2 teams combined probability

[Gavlor]

Hi, first timer here looking for some guidance.

I’m trying to establish what the combined probability would be for a certain event to occur, where there are 2 teams involved, and I know the probability of the event for EACH team.

So....

- Team A scored 2 goals within their previous 5 matches a total of 4 times
- Team B scored 2 goals within their previous 5 matches a total of 3 times

I believe the probability of Team A scoring 2 (or more) goals in their next match is 80% (0.8 decimal).
I believe the probability of Team B scoring 2 (or more) goals in their next match is 60% (0.6 decimal).

Team A are going to be playing against Team B in their next match, so I want to establish the following, but don’t know how to:

1. The probability of both teams scoring 2 goals each

I have some additional scenarios/questions, but I’ll keep it simple for now.

Kind regards
G

 

[Deleted member 4993]

Hi, first timer here looking for some guidance.

I’m trying to establish what the combined probability would be for a certain event to occur, where there are 2 teams involved, and I know the probability of the event for EACH team.

So....

- Team A scored 2 goals within their previous 5 matches a total of 4 times
- Team B scored 2 goals within their previous 5 matches a total of 3 times

I believe the probability of Team A scoring 2 (or more) goals in their next match is 80% (0.8 decimal).
I believe the probability of Team B scoring 2 (or more) goals in their next match is 60% (0.6 decimal).

Team A are going to be playing against Team B in their next match, so I want to establish the following, but don’t know how to:

1. The probability of both teams scoring 2 goals each

I have some additional scenarios/questions, but I’ll keep it simple for now.

Kind regards
G

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[HallsofIvy]

Hi, first timer here looking for some guidance.

I’m trying to establish what the combined probability would be for a certain event to occur, where there are 2 teams involved, and I know the probability of the event for EACH team.

So....

- Team A scored 2 goals within their previous 5 matches a total of 4 times
- Team B scored 2 goals within their previous 5 matches a total of 3 times

"scored 2 goals within their previous 5 matches" could be interpreted as "scored a total of 2 goals in 5 matches" but then "a total of 4 times" makes no sense. I presume you mean "scored two goals in a single game 4 times out of 5."

I believe the probability of Team A scoring 2 (or more) goals in their next match is 80% (0.8 decimal).
I believe the probability of Team B scoring 2 (or more) goals in their next match is 60% (0.6 decimal).

If what my interpretation above is correct, yes that is true.

Team A are going to be playing against Team B in their next match, so I want to establish the following, but don’t know how to:

1. The probability of both teams scoring 2 goals each

The probability of a team scoring a goal is strongly dependent upon their opponent so these are not actually independent events but, given no other information, you will have to treat them as independent. If a and b are independent events then the probability of both happening is the product of the probability of a happening and the probability of b happening. Here that is (0.6)(0.8)= 0.48 or 48%.

I have some additional scenarios/questions, but I’ll keep it simple for now.

Kind regards
G

 

[Gavlor]

Thanks for the response HallsofIvy, it's much appreciated. Apologies, I should have added a bit more detail as both yourself and Subhotosh indicated, see below:

Team A goals scored in previous 5 matches:
Match 1 - 2
Match 2 - 1
Match 3 - 2
Match 4 - 3
Match 5 - 3

Team B goals scored in previous 5 matches:
Match 1 - 1
Match 2 - 4
Match 3 - 2
Match 4 - 2
Match 5 - 0

I take your point regarding a goal being scored is dependent upon their opponents, and it's a fair challenge. I am however treating them as independent. The assumptions you made were indeed correctly, so thanks for answering, it's much appreciated.

If the same scenario was to be applied to cards (a.k.a. bookings) within a football match and there was another element to consider, the referee, how would that be calculated? So, if I was looking to establish the probability of the referee showing the following within the match between Team A vs Team B, what would the calculation be for each of the following:

1) A total of 4+ cards in the match
2) 2+ cards to Team A in the match
3) 2+ cards to Team B in the match
4) 2+ cards to Team A & 2+ cards to Team B in the match

For example:

Team A received cards in previous 5 matches:
Match 1 - 2
Match 2 - 1
Match 3 - 2
Match 4 - 3
Match 5 - 3
So, 2 or more cards shown to Team A occurs 80% of the time (0.8)

Team B received cards in previous 5 matches:
Match 1 - 1
Match 2 - 4
Match 3 - 2
Match 4 - 2
Match 5 - 0
So, 2 or more cards shown to Team A occurs 60% of the time (0.6)

Referee cards shown in previous 5 matches:
Match 1 - 1
Match 2 - 4
Match 3 - 5
Match 4 - 4
Match 5 - 6
So, 4 or more cards are shown to either team 80% of the time (0.8)

Hopefully the above makes sense.