I`m not sure it is a luck involved or not, but what I can confirm is that it is definitely helps.
we had a few occasions where players with 6-7 stamina (those who should be playing around 70-75 mins / week) were overplaying like 85 and 90 minutes.
With a phycologist + GS training we could save their GS to be somewhere in the middle of GS 8 which is not bad considering that without it they would definitely dropped to 7.