The bottom line is that distributions are always supposed to spit out probabilities in relation to a certain random variable. The random variable is the outcome to be analyzed, for example the number of hits. In the normal distribution described above, the individual probabilities are calculated with an average probability (90% hits in the example). The Poisson distribution is different. This calculates probabilities using an average value, not an average probability. So go ahead and try it the next time you place a bet at 22Bet.
Of course, this makes much more sense in the world of sport. After all, we know, for example, that FC Bayern scores an average of 2.8 goals per game or that BVB scores an average of 3.2 goals in an away game. These required average values can be easily calculated (number of goals divided by number of games). This value, which is given in the formula as lambda (Greek letter), is then simply typed in and the probabilities for 1,2,3 or 4 FC Bayern Munich goals in the upcoming match can be calculated. Anyone who thinks that calculating their own probabilities is child’s play only knows half the truth. Although this is not a problem in principle, the data used is of course crucial for a good betting model. Bayern’s average goals naturally depend on the opponent, the external conditions, the table situation and much more.
It is therefore crucial which data is used to calculate the desired probabilities with the Poisson distribution. The exact formula for the calculation does not necessarily need to be mentioned here, as it is incredibly complicated on the one hand and completely irrelevant for use on the other. Basically, it is based on an exponential function that has been modeled by some clever minds in the past so that it spits out the desired results.
How can I use the Poisson distribution for sports betting?
This point is at least as important, if not more important, than the pure functionality of the Poisson distribution. In fact, the benefits have already been mentioned. The best example is actually the one with the number of goals. Enter the average number of goals scored by team A (number of total goals/number of games) in the formula, type in the desired probability (for example: 3, i.e. for three goals in the next game) and then enter the command “FALSE” or “FALSE” (depending on whether it is in German or English). The difference between FALSE/FALSE and TRUE/TRUE will be explained later. The calculator then spits out the probability of team A scoring three goals in the upcoming match, regardless of other factors of course.
The same could now be done with the goals conceded by team B and then the two probabilities can be compared. The probability of a 0:0 can also be calculated by multiplying the two probabilities of Team A and Team B scoring 0 goals. The application possibilities are almost unlimited. In basketball, the number of baskets can be calculated, in handball the number of goals, in tennis the number of games, etc. Poisson is the perfect tool for over/under betting. But with a few tricks and tips, you can also calculate the probabilities of a win/draw and loss or the exact results.