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Subject: It's a bad idea to attack without an advantage! rss

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Ben Skellett
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(A mathematical look at melee combat)

I've just started playing this game & I think it's fantastic. I find the melee combat system really fast & simple to implement & in order to help me better understand the implications of it (& make sure I've got the rules right) I thought I would analyse it a little bit.

I'm quite new to wargames & don't have much experience with CRTs, etc. so I may use some strange language to describe things. Also, there is a chance that you guys already know everything I'm about to discuss (especially since Ancients has been around for quite a while in one format or another). Feel free to correct me if I get anything wrong or if call something a weird name or if you guys already know all this. I'll be quite explicit with the rules I'm using just in case I'm doing something incorrectly.


Here we go.


The results of melee combat are determined by comparing the Final Melee Value (FMV) of the attacking unit & the FMV of the defending unit. The attacking unit is the unit which initiates combat (i.e. actively chooses to fight). I'm going to leave out most of the details of how Final Melee Values are determined but here's a summary:

Final Melee Value (for Attacker) = 1D6 + Combat Strength Advantage* + Terrain Effects** (for Attacker) + Attack Vector

Final Melee Value (for Defender) = 1D6 + Combat Strength Advantage* + Terrain Effects** (for Defender)

*Note that the Combat Strength Advantage will only apply to the side with the higher Modified Melee Strength Value & is zero if both sides have the same Modified Melee Strength. (Here are some other notes about it but these really aren't important for this analysis: the CSA doesn't apply when it's +1 & the stronger side isn't facing the weaker side; no-one gets a CSA if elephants are attacking; it cannot exceed +10. Read the rules for more details on how it's calculated.)

**Note that terrain effect modifiers can be negative but the FMV of a unit cannot be less than 1 (use a FMV of 1 if the die roll plus modifiers results in a value less than 1).

In fact, none of the details are important to this analysis except to note that the FMV = 1D6 + combat modifier, which could be the sum of a few different modifiers. (I included the above summary to make sure I've got the rules correct & that the analysis below isn't based on a false premise.)

So once the attacker & defender have their FMV's they compare them to determine the result of combat.

In this game, units can be in 2 "orders" (Good Order or Disordered) or they can be eliminated.

There are 5 possible results of melee combat:

AE - attacking unit is eliminated outright; no change to defender
AD - if the attacking unit is in Good Order is becomes Disordered, otherwise it is eliminated; no change to defender
EN - Good Order units become Disordered (applies to attacker & defender); no change if already Disordered
DD - if the defending unit is in Good Order is becomes Disordered, otherwise it is eliminated; no change to attacker
DE - defending unit is eliminated outright; no change to attacker

Here's how to determine the result based on the FMV of the attacker & defender (I've written it slightly different than how the game presents it):

If attacker's value is strictly less than half of the defender's value: AE
Else if the attacker's value is strictly less than the defender's value: AD
Else if the attacker's value is less than or equal to double the defender's value: EN
Else if the attacker's value is less than or equal to triple the defender's value: DD
Else (the attacker's value is greater than triple the defender's value): DE

Let me show you that in a table (I'll stop the values at 8 so it doesn't get too big):

ATTACKER's FMV
1 2 3 4 5 6 7 8
D 1 EN EN DD DE DE DE DE DE
E 2 AD EN EN EN DD DD DE DE
F 3 AE AD EN EN EN EN DD DD
E 4 AE AD AD EN EN EN EN EN
N 5 AE AE AD AD EN EN EN EN
D 6 AE AE AD AD AD EN EN EN
E 7 AE AE AE AD AD AD EN EN
R 8 AE AE AE AD AD AD AD EN



So now let's have a look at what is likely to happen when two equal strength units fight without any modifiers. (The conditions for this are fairly common: clear terrain, no leaders, defending unit is attacked from the front.) In this case both units will just roll a six sided die to determine their FMVs. How lucky are you feeling?

Looking at the possible outcomes (in the above table) when the range of values for both attacker & defender is 1 to 6 gives:

AE with odds of 6/36 = 1/6
AD with odds of 9/36 = 1/4
EN with odds of 15/36 = 5/12
DD with odds of 3/36 = 1/12
DE with odds of 3/36 = 1/12

That means if the attacking unit starts in Good Order there is a 30/36 (=5/6 = 83%) chance of it becoming Disordered or worse (chance of outright elimination is 17%)!

If the attacking unit starts Disordered, there is a 15/36 (= 42%) of it being eliminated.

For the defending unit (who didn't initiate combat), there is a 21/36 (=7/12 = 58%) chance of it becoming Disordered or destroyed if it started in Good Order & a 6/36 (=17%) chance of it becoming eliminated if it started Disordered.

Let me calculate a few more numbers before I discuss what this means (even though it's pretty obvious that the odds are not in the attacker's favour). To calculate the probabilities when one or both units have a non-zero modifier we just need to look at the 6x6 grid of possible results based on the possible FMVs of the units. For example, if the attacking unit has a modifier of +1 we're looking at attacker FMVs of between 2 & 7 (& defending values stay between 1 & 6) - so the grid of possible results shifts one column to the left. Shift it one column to the left for each increase in the value of the attacker's modifier. Similarly, shift the grid one row down for each positive modifier for the defender.

If either side has an overall modifier that is negative then we need to count the values in column 1 (for the attacker) or row 1 (for the defender) multiple times since the FMV cannot be less than 1. For example, if the defending unit has an overall modifier of -1 then it's possible FMVs are between 1 & 5 (a value of 1 would occur on a die roll of 1 or 2). There are still 36 possible die roll combinations but only 30 distinct 'cells' on the table - those in row 1 must be counted twice when determining the probabilities.

Here is a table showing the probabilities of units changing 'order' as a result of combat with various different modifiers for the attacking unit & defending unit. The abbreviations are simply: G for Good Order, D for Disordered, E for eliminated. As indicated, the first 3 numbers are for the attacker, the next 3 are for the defender. In most cases I've stopped the calculation, or jumped ahead to where there is a 50% chance of eliminating a Disordered defender.

Attacker Attacker Attacker Defender Defender Defender
Modifiers G to D G to E D to E G to D G to E D to E
A+0, D+2 67% 33% 72% 28% 0% 0%
A+1, D+2 81% 17% 58% 42% 0% 3%
A+2, D+2 89% 6% 42% 58% 0% 6%
A+4, D+2 83% 0% 17% 81% 3% 17%
A+8, D+2 50% 0% 0% 81% 19% 50%

A+0, D+1 69% 25% 58% 42% 0% 6%
A+1, D+1 78% 11% 42% 56% 3% 11%
A+2, D+1 81% 3% 28% 67% 6% 17%
A+3, D+1 75% 0% 17% 75% 8% 25%
A+4, D+1 67% 0% 8% 78% 14% 33%
A+6, D+1 50% 0% 0% 75% 25% 50%

A+0, D+0 67% 17% 42% 50% 8% 17%
A+1, D+0 69% 6% 28% 58% 14% 25%
A+2, D+0 67% 0% 17% 64% 19% 33%
A+3, D+0 58% 0% 8% 67% 25% 42%
A+4, D+0 50% 0% 3% 67% 31% 50%
A+5, D+0 42% 0% 0% 64% 36% 58%
A+6, D+0 33% 0% 0% 58% 42% 67%

A+0, D-1 61% 11% 28% 56% 17% 28%
A+1, D-1 58% 3% 17% 58% 25% 39%
A+2, D-1 50% 0% 8% 58% 33% 50%


So what does all this mean?

I'd love to know what you guys think but here's what I think:

The attacker needs a decent advantage over the defender in it's combat modifier to have a fair chance in melee combat. A good result would be something like eliminating the enemy & not being eliminated at the same time. In the table above let's look at the probability of the attacker going from D to E being less than the probability of the defender going from D to E.

These are the boundaries of where "the probability of the attacker going from D to E" is less than or equal to "the probability of the defender going form D to E":

A+4, D+2
A+3, D+1
A+2, D+0
A+0, D-1

So perhaps a good rule of thumb would be: if you want an even chance of coming out of combat no worse than your opponent only attack when you have a combat modifier which is at least 2 higher than the defender's modifier. If you want a better chance (than the defender) of surviving combat & affecting the enemy then your modifier will need to be even greater than that.

I think this is a great feature of the game & highlights the importance of using leaders, strong melee units & good positioning in attack rather than just taking a chance & rolling the dice. If your modifier isn't at least 2 higher than your opponent & there's no critical reason for you to attack then it's better to not attack with that unit - leave it sitting there until you can get a better combat modifier (perhaps the attack vector or a leader in a later round) or just defend with it.

If nothing else I hope this demonstrates that it wasn't just bad luck with the dice in a recent game when my opponent kept attacking me & coming off second best.
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p55carroll
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I went through a small part of that process after the last game of ABD I played. I came to the same conclusion, but I wasn't nearly as pleased with it.

My experience during the game was, "This sucks! I can't get a good attack going anywhere. It's futile to 'soak off' with low-odds attacks as in other wargames I've played. What's with this combat system?"

That motivated me to do some math and create some tables, as you did. Then I saw the same thing and saw why I was having the experience I did.

I've taken a long break from the game, but next time I play I'll be armed with this good information, and I'll have to upgrade my tactics.

Maybe this combat system is indeed a feature, not a bug. Last time I played, it bugged me.
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Mike Nagel
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Ben,

Freakin' brilliant! :-)

I'm really pleased that you would go to such lengths to dissect the ABD combat system. I'm also happy that you reached the design conclusion that I was aiming for. Soak-off attacks can bite you in the behind unless used very carefully (I try to limit them to the flanks or if a follow-up melee will break up a critical formation). As you indicate, leaders are key to success in combat, but you still have to be careful where and how they're committed as losing one can be disastrous.

Thanks for the effort!
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p55carroll
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hxbx wrote:

So what does all this mean?

I'd love to know what you guys think but here's what I think:

The attacker needs a decent advantage over the defender in it's combat modifier to have a fair chance in melee combat. . . .
Another thing I think I've learned (I may be proven wrong yet) is that since it's usually so hard to kill an enemy unit, the old one-two punch is called for: first attack for the purpose of disrupting the enemy, then attack to finish him off.

But I've tried and failed to make that work by starting with a weak attack. That doesn't work; it just gets your attackers killed. Even the first of the two attacks has to be pretty strong--strong enough to get a likely Disruption result.

Archers, at least in the early eras, generally can't pull it off. It's sometimes worth a try, though, if you can organize it right. To do that, you have to fire first, while there's an open line of sight, and get lucky. Then move the melee forces up (possibly blocking the archers' LOS in the process) and clobber the disrupted enemy.

When your whole army consists of light troops and archers, sometimes a lot depends on those lucky shots--and when you do get lucky, melee may not be necessary at all.

Just some random memories based on the half dozen or so scenarios I've played so far. I'm sure I still have a lot to learn. Thanks to this thread, I'm getting inspired to play this game again.
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Ben Skellett
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Hi guys,

It's great that you were interested by my analysis. It was pretty simple to do but the results have really helped me understand & appreciate this game.

Anyway, Patrick's thoughts about archers & the "one-two punch" got me thinking about some more stuff. Hopefully I'll be able to put my thoughts into a structured response & not just pour the jumbled contents of my mind onto the page (though there's a real chance that might happen).

Basically, if one's aim is to eliminate their opponent's units (& I suspect it usually is, though perhaps not always) then the most important thing to increase that likelihood - in melee combat at least - is to get a large combat modifier. That was the conclusion to the analysis.

Then, to my way of thinking, ranged combat & the "one-two punch" are just two such ways to increase an Attacker's melee combat modifier by disrupting an enemy unit (which generally decreases its combat strength) & should increase the Attacker's Combat Strength Advantage when the Disordered enemy unit is attacked in melee. Although, the probabilities indicate that a Good Order unit still needs an advantage when attacking a Disordered unit if they want a fair chance of eliminating the Defender & not being eliminated themselves!

In the table of probabilities, when the Attacker & Defender have the same combat modifier then the likelihood of a Good Order Attacker being eliminated is exactly equal to that of a Disordered Defender being eliminated. See for example this row where they're both 17%:

Attacker Attacker Attacker Defender Defender Defender
Modifiers G to D G to E D to E G to D G to E D to E
A+0, D+0 67% 17% 42% 50% 8% 17%


Even if my unit is in Good Order & I'm attacking a Disordered unit, I would still want a combat modifier of at least 1 higher than the Defender before I initiate an attack. And it seems that having a modifier of 2 higher than the Defender usually gets rid of the chance of my Good Order unit being eliminated outright (but not in the case of A+1, D-1 for example ... it's 3% there).

(This is probably a good place to point out that while the probability of a certain outcome may be higher than that of some other outcome we're only talking about probabilities of a one-off dice roll. If it is important that I don't lose a certain unit then I might be extremely reluctant to attack with it. On the other hand, like Mike points out, if the loss or disruption of a particular unit wouldn't seriously impact my plans & especially if a favourable result of such an attack would greatly improve my position then I may just test my luck & attack where I only have a low probability of success. Who dares wins, right? I also want to point out that when I play any game I'm never this dry & analytical - I save that for times when I'm not actually playing. I'm much more a "What would Hannibal do?"/gut-instinct kind of player than what it seems like here.)

The last thing I want to point out in the table is the 3 mutually exclusive outcomes of combat between a Good Order Attacker & a Disordered Defender. Only one of these 3 things can happen & as such the probabilities will always sum to 100%:

- Attacker G to D (no change to Defender)
- Attacker G to E (no change to Defender)
- Defender D to E (no change to Attacker)

It's quite sobering when I look at the table in that frame of mind, as it says that when a Good Order Attacker only has a moderate advantage on a Disordered Defender then the most likely outcome is: Attacker G to D. Here are the "break even" points where there's a 50/50 chance of either the Attacker being Disordered (no change to Defender) or the Defender being Eliminated (no change to Attacker):

Attacker Attacker Attacker Defender Defender Defender
Modifiers G to D G to E D to E G to D G to E D to E
A+8, D+2 50% 0% 0% 81% 19% 50%
A+6, D+1 50% 0% 0% 75% 25% 50%
A+4, D+0 50% 0% 3% 67% 31% 50%
A+2, D-1 50% 0% 8% 58% 33% 50%


That's a pretty significant advantage that the Attacker needs given that they're in Good Order & the Defender is already Disordered. No wonder Patrick says it's so hard to kill an enemy unit!

BUT, as I said originally (& I was glad when Mike confirmed that it was his intention), I think the "need" for a significant advantage when attacking is a great feature. It means that your decisions really matter & puts a lot of importance on doing the things which improve your chances of a successful attack:
- Leader bonuses
- Getting an attack vector modifier (by manoeuvring units & also being able to attack a Defender with multiple units)
- The "one-two punch" approach to first disrupt an enemy unit & hopefully increase the attacker's Combat Strength Advantage (& to bring it one step closer to elimination, although I think this is less important since Disordered units are still hard to kill without a decent combat modifier in attack).

Which brings me to my final thought about CPs, activation & ranged combat:

Ranged combat is great! There's no chance the attacking unit can be damaged & usually a reasonable chance of disrupting the Defender ... but then again it does cost a CP (& there are the LOS restrictions). Also, if the Defender is disrupted & hasn't been activated yet then they can be "rallied" back to Good Order straight away ... but that costs the opponent a CP too.

So the trick with ranged combat would seem to be: either attack an already Disordered unit (in the hopes of eliminating them outright) or attack a Good Order unit that has already been activated (& so can't rally this turn). Ideally, you then want to attack the Disordered unit this turn (with either melee or another ranged attack) before it can be rallied in the activation phase of next turn.

But all this costs CPs (which can be quite limited) & even if you've got enough, what order do you do things in?! Do you attack your opponent's unit before they can rally or do you rally your own unit(s) before your opponent can attack them?! And then since manoeuvring is so important for getting attack vectors, etc. (& avoiding your opponent's attack vectors & so on) you have to have CPs for that too. And how great is Panic Movement! Except that it also costs precious CPs!

So this is the other thing which I find great about this game - the really difficult decisions about how & in what order to spend your limited CPs.

I'm going to have to play this game a lot more to test these ideas in practice & see what else I can learn & I'm going to have a great time doing it. In spite of all this probabilistic analysis & strategising beforehand, there are no certainties & if my opponent gets lucky with the outcome of a few melee encounters or ranged attacks then it could certainly turn the tide of the battle & make all this analysis look very theoretical indeed.


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p55carroll
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hxbx wrote:

I'm going to have to play this game a lot more to test these ideas in practice & see what else I can learn & I'm going to have a great time doing it.
Me too.

Bravo--another great post!

 
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Joshua Gottesman
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This article inspired me to post a spreadsheet (currently pending admin approval) giving all of the possible outcomes for an attacker with a DRM of +0 to +10 against a defender with a DRM of +0 to +4.

And yeah, getting good attacks going in this game is tough! EN is by far the most common result. At the same time, with relatively low unit density, each unit lost can be critical. In many ways, it comes down to being able to rally more of your guys than the other guy can (at least in older, more set piece battles) and being able to attack disordered units with fresh ones. And even there it can be frustrating.

That's not a criticism, I'm really liking the game. I think it gives that feel of a tough clash with finally one side's line breaking in parts. Once a line is fractured and troops can start getting additional DRMs for angle, defending is much tougher!
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Scott McGinnis
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It seems to me that regardless of how difficult it is to make an attack or succeed, how does this reflect actual ancient battles? If it's accurate then system ain't broke.
 
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p55carroll
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Watti wrote:
It seems to me that regardless of how difficult it is to make an attack or succeed, how does this reflect actual ancient battles? If it's accurate then system ain't broke.
It's hard to test that, though. We know so little about how ancient battles actually worked that one educated guess is about as good as another.
 
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Mike Nagel
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From what I've been able to glean, ancient combat was pretty much a massive shoving match with trampling and stabbing. Whoever could throw enough weight to break an opponent's line and thereby reveal it's less protected flanks to more stabbing would generally win the battle.

In ABD, this is why so much more weight is required to accomplish a breakthrough. A melee result is typically a temporary stalemate until one side can apply sufficient pressure.

I'm hoping that my new ancient design, "Blade and Bow" (title subject to change) will reflect this a little better.

http://www.relativerange.com/#!blank-3/cybxx

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mpnagel wrote:
I'm hoping that my new ancient design, "Blade and Bow" (title subject to change) will reflect this a little better.

http://www.relativerange.com/#!blank-3/cybxx
Ah, interesting!

Quote:
To my memory only one other game, "Men At Arms" from Strategy & Tactics magazine, attempted to adopt a grid of squares to regulate movement.
There's also Philip Sabin's unusual-sounding Lost Battles!


Probably there's some geeklist of square-grid wargames but I'm too lazy to search for it...
 
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p55carroll
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russ wrote:
There's also Philip Sabin's unusual-sounding Lost Battles!
I was thinking of that too.

Quote:
Probably there's some geeklist of square-grid wargames but I'm too lazy to search for it...
A couple others that pop into my mind are Tactics II and Lock 'n Load Tactical: Day of Heroes. Oh, and Gettysburg. Maybe Boots on the Ground (I'd have to take another look to be sure).
 
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Russ Williams
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Patrick Carroll wrote:
Quote:
Probably there's some geeklist of square-grid wargames but I'm too lazy to search for it...
A couple others that pop into my mind are Tactics II and Lock 'n Load Tactical: Day of Heroes. Oh, and Gettysburg. Maybe Boots on the Ground (I'd have to take another look to be sure).
A little bit closer to "ancient" times is Manoeuvre, but still too modern to count as ancient.

I think I've seen mentions of some other ancient wargames on square grids, but cannot remember for sure.
 
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Avalanche Press' Rome at War series uses areas that are somewhat like squares. I have only looked at the system briefly, so I don't know much more than that.

This thread has me wanting to get ABD back on the table.
 
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