I touch some of this briefly in the
The Amazing Human Visible Feats Of The Millisecond.
Sometimes the millisecond doesn't matter (big whoop) while other times it makes a massive difference (holy cow). It depends on the variables & the context.
Remember the olden days when people laughed about going beyond ~60Hz-85Hz? We know better now. Or even
humans can't tell 30fps versus 60fps
There are multiple effects of pollrate here, some visible, some not visible but affects scoring ("I seem to be missing more of my shots") effects.
1. Microstutter harmonics of pollrate versus Hz (low Hz microstutter = extra jitter, while high-Hz microstutter = extra blur)
2. Microstutter harmonics of pollrate versus fps (low Hz microstutter = extra jitter, while high-Hz microstutter = extra blur)
3. Stroboscopic stepping effect when pollrate is below fps & Hz
4. Non-interpolated granularity for the mid-flick shoot
5. Etc. (There are additional niche factors, but the above are the most easily explainable)
Now for #4, it interferes with the
Latency Aim Training Effect. If you're trying to stop an 8000 pixels/sec flickturn onto a more exact pixel, 1000Hz poll gives you a granularity of 8 pixels. So shooting mid-turn, your shot will round-off to the nearest 8 pixels. Now
on an 8K television, a 8000 pixels/sec mouseturn is a slowturn! since the screen is scrolling slow enough to allow you to shoot objects mid-slowflick, much like a sideways-scrolling archery target.
Now your latency training in aiming mid-flick will have natural human jitter (e.g. your reaction time might be fairly consistent 150-160ms for a well-trained pre-primed predictable stimuli like an object about to scroll past crosshairs, a reaction time variance of 10ms -- but most of your hits may hit close to the 155ms mark, in a tighter 3-to-4ms span). This is pre-primed reaction, not the wider >10-20ms variances seen in reaction time benchmarks using random-flash stimuli. With such a tight latency training effect for pre-primed stimuli (e.g. turning past a stationary target at constant speed predictably scrolling past your crosshairs), a 1ms granularity error can create significant feel of miss. You don't feel the millisecond, but you feel the increased misses.
This is easier to test at 125Hz poll rates -- 8ms misses are easy to feel. But with the Vicious Cycle Effect at play, we're starting to reach the point where (4) actually is a legitimate factor.
For me, personally, I'm all about motion (1) and (2), because 1000Hz poll creates human-visible microstutter during ultra-Hz or strobed operation, so microstutter-futureproofing for future displays requires >1000Hz poll rates for retina-resolution ultra-Hz displays.
Internet latency will usually make (4) not matter, but in solo/LAN, can emerge. Thus, I'm more about the issue of (1) and (2) personally myself, smoothing out motion further, which affects all situations (solo and non-solo)
You can see this effect much more easily with low-DPI high-ingame-sensitivity situation, where your slowturns are steppy-steppy (e.g. mouseturn 1 mousepad dpi turns into a 10 pixel onscreen mouseturn). Easy to see when moving mouse really slowly during low DPI (e.g. 400dpi) with in-game sensitivity cranked up high. This is a great demo of 400dpi being absolutely shit. (Even 800dpi is getting there). Now if you reduce sensitivity, the slowturns get smoother. But if you increase DPI again, the slowturns get coarser again.
Now, pollrate won't affect slowturns (much like high DPI will) nearly as much as fast-turns, but the granularity effect is still there, just harder to see because you cannot see it except via single-stepping YouTubes or high speed videos.
The best of all worlds is super-high-DPI (native, non-interpolated) combined with super-high-pollrate, combined with retina refresh rate and retina resolution, bruteforcing the weak links away, so that it's smooth even for sloooooow turns and fast flick turns (no steppy-steppy effects seen visually OR in high speed videos).
Also, the rule of geometric upgrades that I recommend for the diminishing curve of returns, apply here. This is especially true when upgrading refresh rate (1.5x upgrade like 60Hz->144Hz->360Hz or 2.0x upgrade like 120Hz->240Hz->480Hz). But also applies to upgrading mouse poll rate. For pollrates, even suggest upgrading 4x-8x though, much like 125Hz->1000Hz->8000Hz, for human-feelable benefits though, though low-sensitivity low-framerate users will not notice, especially for 144Hz-and-under.