We have all been told breakfast is the most important meal of the day but does the science back that up for strength gains? In this study Breakfast Omission Reduces Performance they take trained athletes who eat breakfast on a regular basis and had them either train with breakfast or with just water.
The athletes needed to have eaten breakfast at least 3x a week and trained for 2x per week for at least 3 years. The strength training protocol consisted of 4 sets of squats until failure and 4 sets of bench press until failure.
What they found was that the group who just drank water performed significantly fewer reps than the group who ate breakfast. The interesting thing was that significantly more reps were performed in the first 2 sets of both exercises for the breakfast group but tapered off pretty drastically for the 3rd and 4th set almost matching the water only group.
What this study shows to me is that if you typically eat breakfast keep doing but it may be more important for days that volume is higher. If you are getting into fasting and wanting to train on an empty stomach your performance will drop off pretty substantially in the beginning but I have a feeling once you get used to it you will be fine but will always suffer a bit if the volume is high.
If the goal is to optimize performance I don't think you will ever hear a coach say to train fasted. Food provides energy for your body and if you want to have successful training days you need to eat. Any changes you make may hinder performance initially but once you get used to it you will more than likely be ok and adjust.