out of baseline at home plate

[gordon30307]

Watching the Cubs vs. Mets yesterday evening Hill the Cubs catcher has the ball well before the Mets runner reaches the plate and is bracing for the collision. The runner runs around Hill who lunges for him and misses and Hill loses the race to the plate. Any other base and the runner probably is called out for being out of the baseline. I had no problem with the call but I was just wondering how far in the vicinity of the plate must the runner go before he would be called out for being out of the baseline? I know more leeway is given around the plate but how much?