Apparent delay with shooting and meleeing

I’ve just now started playing War Games team slayer with regularity, and I’ve been having an issue with some apparent delay when trying to shoot or melee an opponent. I know Halo 4 has had it’s share of lag issues – which I’ve also experienced – but it seems like the delay problem is not due to lag (though I could be wrong).

To give you a better idea of what I’m talking about, it seems that when I have my sights on an opponent and fire, the shots tend to miss – like I’m just a split-second too late. On the other hand, when I anticipate an opponent’s movement and start shooting a second early or kind of lead the opponent, I have much greater success. Anyone else have a similar experience? Am I crazy? Or is this all just a function of lag?

I considered the possibility that it’s attributable to the slight delay from my DLP projector to the screen, but I tend to doubt that’s the explanation. I haven’t experienced any noticeable delay with FPS games in the past (Halo Reach, specifically) and my understanding is the delay time is only about 20 ms, which is comparable to a number of TVs on the market.

Anyone have any input here?