Whats the best way to capture a speed run using a PS4?
to capture from a PS4 use a supported capture card or device. then disable the HDCP in the PS4's system settings, without this off you cannot get an outbound signal to your capture card or device. ¤Note¤ Having HDCP turned off will prevent you from using things like youtube and netflix and playing dvds etc, so make sure to re-enable it afterwards if you plan to use those features.
Alternatively you can get your self a working and supported HDMI stripper/splitter that removes the HDCP which would allow to to ignore the HDCP setting on the PS4 by default and not have to toggle it on and off.