Not to answer with a tautology, but it becomes a problem when it is a problem. For example, when you are missing work (or drunk/hungover at work leading to consequences), or it is causing problems in relationships, you spend an inordinate amount of time or money getting/using alcohol, etc. I would also add when you develop physical dependence as manifested by alcohol withdrawal symptoms, as alcohol withdrawal can be life threatening. People joke about "the DTs" (short for delirium tremens) but not many realize that you can die from them.
Check out the DSM for more detail about how addiction criteria are currently operationalized.
Still, I wish I had a number. I am sure there is a datapoint out there but I haven't seen it.
Even if it is, "on average a heavy drinker that claims to have a problem and registers with a psychiatrist says that they drink on average '10 drinks a week'".
Check out the DSM for more detail about how addiction criteria are currently operationalized.