Yeah. First I was confused about the edit and changed it (people get mistaken by the half second display) but then I rechecked it myself: http://www.youscreen.de/muobcduwu28.jpg
And ingame it is per second so 1 % per half second is correct
And if u go into a custom game with the described maximum damage setup ( 1 Infinity edge, 5 Cloacks of Agility, 45.51 % in runes, be level 18 and 5 points in judgement ) u have 204 ad and deal 1908 dmg vs a single target but putting these numbers in ur formula does not result in 1908 dmg
After some testing, I found some interesting stuff.
Increased damage against a single target is actually 33% and not 4/3 (= 33.333333%).
And the bonus damage from crit, your formula is actually correct: 100% × (0.5 + bonus critical strike damage)
Practice Tool is actually a bit broken: it gives wrong damage for damage over time abilities, for Judgment it shows damage deals for 11 spins instead of 10. The actual damage can be seen by looking at the target's health bar.
And another crucial thing to consider is the target's armor and the armor reduction of Judgment after 4 spins.
Against a target dummy:The 4 first spins hit against a 100 armor target -> 50% damage. And the 6 others spins hit against a 75 armor target -> 57.14285714% damage.