First, Wisconsin has its own plumbing code that deviates from the IPC and UPC, so the answer may be slightly different in Wisconsin.
But the basic answer is that the shower trap arm is limited to one pipe diameter in fall, while it must fall at least 1/4" per foot. Note here that the trap arm is defined as the drain from the trap outlet to the vent connection. And that the shower fixture drain (drain carrying only the shower) must be vented before or as it joins another drain (with one exception in the IPC). Note also that the UPC imposes a further length limit on trap arms: 42" for a 1-1/2" trap arm, and 60" for a 2" trap arm. I suspect that Wisconsin has similar limits.
So if your shower trap is just 3' from the main stack, there are various reasons that it may have an AAV on it rather than relying on the main stack for a vent. Here's a non-exhaustive list:
- The shower fixture drain has to drop more than one pipe diameter to make its connection to the stack.
- Some non-bathroom fixture joins the shower fixture drain before it joins the stack, which precludes wet venting.
- A WC or some other disqualifying fixture drains into the stack above the shower drain connection, so the stack can not function as a vent for the shower.
Cheers, Wayne