4 Amps does seem to be a lot at first glance, but it depends upon how new and 'feature-packed' the vehicle is.
Q - What exactly is the year, make and model of vehicle?
Another factor, associated with the vehicle age/features, depends upon the time at which the parasitic current draw is taken.
As more and more electronic control units began to be introduced into vehicles, the standby current draw obviously increased. Automotive technology has advanced quite a lot over the years, bringing bus systems into the mix and control units practically monitoring/supplying power to almost everything on a vehicle. IIRC, a high end 7 series (E65) BMW had around 70 different Electronic Control Units distributed all around the vehicle, each with it's own power supply. At the moment of connecting the battery, each ECU would be fully awake and consuming current. (This would be the same condition when initially checking the parasitic draw)
When the individual systems sense that they are no longer required to be in operation, such as there being an absence of ignition/accessory power feed, they shut down to a 'sleep' mode. The whole process, for a complete shutdown of non-essential systems, can take up to/exceed 30 mins on some vehicles.
The current consumption can be observed to drop gradually during that time, due to load-shedding, then a more-accurate reading can be taken once the reading stabilises.
As noted in previous posts, if the vehicle is an older, more basic model, try disconnecting the alternator first and measuring the drain Vs when the alternator is connected.