Classifying sparse binary data for int value

I’m very new to data science and still trying to get the grips. The problem I’m trying to tackle is, we have a pool of footballers from a league and data objects representing a group of 11 footballers for a given match and the number of goals scored by that team on that match.

The goal is to estimate the number of goals that are potentially to be scored given any random line up of footballers from this pool. This data set spans over a long period of time and footballers transfer between teams, so, teams don’t matter.

I thought about representing each footballer as a separate binary attribute to mark if they were present on a given object or not. Then, do some pruning by dropping the attributes that occurred less than a threshold and then what? What kind of classifiers should I be considering to classify such a spare binary data set for an integer value?

From what I know, neural networks is one potential candidate but I do not understand them enough to use, so, a few other options to play with would give me some direction I hope.