I would respectfully disagree that aging does not help. We age every big game animal and it can make an appreciable difference. I even installed a walk-in cooler in my shop for the purpose. I try keep as much meat on the bone until after rigor mortis has passed at bare minimum--hanging past then will allow the meat to loosen up and then start the breakdown of proteins that makes the meat more tender. Hanging also drains the blood out and improves flavor. I've cut up bull elk directly after the kill that would bend your teeth.
Aging helps more in bulls and bucks than in cows and does. The meat will be more tender and less gamy. Of course appropriate field care is still critical and in no way will aging help undo damage done by poor field handling. Before I had a cooler I often aged animals in unheated garages, maintaining temps the best I could by cracking or closing the door, using fans, etc. I monitor the temp of the meat with a thermometer stabbed in a rear quarter (the automotive a/c thermometers work well, as they work in that range). The higher the temp the less time you will want to age the meat. If it is too warm you won't want to age it at all, but if I can get the meat cool and in my cooler I will try to age elk between 2-3 weeks. You won't want to age smaller game as long. In bad times and without my current walk-in cooler I've even aged elk in coolers with ice in the bottom, a rack, and the meat on top. The meat has to remain dry or bacterial growth will ruin it. I try to age with the hide on as it results in less meat loss, but aging will result in shrinkage and you will have to trim any exposed edges off. Your yield will suffer but what you get will be better table fare.
Much of my advice will likely be useless to someone in warmer climes. In MT, the ambient temps often allow for fast cooling in the field. Sometimes I'm trying to keep elk from freezing so that it can be aged.
My cooler currently:
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