Can we compute the expected value of a football match final score? I am asked to make predictions for the exact final result of some football matches. To be clear, I do not have to place any bets on them, just guessing the final score.
To do that I was thinking about an approach that assumes that bookies know best and leverages that information. For example, I can check the odds for the final scores and take the score associated to the lowest odds (i.e. highest chance).
Take for example this (partial) piece of information:




Home Goals
Away Goals
Odds




0
0
8.65


0
1
7.93


0
2
9.19


0
3
17.34


1
0
10.44


1
1
6.52


...
...
...




Here one strategy may be picking 1-1 since it has the highest probability of happening.
However, thinking about the concept of expected value of a random variable, I am wondering if we can compute a sort of expected value for the random variable "final score".
I mean, since I can convert each odd $o_x$ to its corresponding probability $p_x = \frac{1}{o_x}$ (actually, the normalized probability since odds always have a small margin), I feel I can do something like:
$$
E[X] = \sum_{x} x p_x 
$$
The thing here is that $x$ is not a number, rather a pair of numbers (the final score).
Is there a way I can go around this? Does it make any sense?
I was thinking about splitting the problem into two subproblems, e.g. finding 1) the expected value for the total number of goals scored and 2) the expected value for the goals "delta". Is this a valid approach?

Expected values can be defined for vectors of length larger than one, and they can still be computed according to your formula. So this is fine also for pairs of numbers.Your "splitting" approach should ultimately give the same result.
