Odd yet interesting find regarding missile units

I had noticed odd battle results a few times, so in my last siege I made a specific test to better understand the behaviour of archers.

The result is that the formation missile units are in does not make a lick of difference per se. Wether in two wide lines or in 4 wide, 15 ranks long rectangles, archers, crossbows and muskets do NOT check for obstructions in their line of fire within their own unit.

What I mean is that, while each single archer in a given unit checks wether there's a building, tree, rock or friendly unit between him and his target, and arcs his shot accordingly, the other archers in his own unit are not taken into account. Archers in the back row fire straight through the previous ranks as long as they have an otherwise clean line of fire.

In other words : to an archer, the other archers in his own unit are translucent (and intangible).

It's of course very counter-intuitive, but it does make sense to a point : ranks in TW are all one-man-behind-the-other, while archer formations IRL would probably be more staggered, either checkerboard or diagonal... Anyway, my guess is that this is either an overlook in battleAI, or a conscious decision to avoid friendly-fire when on the move, for HAs especially.

Of course, using archers in box formations instead of long lines impacts their results, because their fire will be much more concentrated and focused (ie a 4 wide archer unit firing on a 15 wide spear unit will only target the 4 men in the middle), so there is still a point in having wide archer formations.

But it's something to keep in mind in siege situations for instance : if you have breached a gate/wall, sit your archers in front of it in 4x15 instead of 30x2, they'll be more accurate this way.

So the deeper the formation the better for accuracy ?

I've noticed the same about archers firing through their teammates, only I was'nt too sure as i't's always happening very fast and you really have to sit and look at it.

Hmmm yes and no. On flat, unobstructed ground the accuracy is the same wether deep or thin. But when Line Of Sight is somehow obstructed (by walls, trees etc...) accuracy is better if you put more archers in the area where LOS is good.

I don't know if I'm being clear, so I'll whip out another of my artistic ASCII's :laugh4:

____XXXXXXXXXXX
____XXXXXXXXXXX
____XXXXXXXXXXX

======O-----O======

____AAACCCCAAAA
____AAACCCCAAAA
____AAACCCCAAAA

- is breached door
X is the enemy
A is an archer, C is an archer with a clean LOS


In this example, only the 12 C archers out of a total 33 will have a direct line of fire on the X unit, and only those 12 will fire right at them. The A archers will fire straight up and over the wall/towers and, more often than not, miss.

If you put them this way :

___XXXXXXXXXXX
___XXXXXXXXXXX
___XXXXXXXXXXX

====O------O======

______CCCC
______CCCC
______CCCC
______CCCC
______CCCC
______CCCC
______CCCC
______CCCC


Then all archers will fire straight and true. Losses in the X unit will not be much higher per volley, because all arrows will land on the same few men, but said losses will be much more consistent overtime, and you'll waste less ammo too.

Got it.

Good tip, thanks!:2thumbsup:

I was having a hard time yesterday trying to get catapults to fire through a breached door...they were aiming at the center of a unit and hitting the wall instead.

Yes, the breached wall is an excellent example where you can see this behavior in action. It is my habit take out the towers and then march crossbows up to the breaches. For this, you want to put them in a longer narrow box.

If you watch them, you will see some shoot straight, some of them shoot up in the air, and some not shoot at all depending on whether they are blocked by the walls. You can see the line of demarcation fairly easily when the guys who are shooting squat to reload and the blocked guys stay standing.

The guys in the back of the box will still shoot straight if they are not blocked by the walls. Apparently, they are capable of shooting between the heads of the ranks in front of them.

Excellent find. This is a big deal. It's going to change the way people fight in SP and MP. I wonder if this works for muskets as well.

Ok, I did a custom battle test... 1 unit of muskets vs 1 unit of muskets. The AI spread its muskets out in two rows while I used a square formation. Only the muskets in the front row will fire. When they finish shooting they will run to the back of the formation to reload so the next rank can fire. I can confirm that this does not work for muskets but even though it was only one test, the square formation beat the 2 rank formation. Hmmm...

With muskets and arquebusiers, the front rank is all that fires, yes. But, they pretty much fire as soon as the back rank finishes reloading. Because of the larger number of men moving in the wide formation, and the resulting hangups as men get stuck on obstacles and other men, the narrow formation is probably finishing first and getting a higher rate of fire as a result. Rate of fire seems higher to me in a 4 rank formation than in a 2 rank line, from using my Spanish musketeers.

There is also less surface area for the enemy to shoot at.

I mentioned this a while ago:

https://forums.totalwar.org/vb/showthread.php?t=74980

sorry, have not yet found the right program to edit my tga files to post screenies.

To me, this is not so much an interesting feature as something that got lost from MTWI, probably to accommodate "wider public" by dumbing down the game in RTW. In MTWI only the front row of crossbowmen would fire while the second row would reload. Anyone beyond the first two rows would just stand. Archers would actually shoot, but, unless on an elevation anyone beyond row 3 would cause friendly fire losses among the archer unit itself. So it always made sense to deploy them in 2 rows if on flat groun.

Yes, I think it was changed in Rome. Don't remember worrying too much about ranks in RTW. Certainly not for Horse Archers.

This means I can have a 4 rank archer unit with just as much fire power as a 2 rank one and THAT means that my center formation has room now for units other than missiles.

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To me, this is not so much an interesting feature as something that got lost from MTWI, probably to accommodate "wider public" by dumbing down the game in RTW. In MTWI only the front row of crossbowmen would fire while the second row would reload. Anyone beyond the first two rows would just stand. Archers would actually shoot, but, unless on an elevation anyone beyond row 3 would cause friendly fire losses among the archer unit itself. So it always made sense to deploy them in 2 rows if on flat groun.

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*shrug*. Personally I think friendly fire within units was silly back then. You don't shoot your own mate who's half a meter away from you in the back just cause "he was in the way" :dizzy2:. Unless of course said mate cheated at cards the night before :laugh4:.

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Originally Posted by Kobal2fr

*shrug*. Personally I think friendly fire within units was silly back then. You don't shoot your own mate who's half a meter away from you in the back just cause "he was in the way" :dizzy2:. Unless of course said mate cheated at cards the night before :laugh4:.

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Agreed. Unless the target is point blank, there will be a slight arc in your shot. Fire an arrow level with the earth and see how far it goes... not far at all.

Quote:

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Originally Posted by Kobal2fr

Of course, using archers in box formations instead of long lines impacts their results, because their fire will be much more concentrated and focused (ie a 4 wide archer unit firing on a 15 wide spear unit will only target the 4 men in the middle), so there is still a point in having wide archer formations.

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So if a 4-wide unit of archers only targets the 4 men in the middle of the enemy line... then the widest your archers ever need to be is equal to the width of the unit they're firing at, as that assigns one full column of your archers to each man in the enemy front line, right? Do we know what happens when there are more archers in your line than in your enemy's front line? If the extra ones are arbitrarily assigned to the end man on the enemy line, then you actually achieve optimal fire by exactly matching the enemy's width. I'll illustrate:

____XXXXXXXXXX
____XXXXXXXXXX
____XXXXXXXXXX

____AAAAAAAAAA
____AAAAAAAAAA
____AAAAAAAAAA

Here A's are archers and X is their targets. This would be optimal firing position, as each enemy rank gets assigned 1 3-deep column of archers. I'm unclear whether archers target only the front line, or only the particular column of enemies, so for ease I'll just assume it's the front line that is targeted. It really doesn't make much difference for my purposes here. Here's how they look in a 2-deep formation vs. same enemy:


____XXXXXXXXXX
____XXXXXXXXXX
____YXXXXXXXXY

__LLAAAAAAAAAARRR
__LLAAAAAAAAAARRR

Here it seems that all the A archers will have a clearly defined X or Y enemy to shoot at. However, it's the L's and R's that I'm interested in, since they don't directly line up with any enemy rank. The most natural thing would seem to be to assign them to fire at the Y marked end units of the enemy line. This leaves only 2 archers to each X in the line, 6 on the left Y (2 A's plus 4 L's) and 8 on the right Y (2 A's plus 6 R's). This doesn't seem that bad, but if you analyze it empirically, you'll find that overloading end units with fire is a poor strategy. The right Y who gets shot at by 8 guys almost certainly dies, but possibly 3 or 4 times over, where those archers that scored hits could have killed 3 or 4 enemies if they were all pointed at a different enemy soldier.

Ideally you'd want each archer to have his own enemy to shoot at so no shots that would register as kills are wasted. Failing that, allocating the archers as evenly as possible works the best as you minimize the chances of a second kill rolled on a given enemy soldier that would be wasted as he is already killed by another archer firing at him.

So from that idea, we can determine for sure that having less width than the enemy means you are wasting shots by multiple-targeting the same interior enemies when you wouldn't have to. Also it's likely that using a wider line than your enemy is also disadvantageous, if in fact the extra width of archers multiple-target the end enemy units, or multiple-target any enemy units at all in fact. If they instead choose other as-yet untargeted units than that would prove even more effective than matching the enemy line's breadth... but I wouldn't bet on it, so it's likely that matching the enemy's width is most effective. I guess testing is needed, but as I'm at work right now I can't do it. :wall:

I'm not really certain how individual targeting works. I'm not even certain individual targeting works at all. They might just target the center of the enemy unit and random scatter is determined by the computer.

However, deploying in deep blocks does have one drawback: the unit will only fire when everyone is in range, so they'll have to get closer to the enemy before they fire. This can result in you taking unanswered casualties. Personally, I tend to deploy my missile troops 4-6 ranks deep in most cases. They aren't so wide they become unwieldy and are still shallow enough not to make much of an impact on unit range.

Interesting find, thanks!

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This doesn't seem that bad, but if you analyze it empirically, you'll find that overloading end units with fire is a poor strategy. The right Y who gets shot at by 8 guys almost certainly dies, but possibly 3 or 4 times over, where those archers that scored hits could have killed 3 or 4 enemies if they were all pointed at a different enemy soldier.

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Well, yes and no. It would certainly be true if archers did hit their targets consistently. But in reality, unless they are exped a lot, they have a very noticeable tendency to undershoot or overshoot. Now, the L and R archers undershooting will still miss, but if they overshoot, they have a longer line of "opportunity targets", if it makes any sense to you.

Sinan noted this in his thread relating to HA tactics : shooting the side of the box kills more than shooting the wide front, because overshooting arrows still fall down into the mass of men, instead of safely behind them. Same thing for L and R, I think.

Of course, this is speculating, I'd need to test thoroughly to be sure. But I'm no thorough tester :sweatdrop:.

While I haven't say down and tested it, but from playing for a while, I would say that archers do not ONLY shoot things straight in front of the. If you have a long line of archers two deep and there is a square of spears in front of only the center 10 archers, all the archers will shoot at the square of spears and if there are no obstacles they will all hit with about the same level of accuracy. The point of this thread is that when they don't have line of sight you can improve their accuracy by putting them in a formation so that they all do have line of sight.

Quote:

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Originally Posted by Kobal2fr

Of course, using archers in box formations instead of long lines impacts their results, because their fire will be much more concentrated and focused (ie a 4 wide archer unit firing on a 15 wide spear unit will only target the 4 men in the middle), so there is still a point in having wide archer formations.

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I think I've mostly debunked this, or least determined it to have little effect in game terms. First things first though, the test outcomes.

I ran 10 trials of each setup, utilizing the following conditions:

- 15 minute time limit battle on Grassy Plain, Medium Difficulty
- British Retinue Longbowmen vs. HRE Armoured Seargeants, both set to attack

The thing I varied was, of course, the configuration of the Longbows (which I controlled). In each case I configured the longbows and then allowed the Armoured Seargeants to march at them, while the lonbows fired at will into the Seargeants (i.e. I did not order them to fire, for the sake of consistency. They don't move at all, and so remain more organized and consistent). When the archers turned tail to flee, I ended the battle and counted kills. The archers seemed to get off 7 or 8 volleys each engagement.

Retinue Longbows in Standard configuration (not repositioned from default):

Trial Kills

1 18
2 24
3 28
4 20
5 19
6 25
7 29
8 32
9 24
10 30

Total 249/760
Percent 33%

Retinue Longbows in 2-Row configuration

Trial Kills

1 31
2 19
3 25
4 32
5 34
6 22
7 30
8 25
9 32
10 28

Total 278/760
Percent 37%

Retinue Longbows in 4-Column configuration

Trial Kills

1 28
2 24
3 19
4 25
5 30
6 26
7 24
8 17
9 28
10 27

Total 248/760
Percent 0.33

The results, while not completely conclusive, suggest that the spread of your archers horizontally has little if any effect. They did slightly better in 2-row configuration, but there is no difference going from the 4-column which is very narrow to standard configuration which is considerably wider. If the horizontal spread was a major factor, I would assume that each step of further spread would improve kills, yet that clearly didn't happen, so it's likely some of the difference is due simply to randomness in the game engine.

One major reason for the very similar results in all conditions is probably linked to the following: I observed from watching the volleys that the archers, no matter the configuration, appear to aim for the center of the enemy unit. I conclude this because the vast majoriy of arrows fall inside a few ranks of center, no matter the formation, where they should be much more evenly distributed if each archer picks a target to fire at in the enemy unit. This would of course reflect the realities of missle warfare at the time - everyone aims for the center of the enemy so that even if they miss, they have likely hit someone in the group. Also you can see while you hold the shift key down with your unit highlighted, that no matter where you clicked the enemy line to attack, the red pole indicating your unit's focus is in the dead center of the enemy unit you clicked. This could just be a programming convenience, but as the arrows seem to fall predominantly all around that pole, I can't just write it off as coincidence.

I will admit that the 2-row archers did a bit better on the whole. Likely this is partly luck, and possibly a little due to a factor someone earlier mentioned: that the very outside archers have a bigger cross section of the enemy unit to hit, and so a few arrows that would be short or long from a more straight on shot are now hits for them. This effect increases the closer the other unit gets, until the outside archers finally have a shot along the longest diagonal (corner to corner) of the enemy unit and thus presumably best odds of making a kill.

____XXYXXXXXX Enemy Position 1
____XXXYXXXXX
____XXXXYXXXX
____XXXXXYXXX
____XXXXXXYXX

____YXXXXXXXX Enemy Position 2
____XXYXXXXXX
____XXXXYXXXX
____XXXXXXYXX
____XXXXXXXXY

AAAAAAAAAAAAAAAC Archer Lines
AAAAAAAAAAAAAAAA

Note how Archer C's shot diagonal (indicated by Ys) gets longer as the enemy approaches, allowing a much worse shot to still hit the huge mass of enemies in front of him. He can miss quite long or short and still he will almost certainly hit an enemy body as the enemy is several extra ranks thicker from his perspective.

So to wrap up the analysis, the 2-row format appeared a slight bit better, but it may be a fluke, and certainly 4% extra kills isn't enough to warrant lots of hard work to get your archers like that. To put that in perspective, 4% is 1 in 25, so the archers only managed to kill 1 extra man in every 25, a fact that easily could just be random. So if you find it simpler to put your archers into other formations to save space, The evidence seems to suggest the impact is minimal in their performance (save for possibly having them avoid obstacles with their fire, where I agree narrowing their line to shoot into breached walls and such is the best play).

This is certainly a letdown. In block formations the archers are less likely to get blocked by objects and are easier to move about. No need for wide formations it seems, while here are certainly advantages to blocks.

I remember well the rankpenalties in STW and MTW. They were great.
At least gunpowder and crossbow units are still affected.

Actually my original test was made using Militia Crossbows :sweatdrop:

EDIT : clarification - Xbows are indeed useless when arc-fired over another unit, but within own unit, Xbowmen are translucent, same as archers. Gunpowder just won't fire through/over troops, and the back rank only fires if/when the unit is in 2 ranks and cannot do a proper reload cycle.

Random thought while reading this excellent thread. I believe the programming for each missile unit to fire on that particular sprites best target would probably be unwieldy, especially if there are lots of missile units in the battle map. Most folks don't have a Cray to run the calculation for this. So I believe CA / Sega did pretty good in general in setting up the fire. I will try some narrow formation in some upcoming battles against the heathens soon. I may even remember to post my results! Hard to remember though since I mostly read and post from work! :2thumbsup:

A 4% advantage isnt statistically significant for the number of tests you did - it could just as easily have been 4% worse performance. It seems clear that there is no real difference - its just random variation.

Of course there is also the matter of what effect incoming fire will have on your archers depending on formation (due to the over/undershoot effect). It would be interesting to see how 2 sets of archers performed against each other with different rank depths.

Thats assuming, of course, that the over/under shoot we see on screen actually makes any difference to the number of hits - i.e. whether the game is actually tracking individual missile arcs to see if they hit anyone or (as is more likely the case, since this is how it works for melee combat) if the game works out a chance to hit for each missile based on all the relevant factors, then displays a precalculated number of hit/miss animations for each volley.

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Originally Posted by Daveybaby

A 4% advantage isn't statistically significant for the number of tests you did - it could just as easily have been 4% worse performance. It seems clear that there is no real difference - its just random variation.

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Yeah I was guessing this as well... but I didn't really want to say it as I couldn't be sure without actually running the statistics. I'd have to approximate the normal distribution (using binomial I think it is?) since my sample size is < 30 (it's 10)... and frankly I don't feel like it for a game, lol. Anyway, let's not bog down the thread with statistics talk!

@Von Nanega: You are correct concerning any kind of code that would make archers select a best target from the enemy unit (or from the entire field of battle in the case of firing at will, which is even more ridiculous), it simply is the long way around. You'd have to run the physics on each possible target and then sift for the best result. I'd have coded it the way it is in the game, even though all those calculations might not slow the game down noticeably at all given the speed of processors currently. The simple reason is this: the way it is should prove to be the best shot for each archer in the group anyway! If your model of the archer firing includes his error in shooting, then it's not hard to see that aiming for the center of the enemy unit gives his shot the best chance to hit an enemy body once his arrow drifts in an arbitrary direction due to his inaccurate shot. Consider the enemy unit to have the following basic areas:

ABC
DEF
GHI

Targeting any of the corners A, C, G, or I, leaves 3 quadrants around the aimed area as open space, which becomes a miss for certain if the arrow drifts that way. This is very likely, at a 75% chance, leaving only a 25% chance the arrow falls inside the group to possibly cause a casualty.

Targeting B, D, F, or H leaves 2 such empty quadrants of open space, and thus a 50% chance of being a sure miss.

The center, E, has no empty space in any direction around it, and thus drift in any direction can potentially still strike a man, and therefore it must be the best place to target the archers at.

This fact also incredibly simplifies the algorithm to check line of sight and for best target in fire-at-will situations, as you just use do one calculation per archer: archer-to-target-center.

@Daveybaby: I too would assume the game rolls to see how many archers score hits, then displays the correct animations to make it happen on the battlefield. Tracking hailstorms of physical projectiles using a physics engine, while again possible, seems like more work than necessary. I'm guessing if the line-of-sight check passes when the unit fires, they assume the arrow can score a hit. There's another thread going on concerning this actually... something about pavise X-bows blocking archer fire from pikes if the archers are positioned in front of and among the pikes. No definitive answer though, so maybe I'll test it later (if the lazy bums haven't already at that point, like I suggested, lol).

Couple of points: Long, thin formations are still harder to hit from the front because of the significant number of "overs and unders."

Second, I'm beginning to suspect that the "box" is more resistant to melee units. It appears to have a "herd" effect.

If a unit is in a long, thin formation, every unit is on the outside edge. All of them are vulnerable to attack by melee.

Now, put two units of 60 archers each, six ranks deep and a total of 20 files wide. Only 48 of them are on the outside edge. The other 72 are on the inside, where they can't be immediately reached by melee units. Sixty percent of them can't be immediately attacked.

Speculating from here, stretch a spear unit of 75 men across the front of those archer units. They can still do that and be almost four full ranks deep. Put another spear unit in the back. Put some melee unit, sword or spear, on each side.

Just a thought.

Quote:

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Originally Posted by Doug-Thompson

Couple of points: Long, thin formations are still harder to hit from the front because of the significant number of "overs and unders."

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Is this factual? My experience has been that my archers miss as badly in the left-right direction as they do short-long, giving them a circular kill zone centered on the enemy unit's center. If they do in fact miss as often in the left-right direction, then unit formation should have little effect. The increased overs and unders you note, however, may be due to the fact that you can make the unit more shallow in the extreme case than you can make it slim width-wise in that extreme case: i.e. a 2-deep line still leaves more miss room than does a 4-wide line with identical kill-zone circles centered on them, so this likely accounts for long lines taking fire better.

Quote:

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Originally Posted by Doug-Thompson

Second, I'm beginning to suspect that the "box" is more resistant to melee units. It appears to have a "herd" effect.

If a unit is in a long, thin formation, every unit is on the outside edge. All of them are vulnerable to attack by melee.

Now, put two units of 60 archers each, six ranks deep and a total of 20 files wide. Only 48 of them are on the outside edge. The other 72 are on the inside, where they can't be immediately reached by melee units. Sixty percent of them can't be immediately attacked.

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If you are indicating they actually fare better (take less casualties and inflict more), then I'm guessing it's not the case since no matter how many archers are engaging currently with the enemy melee unit, they should still kill and die with the same per-man chances. What the box should do, however, is keep less archers engaged with less enemy melee units at the same time. So while the survivability of the archers is no better in that they will still be killed by the melee unit while taking down the same number of the enemy as they would in a thin line, one important thing did change - it will take the encounter considerably longer to be over as you've limited the number of active participants (and so your presumably outclassed archers will die at a proportionately slower rate), and thus your other units have considerably more time to engage the enemy flanks and rear, decisively winning the battle.

So in all melee situations it seems you need to mind formation: if your troops have the edge, you want long thin lines so the maximum number of troops are engaged at once, and the battle ends quickly, before the enemy can make a tactical reaction. If your troops are outmatched, you want a less wide formation to keep less of your troops engaged at once, thus dragging out the engagement so you can make a tactical play and save as much of your engaged unit as possible. You can of course do different things like box up a superior unit to extend the engagement and slaughter the enemy even more effectively with a flank/rear cav charge, but I wanted to point out the most straightforward and easy-to-see benefits and implications of the formations first and foremost, just to illustrate my point.

So can you have your unit of archers target a particular man in the enemy unit?

Just ancedotally, long and thin formations don't seem to wrap around shorter lines in melee as well as they used to. Ends seem to dangle a whole lot more.

@the_foz_4

That's right. Individually, archers chances are no better. It just takes longer to kill them all.

As for the "overs and unders," I forgot something very important: A shallow formation helps most when the unit is moving. Since archers can't fire when they move, you are right. The difference between two units firing at each other while standing still is not that significant.

Quote:

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Originally Posted by Vuk

So can you have your unit of archers target a particular man in the enemy unit?

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Not as far as I've seen. Every time I click the enemy unit to attack it, the red arrow appears right where I clicked, but the archers seem to always fire at the enemy unit's center, which I previously explained is correct behavior if they're trying to maximize their chance to kill enemies. So, can't really fault them for that, though I can see the appeal for instance of wanting to target the enemy general to try for a cheap swing in momentum. It's probably for the best that we can't do so, though.

Quote:

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Originally Posted by Doug-Thompson

A shallow formation helps most when the unit is moving.

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Only forward and backward, yes, I found that also. Turning, absolutely not. The unit rotation in v1.1 seems to take a note from the old STW/MTW unit movement dynamics, in that the units while "wheel" and somewhat rotate in place to face in the new direction, then start running again. This is much much quicker in block formation than in long thin lines, as there's less rotation time.

Quote:

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Originally Posted by Quillian

With muskets and arquebusiers, the front rank is all that fires, yes. But, they pretty much fire as soon as the back rank finishes reloading. Because of the larger number of men moving in the wide formation, and the resulting hangups as men get stuck on obstacles and other men, the narrow formation is probably finishing first and getting a higher rate of fire as a result. Rate of fire seems higher to me in a 4 rank formation than in a 2 rank line, from using my Spanish musketeers.

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Oddly enough, I noticed the same thing except that they didn't rotate when on the walls. Only the men in the gaps between crenelations fire, and they do NOT rotate with the units behind them. The guys in front will stay in front, and they are the only ones who shoot. /shrug If you ask me there's a LOT that could be improved there in terms game code and mechanics.

@whacker

Sorry for the confusion. A shallow formation helps most in avoiding missile fire while moving. Most shots will fly over a two-man line that is moving toward the firing unit.

Quote:

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Originally Posted by Doug-Thompson

Second, I'm beginning to suspect that the "box" is more resistant to melee units. It appears to have a "herd" effect.

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Yes this was always so since STW. Having more ranks not only 'protects' the men on the inside, but there is a rank bonus on morale. So if a unit is waivering, and you have them 2 deep, increasing that to about 4/5 deep should stop them from routing.

Quote:

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Originally Posted by Doug-Thompson

@whacker

Sorry for the confusion. A shallow formation helps most in avoiding missile fire while moving. Most shots will fly over a two-man line that is moving toward the firing unit.

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Ah, now I get you, sorry I misunderstood. I also agree here, BUT with the caveat that this "hidden bonus" decreases in a linear manner as proximity to the attacking missile units decreases. The simple reason being that the trajectory decreases and the chance of an arrow arcing over or under the target along with it. I must say though, it is interesting that in the numerous tests I did in our previous thread using the Islamic HA's vs NP's, that the kill rate seemed to be pretty constant from maximum range all the way down to melee range. I inferred this mainly by the uniform trail of bodies from the attacking unit leading up to mine, the only time it thinned out was when I was retreating to gain some firing distance again... The exception to the "hidden bonus avoidance" rule seems to be archers shooting from walls, which seems to have it's own problems right now...