Great work, but I believe Sharp Shooter gives you +3% critical hit chance natively (i.e., even when it resets, you always receive +3% crit chance on top of what you already had). I haven't used SS in quite a while, so this might've changed.
that's not right, if you critically hit within 2 seconds, then your critical chance profit is less than 3%
No, you're not following what he's saying. The skill sharpshooter increases your base critical hit chance by 3%, and then adds another 3% every second thereafter. For example, if you have 50% critical hit chance without sharpshooter, and then enable the skill, your character sheet will read 53%. Every second you don't crit, you gain 3% crit chance. When you do crit, your crit chance will reset to 53%, NOT 50%. This is a huge difference, and if you haven't taken that into consideration, your formula and paper are incorrect. Sharpshooter has a guaranteed 3% crit chance value 100% of the time.