It is far better for battery life to leave your laptop plugged in while in use than to do deep discharges.Lithium ion battery lifetimes will reduce as you use it. The deeper you charge/discharge your battery, the more it will reduce. If you made 200 full deep discharges (from 100% to 0%), you will find that your battery now has less battery life than doing 2000 light discharges (100% to 90% for example). For this reason it is far better to leave your laptop plugged in than to do deep discharges, you’ll soon find your battery totally worn out if you regularly drain the battery all the way.
If you used a battery for a long time, particularly if you keep it plugged in all the time, the battery fuel gauge might get a bit “out of sync” with the battery (accumulated measurement errors, change in battery life, etc.) and no longer show a correct battery life reading. Doing a full charge/discharge cycle recalibrates the fuel gauge, allowing it to display a more accurate battery life reading. But this is a purely cosmetic thing – it doesn’t do anything for the actual battery life.
A good laptop (or nearly any laptop) is not going to charge your battery constantly. Once the battery is charged, the computer will only monitor its level and recharge the battery occasionally when the level drops below a certain treshold (like 90% but it differs and can be user-set for some systems).
The effect on battery life of running constantly on AC power is minimal by my experience.
Batteries seem to suffer primarily through random and erratic partial discharges/recharges as is commonly seen in business settings where the users just don’t care.