Scott Martin
Think of the threat volume of my missile as a cone with the point away from your ship, and the avoidance area that your ship can maneuver into is a ball (sphere). If the sphere is completely within the cone, you can't avoid the missile, and I can prove mathematically that this is *always* the case unless you have more thrust than I do, as long as my start vector is pointing at the target. (since I fired the missile *at* you in the first place, for the vast majority of cases my start vector either intersects your ship, or isn't divergent enough to really matter)
I see what your talking about. That certainly determines if the missile is even a threat. "Sidestepping" has the possibilty of working because it is the cone that travels with the missile, not a static one projected from the firing site, that determines whether a hit actually occurs. The job for the missile is keeping the base of this traveling cone on target not knowing where that target will be from second to second. The static cone from the firing position to target only indcates that it is possible to hit the target not that a hit is guaranteed. In other words, the target does not need to get out of the initial target cone for the missile to miss.
For example, as the missile approaches the target the angle subtended by the cone doesn't change if the velocity remains constant (if velocity increases the angle decreases), but the area covered by the "base" decreases because the "height" of the cone is getting shorter as the missile gets closer. Thus, the distance the target needs to get out of the way of the missile becomes shorter, much shorter. At some point the target does not have enough time to get out of the way, engines or pilot can not react fast enough. If the base of the traveling cone is on the target at this point the hit occurs.
Now the abstracted movement in a game may not reflect this, especially one that needs to look at movement on the light second scale. However, all that is required for a KKM missile to miss is movement on the meter scale. Hence, such things are usually reflected in targeting, hit tables, agility, etc.
Further, even if the missile can turn at the last "minute" and hit. This will seriously degrade its performance because it is the component of velocity directed at the target at the time of impact (not simply from firing position to final target position) that is important for KE imparted. An extreme example to illustrate the point, if a missile proceeds at a speed of 50 hexes/turn towards the target jukes and the missile needs to turn 90 degrees and proceeds 1 hex in 1 turn to hit. The KE is not the velocity vector from the launch site to the target, it is the velocity vector from that last 1 hex per turn. Trigonometry gives the reduction for other angles. So instead of the KE being based on a 50 hex/turn velocity, it is based on a 1 hex/turn velocity.
The above is working in the artificial game mechanic of turn based movement at the vast scales used for game play reasons. In actuality, the target is continually moving and the relevant scale is on the order of meters or less as the weapon must contact the target and the impact velocity determines the damage. Being off by 1 meter is a miss. I will completely agree that the KKM is also continuosly moving and can adjust. From a damage point of view though the starship doesn't care if it is hit by the KKM as long as the impact velocity is low. The way to do this is to force the missile to turn as much as possible. Each 90 degree turn means the initial velocity vector was brought to zero (or otherwise you don't turn) and all the KE in that vector is gone for damage purposes. Now the missile needs to build up velocity again to have effective KE. Even smaller turns are going to reduced the KE.
The question is do you wish to take these factors into account. The game mechanics are set up as turn based moved meant to capture light second scale combat. If one calculates impact KE based on this alone, then the minimum KE will be determined by the length of the turn, i.e., your game mechanics.
I'd suggest that dodging the KKM and the damage of KKM be assessed without regard to turn length or game hex scale if you are looking for some hard numbers.
As to defenses. An anti-KKM missile should be very effective as it does not need to intercept the KKM it only needs to protect/screen the location the ship is going to be at. Since the KKM must contact the target to hurt it, the anti-KKM needs to only put up a "wall" of ball bearings between the KKM and the place the ship is moving to. The KKM may or may not be able to see this wall in time to steer around it, but any steering wastes the all important velocity needed for damage. The walls do not even need to be that big, the closer to the starship they are the smaller they need to be.
Lastly, a real world example (although antedotal) is the way helicopters avoided SAMs in Vietnam. Now these are just stories mind you but from my best friends father who was a helicopter pilot in Vietnam so I trust them (since SAMs were fired at them and he survived 2 tours in one piece). I think no one will argue that a helicopter can't out thrust a SAM but these guys used to avoid them by pulling sideways at the last second. (If I recall, once they saw the flash they'd start counting then when they got to a certain number they'd pull hard sideways.) The missile could not make the tight turn due to its speed and would shoot past the target. This is a matter of reflexes and the degree of guidance of the missile. And hard to do with modern missiles because of the times and distances involved.
If you are looking for a quick way to determine what distances are too short for a pilot/craft to react. You could take the firing distance of modern air-to-air missiles, assuming relative attack and dodging abilites remain the same. I don't know what it is but lets say it is 100 miles, that's 160 km. That's about 0.0005 light seconds.