Input latency is discussed almost entirely in terms of display refresh rate, which is one contributor among several and frequently not the largest.
The chain
A button press must be detected by the device, transmitted, processed by the operating system, read by the game, incorporated into the simulation, rendered into a frame, sent to the display, and drawn on the panel.
Each stage adds time, and the total is what the player perceives.
Measuring the whole chain requires high-speed capture of the physical input and the screen, which is why reliable figures are scarce and mostly come from a small number of testing outlets.
The device
Polling rate determines how frequently the device reports its state.
Higher polling rates reduce the average wait before an input is noticed, with diminishing returns as the interval falls well below other delays in the chain.
Wireless devices add transmission latency, which modern implementations have reduced to the point where the difference from wired is small enough to be contested rather than obvious.
Switch actuation and debounce handling add small amounts, and mechanical characteristics vary between devices.
The render queue
Where the largest controllable delay usually sits.
Graphics drivers queue frames to keep the hardware busy, which improves throughput and means a rendered frame may wait before display.
Which adds latency proportional to queue depth, and the queue exists to smooth performance rather than to harm responsiveness.
Features that limit queue depth reduce latency measurably, and they can reduce peak frame rate slightly, which is the trade.
The frame rate connection
Higher frame rates reduce latency independently of the display.
Because the game samples input once per frame, a shorter frame interval means input is sampled more recently when a frame is produced.
Which is why competitive players run frame rates above their display's refresh rate — the display cannot show them all and the input sampling still improves.
Display processing
Panels process the incoming signal before displaying it, and processing time varies enormously between models.
Image enhancement features, motion interpolation and scaling all add delay, sometimes substantial.
Game modes disable most of this, which is why enabling one produces an immediately noticeable improvement on many televisions.
Response time — how quickly pixels change state — is a separate specification and is generally smaller than processing delay on modern panels.
Vertical synchronisation again
Enabling it adds latency, since frames wait for the refresh boundary.
Which is why competitive configurations disable it and accept tearing, or use variable refresh rate with a frame rate cap slightly below the panel maximum, which avoids both the tearing and the waiting.
That configuration is the standard recommendation and it is not obvious from any individual setting.
Network latency
In multiplayer, an entirely separate delay affecting when other players' actions become visible and when yours are registered.
Client-side prediction hides much of this for your own actions, showing the result immediately and correcting if the server disagrees.
Which is why your own movement feels responsive on a poor connection while other players appear to teleport.
Lag compensation, where the server rewinds to evaluate a shot against what the shooter saw, is what produces the experience of being hit after reaching cover.
That is a deliberate design choice favouring the shooter's experience, and no configuration satisfies both parties.
Measuring it at home
More accessible than it used to be.
Some graphics drivers and peripherals now report end-to-end latency estimates, which are useful for comparing configurations even if the absolute figures are approximate.
High-speed video from a phone, capturing the input device and the screen together, allows manual measurement by counting frames, which is tedious and genuinely accurate.
Where the effort is worth it
Competitive shooters and fighting games, where timing windows are tight enough that tens of milliseconds change outcomes.
Fighting games in particular are designed around frame-level timing, and added latency directly removes the window for reactions the game expects.
For most other genres the differences are below the threshold at which they affect anything.
The perception question
Studies of latency detection find thresholds varying considerably between individuals and tasks.
Trained players detect smaller differences than untrained ones, which is a genuine effect rather than expectation.
Which means advice calibrated for competitive play is frequently applied by people for whom it changes nothing, and the money is better spent elsewhere.
Wireless controllers
Modern implementations add small and measurable latency over wired connection.
Which matters at competitive level and generally not otherwise, and battery and convenience are worth more to most players.
Frame rate caps
Capping frame rate slightly below the display maximum, used with variable refresh, keeps the system inside the variable range and avoids the synchronisation penalty.
Which is the configuration most commonly recommended by people who measure this, and it is not the default anywhere.
Television against monitor
Televisions generally add more processing delay than monitors, even in game mode, though the gap has narrowed considerably on recent models.