Precision is the player’s ability to consistently and accurately aim circles right to the center. Simply put, maps with more of a risk to aim inaccurately would be weighed more than maps that are very easy to aim consistently. Examples of this would be patterns that are widely spaced and quick, but low cs-maps have an exponential impact on precision difficulty.
t+pazolite & Camellia feat. Nanahira - Boku no Yume, Mecha Kuso Mugen Waki · beatmap info | osu!
It’s not too complicated. $a_{zone}$ is simply the area you can click a circle without missing it, valued as the area of the circle. It scales based off of the equation for CS → osu!pixel provided on the wiki page.
Aim Success Probably is a scale of how hard it would be for a cursor could to reach that circle.
As the circle size decreases, it becomes linearly more difficult to hit a circle, and so that linear scale would apply as well.
$c_{sWeight}$