ZDDP, in used since the late 1920s, is one of the best anti-wear additives one can put in a oil.
However, most oil manufacutes put a prescribed amount of ZDDP (or other related anti-wear agent) in their oils, already.
So, without knowing your application (vehicle and driving conditions) or the oil you have in the car (or are going to put in the car), one cannot say that adding ZDDP will be helpful or harmful.
Modern oils have been reformulated to lessen the ZDDP in oil in an attempt to make catalytic convertrs last longer. The P in ZDDP slowly degrades the catalyst performance as the oil burns over the 120K manufactures warentee on the Cats.
Modern engines need less ZDDP than older engines, as the vavle train has been rollerized, and other bearing surafces are made of material better able to deal with the stresses involved without large doses of ZDDP.
Given in applications where ZDDP is the "cats meow" for protection, you still don't want "too much" of it in the oil (causes deposits). Thus, say you do have an application where you desire more ZDDP. At this point you have to find out how much ZDDP is already present, what other agents are present, what mixed concentration you want to target, and then carefully measure the ZDDP to achieve your goals.
It is FAR from buy a bottle and pour it in. You basically have to know how to calculate these things.
So, summerizing: ZDDP is good stuff::en-the-RAW, too little is bad, too much is also bad.