Minimal subtitle leading/lagging difference
There are lots of tricks to proper subtitling, but none of them involve delaying them. The reason you see large lags is because of "live" captioning -- they're appearing as fast as some trained operator can hear and enter them, which for the very best of them is still a few seconds.

For post-event titling, you want the text to appear at or slightly before the spoken word, but consistent with scene changes -- when a scene changes behind a title, the viewer tends to start reading it again, which is confusing.