Well, I can't answer that, but after shooting 2 different Handi's for 2 1/2 years, and 3 others alternately in that time I do have an answer for what I expect......I expect the rifle to shoot as well as I can hold on a bench. Now that may sound kinda obvious even simplistic, but to get to that point I had to reach the place where I could say a bullet out of the group was in fact a flier.
On average I can say that my 357 Max will shoot my pipsqueak plinking load (7.3 grains of milsurp #107 or Blue Dot, Lee 357-158-RF cast bullet, Winchester small pistol primer) into 1.5" Occasionally it will outdo itself and shoot that into 1", it is not unusual to see the load shoot 2". It will generally put 7 or 8 of 10 into an inch. It will always stay on a tin can. It will always have a well defined center, but the fliers are random enough both in order of fire and point of strike that to say "That was a flier" is not always possible.
I changed my loading practice today for 2, 10 shot groups. I didn't neck size the cases. Instead I simply decapped, reprimed, belled in the expanding die, charged and seated a bullet with enough crimp to straighten the belling. I was rewarded with 2 groups, one 7 of 10 into 5/8" w/ 3 fliers making 1.5", the second 7 of 10 shots into 5/8" w/ 3 fliers making 1". I shot this load enough (over 3000 rounds) to know that this, twice in a row is different. A better different. I'm going to shoot using this loading method again tomorrow, see how it continues to perform. May still be a 1.5" load, but if it has reduced the size of the group center, it is a better load all around.
All this lead me to my accuracy desire, I want the rifle/load to shoot as well as I can see. The light was beginning to fail on the second group, so I could not see the group forming, all I could do was concentrate on the point of aim. It was not till I got down to the target that I saw a 1" group staring at me. And at that moment it struck me. I want my rifle to shoot as well as I can see, and the group I was looking at fit that description.
May sound simplistic, may sound silly, but it is what I look for in every gun I shoot and with every load I use. I don't think it an unreasonable expectation, what is the point of a gun/load that won't shoot where it is pointed? Hitting is the point of shooting. The Handi is not a target rifle, and expecting one to perform at that level is unreasonable. I find that accepting mediorce accuracy to be unreasonable as well. Depending on the rifle and it's mechanical ability, 1" could be awful, and 3" unattainable. But I have never been dissatisfied with a gun that could shoot as well as I could see. This is why I was never happy with a pistol that would only shoot 4" at 20 yards yeat a rifle that shot 2" at 100 with iron sights was great. And this is why I have continued to seek a higher level of accurcay from my Handi.