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I have a unit with 85 aim, if I give them a light plasma rifle with a scope that would be +20. What would an aim of 105 mean? Is there a reason to ever go over 100 on any stat except Hit Points?

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penalties reduce your stats, but if you have an extra, you keep the 100 =) – Michel Dec 20 '12 at 16:10

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up vote 13 down vote accepted

The maximum hit chance you are gonna get is 100%, even if you theoretically have more that that.
But, and this is important, the total value of 105 (from your example) will be taken into calculation when an enemy is behind cover and thus lowering your hit-chance.

Example calculation:
85 Aim
+ 10 Scope
- 20 Low cover
= 75 Hit chance

Also have a picture:
Ingame calculation of hit chance

Keeping these examples in mind, if you are able to boost the aim of a soldier with a bonus or 2 up to 120 you will render low cover useless to enemies.

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"...to enemies without natural defense", that is :-) – Orc JMR Dec 20 '12 at 17:55
Towards the end of the game you start to encounter enemies with 40 defense - i.e. you automatically lose 40% chance to hit against them, even before cover is taken into account. Those snipers with 120 Aim start to become real handy ;-) – Simon Waldman Dec 21 '12 at 16:00
up vote 2 down vote

Having a 100 Aim does not mean a 100% chance to hit - enemy's defense bonuses will lower it. To have a 100% chance to hit against a sectoid in high cover (-40% to hit), you'd need an unattainable 140 aim, not to mention enemies with defense bonuses. The same principle applies to other stats - it is almost always beneficial to to have more than a 100 in a stat.

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