Low DPI can cause a reticle to skip over hitboxes.
Imagine in the extreme case where a DPI hipster plays using 1 DPI and hacks in-game sensitivity to allow the sensitivity to be set to 4000. This actually results in a very competitive 34.64 cm/360°, but the reticle will be skipping by 26.4° at a time! The DPI hipster will not be able to hit anything.
How much DPI does one need? What is enough DPI such that the reticle can be placed anywhere on the screen? This depends a few factors: DPI, in-game sensitivity, FOV, screen resolution, and screen ratio.
This tool will calculate if a given DPI, in-game sensitivity, and FOV is good enough for various screen sizes.
The key thing to figure out is for a given DPI, in-game sensitivity, and FOV, how many samples per degree does that that result in. This is the overall sampling rate of the mouse, which is then compared to the actual resolution of various monitors. If the sampling rate is 2x of the resolution of the monitor for a single degree, this means the settings are enough to reach any part of the monitor.
The sampling rate has to be 2x of the resolution due to Shannon's law. For our purposes this effectively halves the calculated sample/degree.
To use this tool enter your DPI, in-game sensitivity, and FOV, then find your screen resolution. If Shannon's law sample/degree is greater than your screen's pixel/degree then it passes with blue, otherwise it fails with red.
If you have any questions feel free to tweet me @pyrolistical.