When in it comes to designing a solar + battery system versus just a solar system, the key is understanding how much power is going to be consumed by the home directly during the time of production, and how much is produced in excess that needs to be captured and stored by the battery. Depending on someone's usage pattern through each 24 hour day, a household with the same overall usage could need two different sized batteries. Let me explain.
Let's say we have two homes. Each home uses the same 12,000kWh annually...
Example 1 :
Home number one consists of a young family with a couple of kids under the age of 10. Usually this family wakes up around 5-6am, takes care of morning tasks in the house and uses appliances to cook. Then after they get the kids off to school, they both go to work most days where they will be out of the house the majority of the day. Then in the afternoon/evening time, everybody comes home, homework is being done, dinner is being served, etc.. The energy usage of this house would be a spike in the morning and a spike in the evening with a lull mid day and less usage at night unless they are running an AC all night. This family is going to need a larger battery than in the next example because they are consuming power mostly outside of the peak production hours.
In this theoretical example, the system is producing around 33kWh a day total and about 10kWh is actually used in real time from the live production. They would need at least a 23 kWh battery pack to get them through an average day. To truly be fully self sustaining, we would have to use winter month production although this is not how most will design.