The extra minute has often meant the difference in me getting home 45 minutes earlier or not.

All the clocks in Grand Central are all set to the same. When you look at the monitor to see what track your train is on, you also look at the time in the upper right (because the time on your watch really doesn't matter) to see if you can make it or not. The people who know they actually have that extra minute rush for the train. Those who don't look down the list to see what track the next train is on and head for that.

For some lines it's no huge deal, there may be another train in as little as three minutes. For other lines, it could be another 35 or 45 minutes till the next train.