I can't totally disagree with any suggestion that have been made thus far, but I can take exception to some.

To begin with I wouldn't go out and "trash" the scope just yet. I'm not a fan of Simmons scopes at all but there is no need to scrap it yet. I wouldn't even change ammo yet. Granted I believe to get the best accuracy you will eventually do both of those things but not just yet.

My first suggestion would be to stop using the site and clean plastic tray to shoot from. It may be sufficient for an air rifle but "powder burners" are another story. I would guess that you would have much better results with plain ole sand bags. that plastic tray is too rickity to shoot from. Get at least three Lead shot bags and fill them with sand. Use two to support the forearm andone to support the butt stock. Now you are shooting from a reasonable rest.

My second suggestion would be to turndown the pull weight of the trigger. Your savage hopefully has the accutriger, if so I'd turn it down as far as itwould go. that would probably give you a trigger pull of about 3 lbs thats a good place to start.

Now, its a good thingfor the shot to be a surprise solong asitisn't such a surprise that you jump.Rather than say a surprise I like to think of it as controlled. Ialways know when my trigger is about to break over. I now this because I've shot them so much. So my shots are never a surprise,But I certainly try to control them. I never want to jerk at the trigger, or slap at it etc. I try to push it with the tip of my finger rather than pull it with my whole finger.Push the trigger straight back towards the buttstock, don't pull it to one side or push it towards the over side. its veery important thatyou "follow through" That is to say that you should not pull away from the rifle. You should try to see the bullet hole form. Continueto hold your position for as long as you can.At some point the muzzle risemay cause you to lose your site picture though. With my heavy barreled 223's its not uncommon to maintain site picture and observe my hits/misses.

Now if you do all these things and you feel like you're shooting ability has exceeded the capabilities of the rifle then you can start experimenting with ammo or buying a higher quality scope etc.