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In an answer to "How do soldiers increase their attributes?" there is the following sentence:

Strength (20): Points are given when soldier moves one tile while carrying more than 80% of its maximum carry weight.

What is called the "maximum carry weight" here? Is it the weight a soldier can carry without a TU penalty or is it the total maximum weight, like when the weight bar is full (not sure what the TU penalty would be then).

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I think it's the maximum weight that the soldier can comfortably carry (without suffering TU penalties). I've loaded everyone with gear so that they are carrying slightly above their comfort zone, just to be sure, and they level up STR after every mission.

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The maximum carry weight is the amount a soldier can carry without getting TU penalties. It's calculated by 8kg + 0.3kg * strength. This value and others are described (and can be changed) in Xenonauts/assets/gameconfig.xml.

For example, a soldier with strength 50 would have a maximum carry capacity of 8kg + 0.3kg * 50 = 23kg. Since 80% of 23kg is 18.4kg, said soldier will not gain strength if they carry 18kg or less, but will gain a progress point towards strength for each tile they move carrying 19kg or more. This means that strength increases every mission as long as each soldier moves at least 20 tiles with appropriate weight.

I would recommend filling each soldier's carrying capacity to the brim whenever you check their equipment. That way they'll still continue to gain strength even when you have multiple missions without updating the equipment between missions, toss some grenades, or drop some equipment to empty your hands quicker.

There are no benefits to carrying less weight than the maximum carry capacity, and especially it is unnecessary to carry more than the maximum carry weight which merely causes the mentioned TU penalty.

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