for Bayern and Eintracht.

So, the calculation shows that the most likely total of Bayern’s goals in the match is 3 and 4 (21% and 19% probability). Slightly less chance that the Munich superclub will score 2 goals (18%). The most likely number of goals by Eintracht is 0 goals (probably as much as 60%). The chances of Frankfurt to score 1 goal are equal to 30%, which is also a lot. So we can estimate the most probable score of the match: the victory of “Bayern” with a score of 3:0, 3:1, 4:0 or 4:1.

On top of everything else, the calculator determines the probability of a Bayern win, a draw and an Eintracht win in the match, that is, you can also get a line on the match, dividing 100 by each of these probabilities. Comparing the line obtained by Poisson with the one offered by bookmakers, you can find valuables for betting.

The match between Bayern and Eintracht ended with a score of 5–2 in favor of the home team, while the expected score of the match according to the calculation turned out to be 3.55–0.51. The handicap was guessed correctly, the total match and individual team totals were not quite right.

Conclusion

The Poisson distribution gives an insight into how bookmakers compile a line. However, this calculation is based only on statistics, but does not take into account the human factor, various kinds of force majeure. For example, the model does not take into account many different factors, such as the state of the teams on the day of the match, their psychological mood, recent results, the venue of the game, weather, the credibility of the coach in the team and the strength of his position with the management, etc. Various accidents, which can have a strong influence on the result, are not considered in the Poisson distribution.

This method of determining the probable score of a match by Poisson distribution does not provide any guarantee that the calculated individual totals will pass, and the final score of the match will be one of those 2–3 options that turned out to be the most likely of the calculation. This distribution is just an additional tool for the player, another opportunity to find valuation odds in the line.

Source: https://xgscore.io