Yep, because the variables are (notionally) independent and each has a different distribution of results probabilities, the model is literally just to consider all 311 = 117147 ways through the maze and then sum the probabilities for all the pathways that result in the same total points to get the chance of each points total.
Gets easier if they are "independent identically distributed" variables (IID), like a series of ideal coin tosses.
Of course, these variables aren't even independent, due to "momentum", the fact an injury or a run of good form that contributes to a loss or win may well persist into the next match, morale etc. You could probably simulate the dependence of contiguous results using some sort of sliding probability kernel (a win increases the chance of the next result being a win etc).
