If you were bowling in a doubles championship and you were doing great but your partner admitted he or she was mentally and physically tired, what would you say to him or her? That's what you need to say to yourself in that situation.
As always, focus on your execution not on your results. However, when you're mentally tired, cut out as many distractions as you can. The more distrations you can cut out, the less mental energy you'll expend overall, leaving you with enough "stuff" to focus on executing well. Personally, I do this by sitting on the closest bench/chair to the lane and turning my back to everything but the lane when I'm done with the shot. Make the shot, sit down. Only allow the mind to focus on making the next good shot. Forget about the tournament, forget about your score, your car, your job, your whatever, keep things simple and let your mind focus on only one thing: bowling. It is less mentally fatiguing to focus on one thing than to attempt to multi-task and overclock your synapses.
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Kill the back row