Stuff about PointDefence in particular and Flyers overall in MOO2.

While Flyers (Missiles, Torpedoes, Fighters) are rather important part of game, published info about them is still quite scarce, and, even worse, is often misleading or outright wrong. Patch 1.50 Manual already contains info about Missile Evasion, Spherical Weapons and Lightning Field (read about them there too, if somewhy not yet), but only briefly mention about possiblity to shot Flyers down using "regular and Pd mount beam weapons, Interceptors, Anti-Missile Rockets". While they are supposedly indeed more intuitive than Sphericals, in reality, related mechanics arent so simple. As we have only Beams, Fighters and Anti-Missile Rockets to cover here, Beam mechanics will be the main theme, so Notes on Beam Weapon Mechanics (NBWM) from aforementioned Manual is a required pre-requisite to read prior. This stuff could be seen as update to NBWM (even with some small errata, even we, patch devs, did mistakes and publish misleading info sometimes too).

Part about Beams and how they can shoot Flyers down, and how to chose a better one.
"Missiles can be shot down by regular and Pd mount beam weapons"
Flyers (except Torpedoes) can be shot down by regular beams, and that pretty well described in NBWM, except not precisely explaining how Beam Defence (BD) of a Flyer is exactly calculated (unlike ships, players cannot just scan flyer to check BD). Also not well explained how damage is actually dealt to Flyer stack if dealt, and how Beam Mods affecting it. Those are easy part. But the Game also offer 5 beams with Point Defence modification (always talking Classix ofc), they are unique in a sence they can automatically fire on incoming Flyer, and having other obsure features, not clearly explained in NBWN, making their comparison difficult.

First some easy stuff.
1. Calculation of BD of Flyer.
As mentioned in NBWM, we need to know BD of target to calculate Chance-to-Hit (CtH) and other stuff. Luckily BD of Flyer is pretty simple stuff:
Missile BD = 5*SpeedBonus{BaseSpeed of Missile{10 for any missile} + 2*FTLlevel{0 for NoDrive; 1 for NuclearDrive; 2 for FusionDrive; 3 for IonDrive; 4 for AntimatterDrive; 5 for HyperDrive; 6 for InterphasedDrive} + FastBonus{+4 if Fast}} + MissileBonus{-10 for NuclearMissile; +15 for MerculiteMissile; +40 for PulsonMissile; +70 for ZeonMissile}.
Fighter BD = 5*SpeedBonus{BaseSpeed of Fighter{4 for AssaultShuttles; 6 for Bombers; 6 for HeavyFighters; 8 for Interceptors} + 2*FTLlevel{0 for NoDrive; 1 for NuclearDrive; 2 for FusionDrive; 3 for IonDrive; 4 for AntimatterDrive; 5 for HyperDrive; 6 for InterphasedDrive} + TransdimentionalBonus{+4 if TransD}} + FighterPilotBonus + RacialDefenciveBonus + [in 1.50 only]HelmsmanBonus.
Racial Defence trait affect only Fighters, while provide no penalty or bonus to Missiles. Also note, that FTLlevel bonus not depends on actual speed bonus of drive provided to ships on Galaxy map.
Torpedoes also have speed of 20 for AntimatterTorpedo and 24 for PlasmaTorpedo, aswell as instahit speed for ProtonTorpedo and DragonBreath, but as no stuff in this stuff can destroy or even target them, we leave them here.
-
2. Calculation of Chance-To-Hit.
Knowing BD of target its already possible to calculate stuff for Regular Beams using NBWM (keep in mind that speed of Flyer is always calculated using the best Drive player have, so they could use better one than ship launching them).
Doing the same for PD beams could be misleading: "Beam weapons get additional bonuses based on their mount type (PD +25 BA) and/or mods (Co +25 BA, AF -20 BA)." Its could be overlooked (while Manual is not actually misleading about it, it is not directly stressed there) that PD bonus is calculated unique way, leading to different outcomes sometimes, and cannot just be added to BA (BeamAttack) like other bonuses (note: 1.50 patch parameter simplified_beam_formula also modify PD bonus to act like a flat BA bonus, like CO, contrary to explanations of Classix mechanic below; refer Manual for details). Important difference occurs only in 3b of CtH formula, but that formula is pretty important, as it directly affect DamageDistribution, and could lead to overestimating of expected damage dealt.

[3a] BA+CO-AF-BD + random(100) roll >= hit_threshold
[3b] hit_threshold = min(40 + range_penalty * - PD_bonus; 95)
* doubled for inherent range penalty mod

For CtH formula 3a PD bonus indeed work just like CO analogue:
Example 1
a) Ship with BA (sum of all non-CO non-PD factors) of 115 fire a Regular CO beam at range 0 at Flyer with BD 100:
115{BA} - 100{BD} + 25{CO} + Roll[1-100] >= 40 + 0, thus ensuring hit no matter roll is.
b) Ship with BA (sum of all non-CO non-PD factors) of 115 fire a PD beam at range 0 at Flyer with BD 100:
115{BA} - 100{BD} + Roll[1-100] >= 40 - 25{PD}, thus ensuring hit no matter roll is.

Cases a) & b) have no difference in PD or CO effect, but guaranteed hit is end of stuff only for beams with Min=Max damages, like MassDriver. For them PD bonus is effectively just a free built-in CO, and its a big deal. But in formula about actual damage affected by accuracy of hit results used by all other beams, it will differ from cases explained in NBWM.

Thus leading to a harder stuff.
3. Calculation of ActualDamage.
ActualDamage = min_dmg + (max_dmg-min_dmg+1) * A / B
A = roll_plus_attack - hit_threshold
B = 100 - hit_threshold
roll_plus_attack = min(random(100) roll + BA+CO-AF-BD; 100)
hit_threshold = min(40 + range_penalty * - PD_bonus; 95)
* doubled for inherent range penalty mod

As PD bonus modify hit_threshold instead of roll_plus_attack, like all other Mod bonuses, its presence skew damage potential to lower values instead (while its increase CtH just like other bonuses as shown above). RangePenalties, instead, skew it to higher values.
Well, if i could read i'd be very upset. Will keep it this horrible BS this way and edit other mentions: of course mentioned stuff is not exist in reality. Looks like what i tried (as example 2 is about it) to write a correct stuff about: As PD bonus modify hit_threshold instead of roll_plus_attack, like all other Mod bonuses, its presence skew damage potential to lower values compared to an equal bonus value directly added to BA, but ended with the nonsense instead, sorry. Of course PD bonus skew damage potential to higher values (just effect is less, in comparison to "regular BA Mod bonus"), and RangePenalties skew damage potential to lower values instead.

Example 2
a) Ship with BA (sum of all non-CO non-PD factors) of 175 fire a Regular IonPulseCannon CO beam at range 0 at Flyer with BD 100. For simplicity that IonPulseCannon is actually mindmg3-maxdmg10 to match PD Phasor instead of actual mindmg2-maxdmg10, but this also will show that IPC's special inherent flag of "Damage Internal Systems" is not important for shooting at Flyers, and work just like a normal beam (unlike cases of shooting it at Monsters, Antarans or Planets).
According to 3a hit is ensured no matter Roll is, so we will use worst case of Roll=1, and damage distribution affected by accuracy of it will be:
roll_plus_attack = (175{BA} - 100{BD} + 25{CO} + 1{Roll}) = 101, capped to 100;
hit_threshold = 40 + 0 = 40;
ActualDamage = 3 + (10 - 3 + 1)*(100{roll_plus_attack}- 40{hit_threshold})/(100 - 40{hit_threshold}) = 3 + 8*60/60 = 11, capped to maxdmg of 10.

b) Ship with BA (sum of all non-CO non-PD factors) of 175 fire a Phasor PD beam at range 0 at Flyer with BD 100.
According to 3a hit is ensured no matter Roll is, so we will use worst case of Roll=1, and damage distribution affected by accuracy of it will be:
roll_plus_attack = (175{BA} - 100{BD} + 1{Roll}) = 76;
hit_threshold = 40 + 0 - 25{PD} = 15;
ActualDamage = 3 + (10 - 3 + 1)*(76{roll_plus_attack}- 15{hit_threshold})/(100 - 15{hit_threshold}) = 3 + 8*61/85 = 8, as no rounding occurs.

Thus, while in cases a) & b) sum of BA-BD calculated in "add and subtract" way is 100, its possible to overstimate actual damage by a whole 20%. While Regular beam would already always do maxdmg with BA-BD>=100, to reach the same for PD beam BA+PD-BD-PD>=100 is required (so PD is not included in other BA bonuses sum). Luckily, damage affected by accuracy formula is more friendly to weapons with smaller difference between mindmg-maxdmg.

c) Ship with BA (sum of all non-CO non-PD factors) of 175 fire a Fusion PD beam at range 0 at Flyer with BD 100.
According to 3a hit is ensured no matter Roll is, so we will use worst case of Roll=1, and damage distribution affected by accuracy of it will be:
roll_plus_attack = (175{BA} - 100{BD} + 1{Roll}) = 76;
hit_threshold = 40 + 0 - 25{PD} = 15;
ActualDamage = 1 + (3 - 1 + 1)*(76{roll_plus_attack}- 15{hit_threshold})/(100 - 15{hit_threshold}) = 1 + 3*61/85 = 3, that is maxgmg, reached just "expected" "add and subtract" way, unlike case b).

d) Ship with BA (sum of all non-CO non-PD factors including AF) of 160 fire a Laser PD beam at range 0 at Flyer with BD 100.
According to 3a hit is ensured no matter Roll is, so we will use worst case of Roll=1, and damage distribution affected by accuracy of it will be:
roll_plus_attack = (160{BA} - 100{BD} + 1{Roll}) = 61;
hit_threshold = 40 + 0 - 25{PD} = 15;
ActualDamage = 1 + (2 - 1 + 1)*(61{roll_plus_attack}- 15{hit_threshold})/(100 - 15{hit_threshold}) = 1 + 2*45/85 = 2, that is maxgmg, reached even with "expected" "add and subtract" sum of 85, below 100.

Simple addition of PD bonus to other BA values could lead to overestimation of expected damage for beams with high difference of max-min dmg (Phasor and ParticleBeam), they require more BA to guarantee max damage. On the other hand, beams with very small difference (pretty much a feature essentially of a "weak" PD's) have so few damage intervals to chose from, so even being skewed to lower value via PD effect, they could reach max damage earlier than expected. But what about skewing into higher values? Yes, its not present, example below just shows a skewing up effect of PB bonus itself.

e) Ship with BA (sum of all non-CO non-PD factors) of 175 fire a modded to remove a DoubleRangePenalty Fusion PD NR beam at range 1 at Flyer with BD 100.
According to 3a hit is ensured no matter Roll is, so we will use worst case of Roll=1, and damage distribution affected by accuracy of it will be:
roll_plus_attack = (175{BA} - 100{BD} + 1{Roll}) = 76;
hit_threshold = 40 + 10 (range2 penalty, due to doubling range penalties for PD) - 25{PD} = 25;
ActualDamage = 1 + (3 - 1 + 1)*(76{roll_plus_attack}- 25{hit_threshold})/(100 - 25{hit_threshold}) = 1 + 3*51/75 = 3, that is maxgmg, reached at range 1 just like at range 0 in case c), despite double ranged penalties to hit, because, paradoxically, range penalties skew distribution to higher values in a way reversed of PD effect. No, because they just didnt hit hard enough.

Well, but, in case e) its stuff reached with a gun not present in Game, such NR FusionBeam just making no difference between range 0 and 1 would be remarkably good. But as its actually lack NR, its a subject to Dissipation. And without NR (inherent one like in MassDriver or additional mod like in Laser) Dissipation penalty will be doubled for PD.

In examples above min-max damage for PD been simply min-max of Regular beam /2. Yet except last case it always been directly stated that range is 0. For non-PD beam there is no difference between ranges 0 & 1, but for PD, with its double range penalties, range 1 is effectively range 2 for purposes both for To-Hit calculation (mostly omitted in 3., as its pretty well explained in NBWM) and for Dissipation calculation (sadly not so well explained in NBWM regarding PD, so explained in 4.), and range 2 is where penalties are starting already.

4. Calculation of Min-Max dmg and Dissipation.
Range is units of 3 squares used in various calculations. For firing a beam ship to ship its relatively easy calculated from ship1 edge] [square] to [square] [ship2 edge, with range 1 (3 squares) in that example. Range 0 is more complicated, as its cover squares [inside ship edges]. Good thing its not needed to be calculated for purposes other than shooting Flyers, as ships normally not share a squares. Bad thing its needed to be calculated for purposes of shooting Flyers, and interface not provide a guaranteed way to do so. And its could make a quite difference, say of doing +50% damage, or -33% of it.

Example 3
its fixed e) from Example 2: Ship with BA (sum of all non-CO non-PD factors) of 175 fire a real Fusion PD beam at range 1 at Flyer with BD 100.
According to 3a hit is ensured no matter Roll is, so we will use worst case of Roll=1, and damage distribution affected by accuracy of it will be:
roll_plus_attack = (175{BA} - 100{BD} + 1{Roll}) = 76;
hit_threshold = 40 + 10 (range2 penalty, due to doubling range penalties for PD)*2{Fusion's 2x range penalty} - 25{PD} = 35;
ActualDamage = 1 + (2 - 1 + 1)*(76{roll_plus_attack}- 35{hit_threshold})/(100 - 35{hit_threshold}) = 1 + 2*41/65 = 2, that is only 2/3 of damage at range 0.

Max damage in it changed from 1/2 of Regular FusionBeam to other, lower value, due to Dissipation. NBWM explain how its calculated, but, sadly also use slightly misleading and even directly partially wrong table: Dissipation penalties are doubled for PD same way as they do for CtH, and Regular Laser at -60 penalty will be not 1-1, but 1-2. Lucky thing that latter one is also a good example for PD calculation purposes. PD reduction and Dissipation both (together with Ordnance) calculated at same time and addictive, not cumulative. PD reduction works just like Dissipation penalty of -50, while ofc still being a subject to PD effect on other parts of damage calculation:

Example 4
a), but its modified a) from Example 2: Ship with BA (sum of all non-CO non-PD factors) of 175 fire a Regular Phasor CO beam at range 6 at Flyer with BD 100.
According to 3a hit is ensured no matter Roll is, so we will use worst case of Roll=1, and damage distribution affected by accuracy of it will be:
roll_plus_attack = (175{BA} - 100{BD} + 25{CO} + 1{Roll}) = 101, capped to 100;
hit_threshold = 40 + 55{range6 penalty} = 95;
ActualDamage = 3 + (10 - 3 + 1)*(100{roll_plus_attack}- 95{hit_threshold})/(100 - 95{hit_threshold}) = 3 + 8*5/5 = 11, capped to maxdmg of 10.

b), but its just b) from Example 2: Ship with BA (sum of all non-CO non-PD factors) of 175 fire a Phasor PD beam at range 0 at Flyer with BD 100.
According to 3a hit is ensured no matter Roll is, so we will use worst case of Roll=1, and damage distribution affected by accuracy of it will be:
roll_plus_attack = (175{BA} - 100{BD} + 1{Roll}) = 76;
hit_threshold = 40 + 0 - 25{PD} = 15;
ActualDamage = 3 + (10 - 3 + 1)*(76{roll_plus_attack}- 15{hit_threshold})/(100 - 15{hit_threshold}) = 3 + 8*61/85 = 8, as no rounding occurs.

While difference in +25 bonuses of CO and PD is already explained, Rounding been only mentioned. Its not explained in NBWM too. Examples there calculate percentage of damage for numbers not causing it, and its uncertain what should happens in case of remainder.
While most of calculations in Game are in whole numbers, and usually truncated, some of them seemd important enough to Authors are actually rounded. As Dissipation would wreck beam damage too much otherwise, thats one of such places. As other weapon types (for simplicity lets treat EnergyAbsorber as Beam for its purposes here) not affected by it, or affected some different way, no such rounding used in determining their damage. Another consequence of it is a bigger effect of Ordnance on Beams, as small increase could be large enough to enable gain from rounding.

Example 4 cases already had one, in MinDamage:
MinDamageModifiedByMods&Dissipation = MinWeaponDamage*(OrdnanceBonus{100 for 0% Ordnance, 110 for 10% Ordnance and so on} - 100 + SumOfModifiers {100{Base} + HVbonus{+50 if HV}+ PDpenalty{-50 if PD} + HEFbonus{if HEF} - DissipationPenalty{if ModifiedRange>1 and weapon dissipate})/100, rounded, and cannot be lower than 1.
MaxDamageModifiedByMods&Dissipation calculated same way, but using MaxWeaponDamage instead, and cannot be lower than MinDamageModifiedByMods&Dissipation.

Example 5
a) PD Phasor at range 0
MinDmg = 5*(100 - 100 + 50{100{Base} - 50{PDpenalty} - 0{DissipationPenalty}})/100 = 2.5, rounded to 3;
MaxDmg = 20*(100 - 100 + 50{100{Base} - 50{PDpenalty} - 0{DissipationPenalty}})/100 = 10, rounded to 10.
b) PD non-NR Laser at range 1
MinDmg = 1*(100 - 100 + 40{100{Base} - 50{PDpenalty} - 10{DissipationPenalty at range 2, doubled for PD from range 1}})/100 = 0.4, capped to 1;
MaxDmg = 4*(100 - 100 + 40{100{Base} - 50{PDpenalty} - 10{DissipationPenalty at range 2, doubled for PD from range 1}})/100 = 1.6, rounded to 2.
c) Regular non-NR Laser at range 7
MinDmg = 1*(100 - 100 + 40{100{Base} - 60{DissipationPenalty at range 7}})/100 = 0.4, capped to 1;
MaxDmg = 4*(100 - 100 + 40{100{Base} - 60{DissipationPenalty at range 7}})/100= 1.6, rounded to 2.

Easy to see than cases b) & c) are just the same. Case b) is particularly important is that, contrary to FusionBeam in Example3 PD Laser keeps maximum damage in range 1 even without NR mod. Ofc its not means NR is not needed, as easy to see from values of basic (non-Ordnance, non-HEF) PD Dissipation at ranges:

SquaresDistance Range0 1-3...4-6...7-9...10-12
Weapon
MassDriver .................3-3... 3-3... 3-3...3-3....3-3
LaserNR ......................1-2... 1-2...1-2...1-2... 1-2
Laser ............................1-2... 1-2 ...1-1...1-1... 1-1
Fusion ...........................1-3... 1-2... 1-1... 1-1... 1-1
Phasor.......................... 3-10.. 2-8... 1-4... 1-1...1-1
Particle .........................5-15.. 4-12 ..2-6.. 1-1.. 1-1
Easy to see, that there is little to no reason to fire further than 3 squares with dissipating beam.

Moreother, range penalties of PD require better than expected accuracy, in addition to PD effect on damage distribution. Values of BA-BD required to ensure maxDamage at ranges, assuming AF and CO mods enabled:

SquaresDistance Range0 .1-3...4-6...7-9...10-12
Weapon
MassDriver.................... 34 ...44 ....64 ....89 ....114 (20 less for non-AF)
LaserNR ............... ..........52 ...57.... 67.... 79..... 92 (20 less for non-AF; 25 more for non-CO)
Laser................................52 ...57 ....39 ....64 .....89 (20 less for non-AF; 25 more for non-CO)
Fusion .............................46 ...42 ....49 ....69... ..69 (double range penalty; 25 more for non-CO)
Phasor ............................84 ...84 ....81 ....64 .....89 (20 less for non-AF; 25 more for non-CO)
Particle ...........................92... 91.... 88 ....69 .....94

And finally, values of maxDamage per Size on a given miniaturization level at 360 arc at range 0, assuming enabling only mods, thats positively affecting shooting of Flyers: AF, CO, NR, ENV.
MiniaturizationLevel
Weapon
MassDriver .........0.42 0.50 1.28 1.80 2.25 3.00
LaserNR .....0.28 0.22 0.75 0.85 1.20 2.00
Laser ...........0.28 0.25 0.75 1.00 1.50 2.00
Fusion ...................0.42 0.37 1.20 1.50 2.40 3.00
Phasor ....................................................................1.42 1.25 3.75 5.00 7.50 10.0
Particle ........1.50

Mods and Arc size' increase calculation are subject to rounding down, and its often benefit player, as they could be effectively free in some cases. Great example is PD CO NR AF Laser at miniaturization level 2 - its rounded down to 8 space from 8.95. Similar things happens in other places too, say MassDriver at minia level 5 can just have totally free AP mod. That mod is not useful in shooting Flyers, while could be great in shooting ships. The way mods interact with Flyers overall is worthy to mention:
AP is not make any difference in shooting Flyers, as they have only HP and no armor/structure;
CO and NR modify accuracy and dissipation, respectively; and described above;
SP is not make any difference in shooting Flyers, as they dont have any shields;
AF make cannon to do 3 shots with 20 BA penalty each for a given target, and some of those shots could miss, while not affecting other shots; in Flyers context it means it can destroy up to 3 flyers from targeted Stack per cannon;
ENV is working different than its usual way in shooting Flyers, if cannon hits, then instead of damaging one target ship 4 times, it hits a Stack 4 times, but not a single Flyer from it, thus it can destroy up to 4 flyers from targeted Stack per cannon.
InternalSystemsDamage (Ion's), ESD (Graviton's), aswell as effects of StructuralAnalyzer and AchillesTargetingUnit have no effect on damage to flyers.
All thats not fully usable yet, as there been no explanation how Flyers are actually damaged, because they use a mechanic not used in other part of Combat, Stacks.

6. Calculation of Stack Damage.
Unlike ships in combat, that are separate objects, Flyers exist in Stacks; Stacks are separate objects on their own, but no individual Flyers in them present. Instead of it Stack keeps trace of Amount of Flyers there, and Damage dealt to it. Spherical weapons use entirely special own mechanic of dealing with Stacks, described in Manual, but corresponding Beams mechanic is not that straightforward too:
When Beam hit a Stack, its damage is capped at HP of Flyer there.
Missile HP = MissileTypeHP{4 for Nuclear; 8 for Merculite; 12 for Pulson; 16 for Zeon}, x2 if ARM mod is present
Fighter HP = FighterTypeHP{4 for Interceptor; 6 for AssaultShuttle; 8 for Bomber; 10 for HeavyFighter}*(100 + ArmorBonus{0 for Titanium; 100 for Tritanium; 300 for Zortrium; 500 for Neutronium; 700 for Adamantium; 900 for Xentronium})/200
Thus, even if Regular DeathRay hit a Stack of non-ARM Nukes, it will deal only 4 damage and destroy only one missile there. Its slightly more complex if Beam damage dealt is actually lower than HP. In any case Beam's Damage is added to StackDamage value of Stack, and if its reach HP value, one Flyer is destroyed, and StackDamage amount is lowered by HP value. It lets some damage still "stream" to other Flyer in stack, instead of being wasted.

Example 6
Non-damaged {StackDamage[0]} Stack of 10 {StackAmount[10]} ARM NuclearMissiles hit by DeathRay by 100 Damage:
100 Damage is capped to HP value of 8{4*2 NukeARM}, then added to StackDamage[0 + 8 = 8], as it reached HP value of 8, one missile is destroyed, StackAmount[9] and StackDamage[8 - 8 = 0].
After that its hit by ENV PD FusionBeam by 3 Damage, resulting in 4 hits by 3 damage in a sequence:
1. 3 Damage remained as it, as its lower than HP, then added to StackDamage[0 + 3 = 3], as its not reached HP value of 8, its stay as is;
2. 3 Damage remained as it, as its lower than HP, then added to StackDamage[3 + 3 = 6], as its not reached HP value of 8, its stay as is;
3. 3 Damage remained as it, as its lower than HP, then added to StackDamage[6 + 3 = 9], as it reached HP value of 8, one missile is destroyed, StackAmount[8] and StackDamage[9 - 8 = 1];
4. 3 Damage remained as it, as its lower than HP, then added to StackDamage[1 + 3 = 4], as its not reached HP value of 8, its stay as is.
After that its hit by AF PD Phasor by 9 Damage in first shot, 0 damage due to complete miss in second shot and by 10 Damage in third shot:
9 Damage is capped to HP value of 8{4*2 NukeARM}, then added to StackDamage[4 + 8 = 12], as it reached HP value of 8, one missile is destroyed, StackAmount[7] and StackDamage[12 - 8 = 4];
10 Damage is capped to HP value of 8{4*2 NukeARM}, then added to StackDamage[4 + 8 = 12], as it reached HP value of 8, one missile is destroyed, StackAmount[6] and StackDamage[12 - 8 = 4].
Thus leaving the Stack with 6 missiles and 4 StackDamage.

7. Targeting
From data above its seen that not only firing PD farther than 3 squares from ship is not so useful except NR beams. There is also very big difference between range0 and range1, especially for Fusion, but how to operate it in game?
PD beam could fire at a Flyer manually or in automatic, just prior impact. Ship, targeted by Flyers on its own can manually shoot at them only from range1 at best (except a case of Fighters already performed their hits this or previous turn, so already located inside ship's edges), but other friendly ships could freely move on a squares, occupied by flyers not targeting them, enabling to manually shoot Flyers down from range0. Above it was mentioned its cover squares inside ship's edges.
Sadly actual calculation is distance-, not squares-based. In practice it means that for 3x3 ships some (outer diagonal) area inside edges treated as range 1 still. While its make no difference for Regular beam, PD beam could perform worse than expected, and there is no practical way to know it from game. Preferable to shoot them by moving ship's center closer to them, if 3x3 ship is used, as merely covering a Flyer's square with one of ship's squares could be not enough to reach range0. This is seems to be of no problem for 2x2 and 1x1 ships. Such manual fleet-level use of PD could be particularly useful with Fusions, one especially bothering for range0 beam. Another way PD could fire at Flyer is automatic fire just prior impact. Sadly again, its even less intuitive than manual fire. No, player cannot expect such fire to happens at range0, despite its literally about Flyer reaching a ship 's square. In reality there is no practical way (known to me) to determine if incoming Flyer would trigger PD fire at range1 or range0; collision detection depends on Flyer's speed and distance to its target, and no matter if target is stationary or impact happens during its move. This effect severely hit beams relying on firing at range0, as player expect automatic fire to happens on it, but cant reliably have it in reality. Weird, but some workaround solution could be RangemasterUnit, that effectively turn all the uncertain area inside and up to 3 squares around a ship into range0 for a purposes of PD targeting (as RangemasterUnit affects already Modified by Mount Range, in reality it remove entire targeting penalty up to ModifiedRange 6, and keep only -10 BA for ModifiedRanges 6-8 (thus squares 7-12 for PD purposes)).
But luckily there is also another important case, manageable by player - point-blank hit. Point-blank hit happens when ship fire Flyer to other ship on adjacent non-diagonal square. It effects in immediate impact, and, ofc, also in potential automatic PD fire. But, unlike "free" Flyer's movement its predictable: 3x3 ship targeting other 3x3 ship will trigger it at range1, in other combinations it will be at range0, making bigger ships sometimes more effective point-blank than expected.
Another important, while mostly intuitive thing about targeting is Arc. Examples above used 360 arc; not only it offer overall versatility, but Flyers located near center of ship could be out of reach for some other arcs. Ofc its possible to use some special non-360 arc PD on ships, but mostly its purely anti-AI exploits.
There is another stuff about "out of reach". It is possible to have more than one Stack of flyers on very same coordinates; they could be thought of as located one above other for game purposes, with top object move prior ones below it. Usually such groups appears when ship fire different Flyers into same target (identical Flyers would "glue" into one Stack in such case, unless its happens point-blank, triggering impact outright). Flyers from top slots of firing ship also will be located at top position in group, and will hit first when group will reach its target together (assuming equal speed of it). Its useful for draining automatic fire by cheaper/robust Flyers first, enabling more powerful/fragile ones from below to hit. But also its useful measure against manual targeting of such group - Stack at top of it will be targeted first. Possibly overlooked fact is that manual targeting effect is purely interface-based. There is no rule about targeting one at top, just there is no way to do it other way for player. Contrary to it, AI could target any object in such group at will (even when move player's ships on Auto), and often do it (it doesnt mean its always chose actually most dangerous stack as target).

While not essentially PointDefence, but directly related are Part about Non-Beams, and how they can shoot Flyers down
8. Fighters and Anti-MissileRockets.
Fighters related to PD mostly due to fact that weapon must have a possible PD modification to be installed on them, while actual damage calculated from Regular instead. Thats pretty well explained in Manual, and here its worthy only a briefly mention - Interceptors could target Flyers aswell as ships, and using same mechanic as for dealing damage to ships. Their weapon not use any mods except inherent ones, so they get no actual PD bonus (but have own bonus of +50BA), and not affected by DoubleRangePenalty of Fusion, as they always fire at range0. NR of MassDriver of no matter for the same reason, while they benefit from its dmgMin=dmgMax effect, acting as essentially huge bonus to accuracy. Ofc SP of Particle do works too.

Anti-MissileRockets is a Special Weapon famous for horribly wrong descriptions over years.
AMR have a range of 15 squares and can target only Missiles indeed, both manually or automatically on impact. Missile Type or HP etc of no matter for their effect, only distance to target is; if AMR successfully hit a Stack, it destroy one missile from it. Unlike most Special Weapons, that fire all weapons from their stack simultaneously, AMR fire in a beam-like manner, one Rocket at time, and each lauch use own CtH roll. In addition to its weird To-Hit unique formula, AMR use special rounding up way (ceiling) to determine a distance, effectively shifting Squares-to-Range conversion by one, to [0-2; 3-5; 6-8; 9-11; 12-14; 15-17], thus treating range0 as range1 for own purposes (with one special exclude)):
AMR Chance-to-Hit = 70 - (10*(AMRRange + 2)/3 - 1)
This one is pretty weird, and im not even sure if its actually represent author's intent, especially -1 part. Chances are pretty easy to calculate tho (keeping in mind inabilty to always reliably know an actual distance to Flyer by in-game means):
SquaresDistance 0-2.. 3-5.. 6-8.. 9-11.. 12-14.. 15
AMRCtH .............. 61 ....58 ... 55 ....51. .... 48 ......45
For practical purposes it means that all automatic or manual fire in 2 squares vicinty of ship will succeed at flat 61% chance of success, no matter missile type or mods, making it very useful against high-level missiles. More distant targeting is also nothing near of misleading description claim about -3% per square, with chances being pretty high even at edge of weapon's range. Again, maybe original intent indeed been about measuring squares, and not Ranges, but it works this way in game.
As a pure bonus: its actually possible (thought impractical in reality) to fire AMR from range0, in case target Missile's coordinates perfectly match center coordinates of a firing ship. In this case chance to hit will be a whooping 65%.


Ill put one more curiosity as update here, as it somewhat related to PD: Player's Missile Warning option is shared with AI, so its possible to change AI's combat behavior by toggling it. Likely not essentially bug as is, but authors inability to decide at playtesting do AI should always or never use Missile Warning, eventually resulting in an odd mechanics, where it use Player's settings thats supposedly should been overridden by AI (routine needed for it is implemented, but not enabled). As Missile Warning could lead to making some ship moves impossible (it will halt ship on some nearest square if triggered mid-flight, and original target square could be out of reach from the new one), its twice exploitable. Not only player can receive a better suited benefits from it regarding own ships movements: preventing accidental flying into Flyers, or, optionally, flying through them without losing a speed. Player also can decide for AI: if AI ships will move into Flyers, or, optionally, potentially lose a speed while approaching them. And Player can toggle option just prior giving a commands to AI. For example this exploit make it possible to pretty reliably beat Guardian just with 9 relatively low tech destroyers; Missile Warning have to be on during AI move. Strictly speaking i think for AI is better to "play" without Missile Warning, but it definitely do some unneeded runs into Flyers packs sometimes. In any case when Player's interface settings control AI's combat behavior is absolutely not good.