📄Annex 1 - Basic concepts

Basic concepts of Statistics and Probability that applied in Betting

Object (O)

An object (of observation) is the basis of every bet, for example: (1) The winner of the match between Liverpool (LIV) and Manchester United (MU) (2) The champion of the Champions League 2021-2022 (3) Number of goals of Erling Haaland in 2022-2023

Ability (A)

Is the possible result of an Object, for example: (1) A1 = LIV A2 = MU A3 = draw (no winner or loser)

(2) A1 = Man City A2 = Liverpool A3 = Bayern Munich A4 = Chelsea A5 = Real Madrid A6 = Aletico Madrid A7 = Villareal A8 = Benfica

(3) A1 = an integer between 18 and 20 A2 = an integer between 21 and 30 A3 = an integer greater than 30 Incompatibility: A1 and A2 are incompatible if there is only one scenario that A1 or A2 occurs: (1) If A1 occurs (LIV wins) then it is impossible for A2 (MU wins) or A3 (draw) to occur. (2) If A2 = LIV is the champion then it is impossible for another Ai to occur (another team cannot be the champion).

Space of Abilities (S)

Is a set of all abilities of an conservative object: S = {A1, A2,.., An} Sufficiency: There does not exist an ability Ax that does not belong to S to occur. For example:

(1) There is no result other than (LIV wins), (MU wins), or draw.

(2) The champion cannot be the team that is not one of those in the tournament.

(3) The number of goals of Erling Haaland cannot be a non-integer number, and cannot be less than 18 (because at present, he scored 18 goals)

Probability (P)

The possibility of an ability A, known as P(A), represents the possibility that A will occur. P(A) is an actual number that satisfy below properties: With every ability: 0 < =0 P(A) <= 1 With the two incompatible abilities A1 and A2: P(A1 or A2) = P(A1) + P(A2) P (A1 and A2) = 0 With the space of abilities: S = {A1, A2,.., An} then P(S) = P(A1) + P(A2) + … + P(An) = 1

For example: (1) Because LIV is in the best performance, the possibility that LIV wins is higher than MU wins, or draw: A1 = 0.5 A2 = 0.2 A3 = 0.3 Sum (Ai) = 0.5 + 0.2 + 0.3 = 1

(2) The stronger teams will have higher possibility to win than weaker ones: A1 = 0.4 A2 = 0.2 A3 = 0.2 A4 = 0.07 A5 = 0.07 A6 = 0.03 A7 = 0.02 A8 = 0.01 Sum (Ai) = 0.4 + 0.2 + 0.2 + 0.07 + 0.07 + 0.03 + 0.02 + 0.01 + 0.01 = 1

(3) Erling Haaland has much possibility to score more than 2 goals but the possibility to score 12 more goals is low: A1 = 0.1 A2 = 0.7 A3 = 0.2 Sum (Ai) = 0.1 + 0.7 + 0.2 = 1