Input lag, or latency, for projectors refers to the time between when the audio/video signal from the input source (the gaming console) is received by the projector and when the projector actually projects the video that corresponds to that signal, which can cause things such as lag time or image stuttering. Because of this phenomenon and how it may affect your ability to play at the highest level, low input lag time is one of the key things to focus on when determining whether a projector will boost or hamper your gaming abilities, as you want a projector that instantaneously projects the video that the console is transmitting to it so as to make sure that you’re able to make those split second decisions.
It’s worth noting that input lag time is somewhat different then response time. Response time in gaming refers to the duration of time between when a button is pushed on a controller and when the character performs the corresponding action and thus involves all the hardware involved in the gaming setup, while input lag time refers only to the part of the equation involving the input signal and projector.