Towards that end to execute successful evades I think the ships are maneuvering with heavy use of roll pitch and yaw plus some moves 'up' or 'down' relative to the plane between firing ships and the target.
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A miss also doesn't have to be a clean miss, having the ship be on an unexpected roll spreading the hit across many more square meters of hull or hitting the edge of the ship such that sloped armor effects start occurring can avoid damage.
Lasers, PA, and Meson Guns are "burst" weapons. Witness the X-Ray Detonation laser. Lasers do not kill things by sitting on them in one place. They overwhelm the target with a burst of energy, or they bounce off. It's hard enough to deliver enough energy per cm^2 in the first place to do any damage at range, much less rely up sitting on the exact same cm^2 and waiting for it to melt.
So, rolling doesn't do anything (save perhaps randomly change a hit location). If rolling could make a difference, so does relative velocity of the attacker, for the same reasons. I'd hate to be in a ship that's rolling at a rate of 1000's m/s, gravitic compensators or no.
Every energy weapon shot is as a ballistic computation like most any slug thrower shot. Even gravity effects the trajectory. The gunnery computers are not making "snap shots", they're making well planned ballistic projections based on a long history of analyzing the ships vectors an behaviors. The computers are making these decisions at a sub-millisecond scale (even if it takes 100's of ms to execute the decision). So, while things look like they're happening fast to us meatspace carbon based lifeforms, the computers see everything in "slow motion".
Consider: https://www.youtube.com/watch?v=ZVNnoOcohaU
Simply, all of the reactions that your ship must do in order to defeat the computers prediction system must happen within the reaction time of the computer system. Your thrust changes have to happen faster than the computer. Your thruster directional changes have to happen faster (and remember, your ship has momentum to be overcome for your thrusters to start it's maneuver, as well as overcome to stop that maneuver -- and those are all predictable).
The best you can do is random thrust inputs, random acceleration bursts, and perhaps random gimbal motions (depending on the response time of the gimbals). On larger ships, I don't think this is enough to matter. Smaller ships may get some benefit. But even still, it's been argued that an attack is a bunch of bursts over a period of time, thus filling the projection window with fire.
The firing solution is watching your every move, and predicting all of your possible outcomes 2-4s out in advance. It's watching you like a hawk. Then it fills that projected area with energy in hopes that you'll intersect with some of it.
And if you ever stop, if your random inputs stop for any reason (such as a dramatic, controlled vector change), the projection window gets very small, very fast.
All of the rest is noise in the system. The latency within the firing ship does not weaken the solution directly, it simply allows the input of noise from other sources (such as random thrust inputs by the target) to possibly expand the projected window. With no noise, it has no impact whatsoever.
Also, note, that random inputs by the evading ship don't necessarily undermine it's firing solutions back at you. It KNOWS what it's going to do. While each thrust input may be random to the observer, the control computers already know when and how much each burst will be, and can be compensated in the solution.