In the context of competitive online games, ping is going to be ~10-60ms, depending on your connection to the particular server you're playing on, and not particularly noisy (and that's a roundtrip time. Client-Server latency would be 5-30ms). In order for one value to "dominate over" another in an adversarial context, the variance of the former must be much greater than the base rate of the latter.

Imagine a game that's just a pistol duel. When the kerchief hits the ground, players press a button, first person to press the button wins.

In an ideal world, with no delay whatsover, the probability P(A) of player A shooting no later than player B is 100 (because both players shoot at exactly the same time). If we add 5 ms of delay to player A, then P(A) = 0 (he will always lose). If then we add 50 ms of network latency to both players, P(A) = 0 still, because 55 > 50. If we instead make that 50ms delay 50ms +- 10ms (ignoring normal distribution for the moment, pretending every value in that range is equally likely), there's a 25% chance of player A experiencing an unwinnable delay (any network delay value > 55ms results in a value greater than player B's max of 60ms), resulting in a probability of P(A) = 75% * 50* = 38%.

If we make the network delay 50ms +- 5ms, then P(A) drops to 25%.