ZDDP (aka ZDP, Zinc DialkyDithioPhosphate) is a common antiwear additive in engine oil and engines rely on the antiwear additives in the oil to prevent wear in the boundary and mixed lubrication regimes.  ZDDP was originally used as an anti-oxidant and it still has this function today.  In bearings, ZDDP provides sacrificial protection, meaning that once it is worn off, it needs to be replenished. ZDDP is a polar compound, meaning that one end of the molecule is attracted to the iron wear surface and must compete for location with other polar additives (like detergents and friction modifiers).  ZDDP only plates out (adsorbs) onto the wear surfaces when activated by heat and pressure from close contact between moving parts.  If the ZDDP layer is worn away, adhesive wear can occur which could cause surface irregularies larger than the ZDDP layer.  If this happens, there is no way to stop the wear from accelerating and it's only a matter of time before a camshaft lobe is wiped.  See Friction Modifiers.

The rate at which the protective ZDDP layer is worn away depends up on the bearing loads and the length of time the wear surfaces remain in the boundary lubrication regime.  Once the oil is hot, the protective ZDDP layer will rebuild itself from the remaining ZDDP in the oil.  Once the ZDDP layer has repaired itself, any additional ZDDP will not make this layer any thicker.  Effectively, greater amounts of ZDDP extend the driving distance of the oil in the sump.  According to a GM Techlink service bulletin (December 2007), Bob Olree (GM Powertrain Fuels and Lubricants Group), excessive amounts of ZDP is not beneficial:

A higher level of ZDP was good for flat-tappet valve-train scuffing and wear, but it turned out that more was not better. Although break-in scuffing was reduced by using more phosphorus, longer-term wear increased when phosphorus rose above 0.14%. And, at about 0.20% phosphorus, the ZDP started attacking the grain boundaries in the iron, resulting in camshaft spalling.

It's better to use an oil formulated with the right amount of ZDDP and other additives than guessing you've added the right amount.  The main reason for using an engine oil with sufficient ZDDP is to protect the lobes of a flat tappet camshaft. Modern engines with roller lifters don't have this need, which is why Starburst Oils contain 0.06% to 0.08% phosphorus to prevent poisoning of their catalytic converters.  Pre-2007 (ie, before API CJ-4) heavy duty engine oils typically had phosphorus contents less than 0.14% (1400 ppm).  The current CJ-4 and CK-4 categories phosphorus limit is 1200 ppm and this concentration has been found to work well to protect flat tappet camshafts.  ZDDP additive manufacturer ZPlus also suggests a target of 1200 ppm of phosphorus:  see ZDDPlus™ Tech Brief #2 - ZDDP and Cam Wear:  Just Another Engine Oil Myth?