While answering this question, I researched some formulas for energy expenditure when running. None of the formulas I found took into account the factor of exhaustion when calculating calories burned.
To explain what I mean: If you start running, you feel fresh, you know your running technique and you have the fine-motor-skills to use it.
And so you run for an hour, you get exhausted, your legs ache and feel heavy. With this exhaustion your fine-motor-skills decrease. Your technique is inferior compared to when you started.
As far as I can tell, that should have an impact on calorie expenditure, as inefficient technique should burn more calories. Why is this not adressed in most (if any) formulas on energy expenditure? Is the effect just this small? Is it too complicated? Maybe it is indirectly considered when using heart rate as a factor?
EDIT: I feel I might have narrowed the focus of this question by using a running example. I'm interested in the general impact of exhaustion on calories burned in all sports, including running, weight lifting, climbing etc.