The question relates to human perception. From the earliest days of humans interacting with computers, an important question has been how fast response time needs to be for the person to feel like they are interacting with the computer and controlling the action (as opposed to submitting a job and waiting for the result). If you use a pencil, you have the sense that you are controlling it. When you use a GUI interface, you move a mouse and something happens on the screen. How fast does that need to happen to give you the sense that you are controlling the action on the screen, that it is an extension of yourself?
It turns out that there are three response time limits relevant to an application or interface device that humans perceive differently.
0.1 second is the limit for a person to feel that the system is reacting instantaneously and they are directly controlling the action.
Between 0.1 second and 1 second, it will feel like an interaction with the computer rather than something you are controlling yourself. Delays of under a second will be noticed but perceived as the computer working on the command and still interacting live.
1 second is about the limit for a person's flow of thought and a sense that it is a live interaction. Delays longer than 1 second feel like a wait.
10 seconds is about the limit for keeping attention focused on the task. By 10 seconds, you start losing information from short-term memory so it becomes hard to simply resume the interaction without re-focusing.
So what are the implications for trying to speed up an input task (or application interface or web page)?
For any input task, the system obviously needs to keep up with you. However, once the response time is below around 100 ms, it will feel like an extension of yourself and you won't notice small differences in response time. (Possible exception: someone like an avid gamer with extremely fast reflexes may notice that a faster system feels more responsive.)
Response times longer than 1 second will benefit from reduction to under a second and will yield a change in the perceived experience.
Response times less than, but close to, 1 second will benefit from reduction and will seem a little faster. However, as the times get below about half a second, improvements won't make much practical difference. You can perceive the difference in time, but it won't functionally change your experience. As long as the time is above 100 ms, you will still experience a brief delay and the effect of that delay on your interaction with the computer will be the same.
File this under “managing expectations”.
If you are interested in further reading, there is a fair amount of reference material out there. A couple of links that provide an overview: powers-of-10-time-scales-in-ux, and response-times-3-important-limits.