When you want to breed Chocobos...
The Max Dash of a Chocobo bred with Pepio Nut will be the average of its parents' Max Dash stat minus 100 or 200 (randomized), with a minimum of 300. The Dash stat is calculated the same way, though if the result is equal to or greater than the Max Dash stat, it will be reduced by 100 until it is less. The Max Run stat is calculated with an average of the parents' max run minus either 100, 200, 300 or 400, and has a minimum of 300, and if it exceeds the Max Dash stat, it will be reduced by 100 until it is lower. The Run stat is calculated identically, though it can only be reduced by 100 or 200, and if it is greater than or equal to Max Run or Dash, it will be reduced by 100 until it is less. The Stamina is an average of the parents' stamina minus a number between 1 and 255.
If the baby Chocobo's max stat is below 4000, there is a 1/512 chance that a bonus can be applied; a 1/128 chance that Max Dash will be 4000, another 1/128 chance that the stat will be 4100, a 2/128 chance that it will be 4200, a 3/128 chance it will be set to 4300, a 1/128 chance that it will be set to 4500, but a 120/128 chance that there will be no bonus.