Below are excerpts from an article I found at chuckhawks.com. It was written by Schuyler Barnum and is an excellent description of why trigger pull and triggers in general can have such an affect on long range accuracy.
“One of the most neglected points of shooting well by many shooters is trigger pull. This simple concept is, in my experience, the primary culprit after poor position in messing up accuracy, much more so than breath control.
One of the problems on this subject is the fact that there is no definitive “right” trigger pull. It really depends on what you’re shooting at and what kind of gun you are using. In this article I will try to explain how to correctly pull a trigger. However, the best way to get the feel for the correct trigger pull is to practice. “Dry firing” (practicing at home with an EMPTY gun) is crucial to success on the range or in the field.”
(skipping shotgun description and heading straight to rifle…)
“Rifle triggers, on the other hand, are meant to have a slow, gentle squeeze. In most rifle shooting situations, including most hunting, precise shot placement is more important than speed. Actually, in target shooting, unless you’re in the biathlon or some sort of action shooting contest, you really don’t want to know when the rifle goes off. Anticipating the shot is a major culprit when it comes to flinching. Instead of pulling a rifle trigger back suddenly, you gradually add pressure at the same rate to the trigger, with the sights correctly aligned, until the rifle fires. This keeps the rifle pointed steadily at your target and helps to avoid flinching. This kind of trigger release is called a “surprise break.”
Achieving a good surprise break is even more crucial to top accuracy with a handgun than it is with a rifle. This is because a pistol is lighter in relation to the weight of its trigger pull than a rifle. For example, my .270 hunting rifle weighs 9 pounds with scope and has a 3 pound trigger pull. The trigger pull is thus 1/3 the weight of the rifle. If squeezed gently and properly, the trigger should release without appreciably moving the much heavier rifle. Now consider a 3 pound hunting revolver that also has a 3 pound trigger pull. The trigger pull is suddenly 100% of the weight of the gun! Clearly, applying enough force to the trigger of that revolver to make it go off is much more likely to move the gun. Unless the shooter is a very experienced pistolero, a surprise break is absolutely essential to achieving any kind of accuracy with a handgun. The two key factors to shooting a handgun are focusing on the front sight (not the target) and squeezing the trigger until the gun fires, seemingly by itself (a perfect surprise break).