My recommendation:
Speak to or think as a football fun, obviously I am not a that type person :)
Try to find out what can help us to predict "next" game's result as an expert. Collect that data to feed in your model.(and/or any relevant data available)
For example, all matches have been played between Arsenal and Chelsea so far might have a value in your model. Also the last games each team played might have an affect at the next match's result.
As you stated in your question go with pre-match variables to "predict" next game's score.
Another model could be:
You can take the features(data) in your question for the first t minute of the match and try to predict the result. Let's say use the data belonging the first half of the match to predict second half's result.
On the other hand, the way you are doing at the moment can be helpful if you are looking for some exploratory analysis. For example which feature(s) has more impact on winning a game.
Hope this helps and looking forward to see other answers/and your analysis results.
ia