But have a look at this webpage.
It gives you the partitions of 7. As you can see there are 15 ways to get a seven.
A team could score all seven runs in one inning alone. That can be done in nine ways.
A team could score one run in each of seven innings. That can be done in 36 ways.
Or from your example: 2+2+1+1+1. That is scores in five innings. That can be done in ways.
So what you are asking requires a lot of tedious workings.
Moreover, once it is done for seven then its must be done for four.
Multiply the two results together. Here are the partitions of 4. There are only five.