Our SJC - LAX flight yesterday was delayed more than an hour, but there was one leaving only a bit late at the next gate. The gate agent let us take that flight without any additional fare. She said "your plane is more than 20 minutes late, so I can waive the additional fare."
So, new rule ----> delay > 20 minutes = "free" seat on earlier flight.
If my memory serves me correctly, the old rule was delay > 60 minutes.