Clay soil has a high CEC value and anhydrous is another cation. The ammonium is attracted to the clay and is in many ways becomes a slow release fertilizer.
The advantage is there is no leaching or volatilization of Fall applied AA, plus there is not the great need for side dressing a crop. Add to this we can compute just how much N is removed by the crop and consider any excess as residual.
The complication part is roughly half the amount of AA applied in any one crop year is available to the crop that year, the other half becomes residual. Then half of the accumulated nitrogen in ammonium form that is part of the CEC complex on the clay platelets is available to the crop in any one year.

Example in it's simplest form.
Starting with a blank slate, you believe you will need 100 lbs of N which is 122 lbs of AA. The very first year you apply 244 lbs AA and make a normal crop, Half to the crop & half as residual.
Year two Half the residual is available to the crop, 50 lbs N. You still want 100 lbs of N so you apply 100 lbs N, half of it is available to the crop but you still have the 50 lbs from the residual pool. Everyone is happy.

If by chance you have a short crop you will be adding to the nitrogen pool. This is good as if conditions are good, and your accumulated nitrogen is adequate you will have the extra fertility there to make a bumper crop.

On a lark or in a wild fit one time I applied way too much anhydrous on 2 acres. Then I sat back and did not fertilize, with nitrogen, till production fell off. The book said this should be about 5 years. In fact all that nitrogen persisted for 7 years. Hint, if you do something like this you should also make sure your other cations (K, Mg, Ca, & many of the micronutrients) are also in strong abundance.

If you are on sandy soil your challenges are completely different. Some of my friends in East Texas must side dress their crops. Those with grass pastures find it pays to apply nitrogen every three weeks, rain or shine.

Lesson to take to heart. What works and is true in one place probably will not be true in a different soil, crop, climate, and/or management style.