Years ago when I was in living in Ohio, I shot a deer with a Ruger GP in 357. Unfortunately the shot hit the deer smack in the shoulder instead of behind it and the deer started to run off. I had to put it down with remington in 308 as it was stumbling to run away.
I would never shoot a medium game without a scope. That few inches of difference is between a clean shot or a long, painful death for the deer.