Psionic Skill
Psi Skill is a rating of the effectiveness with which the soldier can use his inherent psionic ability.
Starting Values
New recruits will always begin with a value between 16 and 24. This is awarded upon completion of first month's Psi Lab training.
Maximum Caps
An X-COM soldier's Psi Skill has a combat increase cap at 100, but can continue to grow past that through Psi Lab training.
Improvement
Psi Skill is increased by use of Psi on the battlefield, and through Psi Lab training. Both successful and unsuccessful psi attempts during combat result in improvement.
Psi Skill will increase from 0 to 6 points per combat mission, depending on how many times you attempt a Psi action (Panic or Mind Control, MC). Only the number of attempts matters - your current skill level does not affect the number of points awarded. With one successful panic or MC, an average of 2.0 points are awarded (range 1-3). With 4 or 5 successes, approx. 4.0 points are awarded (range 2-6). No more skill points are added if you do more than that.
The above numbers are for successful Panics or Mind Controls. Failed Psi attempts cause the Psi experience byte to increase by a third as much as successful ones. So Psi failures do help you gain skill points, but at a lower rate. 12-13 failures (vs. 4-5 successes) will get you all the points you can get.
Because you can get a +6 roll when at cap-1 (99) if you have enough attempts, it is possible to have a Psi Skill of up to 105 (cap+5). For more info, see Soldier Experience.
Unlike any other skills, Psi Skill is not truly capped. Although combat increases stop once you reach 100+, the Psi Lab increases skill as follows:
End of Month _Psi Increase__
Psi Skill Range Average
0-16 16-24 20.0
17-50 5-12 8.5
51-253 1-3 2.0
It has distinct stairsteps, and rolls randomly within each range. Rookies always start with 0, and thus get 16-24 skill points in the first month's training. If you got unlucky and only got 16, the next month's training will give you 16-24 again - if you don't earn a single point on the battlefield! That's about five combats worth of the maximum possible average of 4 points per combat... you might want to not exercise a 16's psi skills at all, if he won't be going on that many combat missions in his or her second month.
Also notice that Psi Lab training keeps awarding 1-3 points per month way above psi skill 100 - about 24 points/year. It breaks down at 253 because the counter byte wraps around to 0. Of course, training can be turned off then. But who needs anything over 60 anyway, if their psi strength is high?
Note: Psi Lab training (for a given month) is lost if the soldier is transferred to another base, even if the destination base has Psi Lab space available.