I actually did the opposite - started with a shotgun then converted to rifle. I like 4x as it gives enough magnification to pick out most obstructions out to 60 yards or so but still has enough field of view to readily find a running deer if necessary.
The key to the latter is to keep both eyes open and shoot as if using a shotgun. The biggest obstacle I have when using a scope on a moving target is the disparity of looking at a target normally with one eye and under magnification with the other. I can handle up to6x without too much problem but more than that and things get confusing. I practice this by pointing an unloaded gun at a light switch or other object keeping both eyes open. I find being close in distance to be more difficult so do my drills indoors rather than outside. When I think I'm pretty good, I'll take a scoped air gun. Into the yard and shoot dandelions, grasshoppers, wasps, and other targets of opportunity. That humbles me initially but later gets to be a matter of pride as I make more shots than I miss. I feel pretty confident I canregularly hit a moving target though seldom need to.
^^^This^^^
I can easily pick up a target immediately when shouldering a rifle with an optic set to 4x at 40 yards. If he missed twice the deer was presumably well within the the scopes field of view. Sounds more like the Indian than the arrow.
The OP says that the deer was jumped at 40 yards, given that. Had he been carrying a shotgun with buckshot the deer would have been on the edge of buckshot range by the time he had the gun shouldered and ready to shoot anyway.
