One thing that I never understood during these discussions was the note on hitchance. This has come up a few times, as I've noted previously. What speed is the hitchance calculated for? 10,000? Most missiles are doing substantially higher than that, so I can't help but wonder-- what happens to that 18% chance for hitting a missile moving at 10,000 when its actually flying at 75,000? Would it be better then to frontload the hitchance with full size turrets? Or would everything be perfectly linear and the crew grade provide the necessary bonuses?
Also, I cringe at the thought of twelve times the quad turrets spamming up my missile screens 
You are right in saying that this is actually not a “hitchance” as in chance to hit something. It is rather a “probability factor”, that is one in many factors that will influence our ability to hit. However the particular form of the function that calculates this ability allows us to disregard all other factors in the analysis (mostly). I.e. by large the speed of the target does not matter in deciding what size of gaussguns is best suited for beam defence – although it would influence the decision whether other forms of protection (AMM, shields, armor), might be superiour (after we have identified what hullsize of gaussguns maximizes their potential).
The particular function – to my best understanding- reads:
P(x,tr,v,grade,size) = p_dist * p_vel * p_crew * p_size
Where p_dist is the probability factor due to the distance, calculated as p_dist (x) = 1 – x / R. Where x being the distance at which the target is engaged, R being the maximum range of the firecontroll (not the 50% range!).
p_vel is the probability factor due to the speed of the enemy, calculated at p_vel (tr) = tr / v_target, unless the tracking speed is larger than the target speed. Where tr is the minimum of the tracking speed of the weapon and the associated firecontroll, and v_target is the speed of the target.
P_crew is the bonus (or malus) from the training level of the crew. Note that the earlier point in this thread would indicate that it is added to the product of the other two factors, rather than multiplied by it.
p_size is the probability due the size, which only applies to Gaussguns and is p_size= HS/6, i.e. the Hullsize divided by 6.
The important bit is that these are all multiplicative, which means that if you decrease one factor by 1/3, then the whole term becomes 1/3 smaller. And because every variable (speed, distance, size and crewgrade) enters only one term, you can easily reduce the much more complicated problem of considering the whole term to the simpler problem of considering only the relevant term for a variable. This way you don’t have to make a bunch of assumptions regarding the other factors, which are not relevant anyway.
An example: When comparing the different Gaussgun sizes you can easily see that Probability for size 6 is P(x,tr,v,grade,6)= p_dist * p_vel * p_crew * 1. Whereas for a size 3 Gaussgun you would have P(x,tr,v,grade,1)= p_dist * p_vel * p_crew * 1/2. So you can see that the second term is always half as large as the first – completely irrespective of the other factors. It does not tell you what chance you would actually have to hit a missile of course. If all other factors amount to 50%, then the first term would yield 50%, while the second would be 25%. If the other factors are a cumulative of 2%, then the first factor would be 2%, the second 1%. Either way, the normal size gaussgun is twice as likely to hit and thus roughly twice as valuable (but also twice as costly).
The last two paragraphs are not entirely true. P is a probability and thus naturally capped at 100%. p_dist and p_vel are always smaller than 1, so there is no problem, but p_crew can be large than one. Suppose a distance of 10k km for a firecontroll with a maximum of 120k km, then p_dist = 0.92. Further assume a tracking speed of 20k km/s, matching a target speed of 20k km/s, thus p_vel = 1. If the crew bonus is 10%, then the first three probability factors amount to 101%. The 3HS gaussgun would thus have a probability to hit of 50.5%, while the full size gaussgun would have a hitchance of 100% (since its capped there). So theoretically the smaller gaussgun would be superior on a per-weight basis. Note that this only applies under fairly generous assumptions (extremely high range of fc, low target speed, relatively high crew grade…), which is why I disregarded it initially.
The other point is that the hitchance is a good first indication but does not tell you everything. (Assuming gaussgun rate of fire of 1 for simplicity of the example) If you are fighting a single incoming missile, one 6HS gaussgun would be certain too shoot it down in the above example. Two 3HS gaussguns would each score a hit with 50.5% probability, which also means there is a chance that both miss of 0.495*0.495=24.5%, so the chance of hitting the single missile is actually only 75.5%, i.e. much worse than the full size turret. One the other hand if you were fighting two incoming missiles, the singe large gaussgun would be certain to hit one missile, but would also be certain to miss the other one. The two gaussguns would actually have a circa 25% chance of killing both missiles. In the long run you would probably be hit by the same amount of missiles, but with more smaller gaussguns the result of each salvo would vary more wieldy (25% of the time two missiles get through, 50% of the time one comes through, 25% of the time, none hits – while with the full size 100% of the time one comes through.
