I retired and bred once already so here are the results of my second attempt:

Retired G2-M
ability:Increased stamina
Max Spd: M-4 F-2
Accelere: M-4 F-2
Enduran: M-3 F-2
Stamina: M-3 F-2
Cunning: M-3 F-2

Fledgling G3-M
ability:Level head 2
Max Spd: M-4 F-4
Accelere: M-2 F-4
Enduran: M-3 F-4
Stamina: M-2 F-3
Cunning: M-2 F-3

The starting chocobo is all 2 star so after my first breeding it gained 7 stars, great I thought so I took it. My second breeding only went up 4 stars and the male side took a hit while the female got much better. My question, is it worth it to try for better or is this an average increase after the first breeding? I could probably afford to try again MGP-wise but I'd rather not in case this is a fine(average) increase. Because of RNG it makes sense to go for the biggest increases at the cheapest costs but is there an average increase that people have seen? Is 31 out of 40 stars good after second breeding?