FPS games are noticeable, however it is possible to easily notice the difference in higher Hz on any occasion. Its possible to do experiments and say with certainty that until we reach 1000hz with true sub 1ms latency people will be able to notice, if they maintain a limited focus. 360hz is probably the big visual leap.
If you want a simple method of realizing hz assuming there is no bug or OS limit(some get stuck at 120hz), just use the mouse on desktop. Move it around in circles and look at the distance between the trail of realized mouse cursors(easiest), and if you want the exact amount, practice trying to perform around 3 circles as large as you can in one second and keep repeating until you can count the number of mouse cursors that you can visually see in only one circle and multiply by 3.
3 circles in one second is easy to realize at 144hz or less. You can complete a single continuous circle in one second, however you wont be able to count the visual mouse trail even at 60hz. You can also do more than 3 circles, however making too many rotations too quickly can also make it difficult to count.
Doing the three circle experiment above on your desktop screen:
- 60hz setting you will see around 20 mouse in one circle.
- 120hz -> 40 mouse
- 144hz -> approximately 48
This is the most readily available method that you can accomplish and backup with math and realize its relation to visual integrity of monitor refresh rates.
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http://frames-per-second.appspot.com/
https://www.testufo.com/#test=framerates
These tests can help you compare differences in a visual space.
However, you will only be able to visualize from your refresh rate and below. They do nothing to help you perceive future developments.
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I like the desktop method because you notice the spatial differences between the mouse cursors, and each increase in hz will decrease the space between mouse cursor trails interpreted by your eyes. This helps an observer calculate and mentally perceive future developments. IE - if there is a 1inch space between 2 corresponding mouse cursors in a trail using high motion speed at 60hz, then there would be a 0.5 inch space between 2 mouse cursors in the trail at 120hz, 0.25 inch at 240hz, and 0.125 inch at 480hz, etc.
NOTE*** I am not talking about turning on "MOUSE TRAILS." I am describing what visually occurs when moving a cursor at high speed on a screen.
RPG/ACTION games can also be more fluid with high refresh rate monitors, however it depends entirely on how quickly units or action occurs ACROSS a screen. MOBAs would likely see zero benefit beyond 120hz. 2d or 3d Fighting Games and TPS games with cameras behind a character CAN benefit from Higher refresh rate monitors. High refresh rate monitors mostly help you perceive FAST actions and motion.