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New dwellers seem to all start with very low starting stats. Is there a way to get new dwellers with higher than normal stats?

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There is! Breed with two max-stat dwellers to get them super-babies.

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As you notice, this is a level 1 CHILD. The second photo is a super baby combined with a +3 stat pet. The specific details to get these higher than normal stat children are as follows:

"Super" Child Formula

max = (male_total_special + female_total_special - 14) / 126

random_number = random(max / 4, max)

if random_number is greater than 0.95 the child will be legendary

if random_number is greater than 0.85 the child will be rare

otherwise the child will be normal

Notes:

  • Parents' total SPECIAL must be 134 or higher to have a chance at a legendary child.
  • Parents' total SPECIAL must be 122 or higher to have a chance at a rare child.
  • Two fully maxed out parents (SPECIAL 140) will have a ~6.6% chance of producing a legendary child, and a ~13.3% chance of producing a rare child.
  • Two maxed parents will produce a child with an Intelligence proficiency.

Source

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  • Intelligence proficiency? Whats that
    – Esqarrouth
    Commented Aug 24, 2016 at 14:54
  • 1
    It is for meeting room requirements. STR for power rooms, AGI for food rooms, PER for water rooms, etc. A child with INT proficiency just means it will have INT as highest.
    – Nelson
    Commented Aug 24, 2016 at 15:56
  • Although the latest version gives you even higher stats doing this when combined with + stat pets, it doesn't actually change the answers a whole lot so I'm just gonna stick in a comment instead.
    – Nelson
    Commented May 29, 2017 at 18:40
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There is technically no way other than breeding 'super babies' or lunch boxes

Although the higher level your radio tower is and the higher the level of the dwellers in it, you have a better chance of getting dwellers with higher stats than normal

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