Bizarre odds in melee

[marioslaz]

I'm thinking since some days to a strange effect of the combat system. Let's say two 8 bases blocks of Roman Hastati/Principes fight. One block is a single BG, the other block is made of 2 BGs in 4. Let's suppose they are absolutely equal (impact foot, swordsmen, protected, average) so they are each round at the same PoA and they hit with a score of 4 or better. We call A the BG in 8 and X and Y the 2 BGs in 4. Now let's examine some cases:

1. A score 2 hits against X and 2 against Y. Both X and Y score 2 hits against A. The fight is a draw. X and Y don't roll for any casualties. A need to roll 3 or better to avoid a casualty.
2. A score 3 hits against X and 2 against Y. Both X and Y score 2 hits against A. A wins, X loses and Y draws. Y doesn't roll for any casualties. X need a 4 or better to avoid a casualty. A need to roll 3 or better to avoid a casualty.
3. A score 2 hits against X and 2 against Y. X scores 1 hit and Y scores 3 hits. X loses and needs a 3 or better to avoid a casualty. A draws and needs a 3 or better to avoid a casualty.

In these examples the number of hits are not too difficult to achieve and from these examples it seems there are better chance for smaller BGs. In a simulation, BGs in 4 win the overall melee (break the opponent) 55% of time and BG in 8 wins 45% of time. A net 10% difference, but 2 BGs in 4 and one BG in 8 have the same cost. Any thought?

[kevinj]

In a straight fight it's true that spreading hits over multiple BGs benefits the side with the smaller BGs but you need to consider the other aspects, such as:

1) A 4 base BG is much more vulnerable to shooting, requiring only 2 hits to force a CT with a -1 for 2HPB compared to 3 and 4 hits for an 8 base BG.

2) One base lost from a 4 base BG is 25% and so -1 on all CTs. If they're average, another loss is an auto-rout.

3) In the example you gave if both sides committed a general, one could only affect 4 bases whereas the other would help all 8.

I think that overall the benefits and penalties of both options balance out.

[marioslaz]

In a straight fight it's true that spreading hits over multiple BGs benefits the side with the smaller BGs but you need to consider the other aspects, such as:

1) A 4 base BG is much more vulnerable to shooting, requiring only 2 hits to force a CT with a -1 for 2HPB compared to 3 and 4 hits for an 8 base BG.

Let's say we deploy a battle line of Romans, both ends of battle line flanked by a BGs of support troops (for example MF in 6 deployed with front 2 and deep 3). Let's examine the difference if Romans are in 4 or 8. I get as opponent Achaemenids, so we have troops with bows and they shoot in 2 rank (1,5 dice for opponent's base). BGs in 4 need 2 hits to test and they get 3 dice rolled against them. BGs in 8 need 3 hits to test and get 6 dice against them. BGs in 4 get -1 with 2 hits, so they always test with -1 (1HP2B). BGs in 8 have the same chance to test with -1 (4 hits on 6 dice I assume is near the same chance to get 2 hits on 3), but they test more times (they test also with 3 hits that is a more likely result). IMO about shooting the situation is the opposite, and BGs in 4 are better than in 8. To get the result you say, you must isolate a BG, but this is not so easy to obtain.

2) One base lost from a 4 base BG is 25% and so -1 on all CTs. If they're average, another loss is an auto-rout.

Indeed, but it's more difficult to obtain a casualty, so IMO in this aspect they are equal.

3) In the example you gave if both sides committed a general, one could only affect 4 bases whereas the other would help all 8.

True.

I think that overall the benefits and penalties of both options balance out.

My opinion is still different.

[hammy]

If a BG of 4 bases loses a combat (actually quite likely as the 8 base BG might roll 3 hits and 1 hit rather than 2 and 2) and then fails its CT and loses a base it drops that BG to only 2 dice with a -2 on CTs.


While the odds are that both sides will get 4 hits it is actually quite likely that one of the 4 base BGs will end up losing and then all your calculations go out the window.

8 bases at evens (I will ignore grading) will get 4 hits 27% of the time but there is only a 14% chance that the 8 base BG will get 2 hits on each BG. That means that although the most common outcome for the 8 base BG is to draw 4 hits to 4 hits the most common outcome for the two 4 base BGs is for one of them to lose.

The overall calculations are not simple but to assume that in a 4 hit per side situation the two smaller BGs will both draw is wrong.

[ShrubMiK]

Funnily enough I was thinking about exactly this yesterday, after watching my 2x4 auxilia lose to 1x8. What was extremely irritating was that even when the opponent BG lost he almost always somehow managed to arrange his dice to concentrate most of his hits against one of my BGs and I would have a CT too. Opponent helped this process by taking both of his base losses from against the same one of my BGs.

Something else to consider in melee - if you are fighting against an opponent that has POA advantage on you, or greater numbers, you expect to lose over some period of time. I suspect the 2x4 BGs will on average lose quicker in such circumstances than the 1x8. With two chances to be forced to take a cohesion test every turn, one of them will failed more often, and once one of the 2 BGs crumbles the other will soon follow. The maths to prove/disprove this is a bit beyond me at this precise moment

Re. shooting, if you consider instead of Achaemenids or similar the opposition is instead 2 ranks of LF/LH or Cav/MF/HF with only a second rank of shooters then the calculations change.

Excuse rounding to nearest integer in the following! Let's assume even POAs, obviously the probability values change if shooting at - POA, but I think the "shape" of the results should be similar.

Against a 1x8 BG there will be 4 dice. 3 hits needed to cause a test. Chance of getting at 3 hits is 4/16, 25%. To cause a -1 on the test 4 hits are needed, 6% chance. So overall chance of causing a test, with or without the additional -1, is 31%.

Against 2x4 BGs, 2 hits on either with 2 dice each is needed to cause a test. Therefore 1/4 chance in each case to cause a test. To cause only one of the two BGs to test, chance is 37%. To cause both to test, chance is 6%. To cause a test on at least one of them is 44%.

So considerably more chance of causing at least one test vs. the 2x4 BGs. And when they do test, it is always going to be with the additional -1. So much more likelihood in this situation of the shooters affecting cohesion.

Set against this:

a) If the 1x8 BG does have to test and fails, the effect of the cohesion loss is greater than if one of the 2x4 BGs tests and fails.

b) There is no chance of causing base losses to the 2x4 BGs, whereas there is to the 1x8 (I make it 7.5% chance).

On balance, I'd prefer to be the owner of the 1x8BG in this situation.

[marioslaz]

While the odds are that both sides will get 4 hits it is actually quite likely that one of the 4 base BGs will end up losing and then all your calculations go out the window.

I didn't make calculation, but only examples. As I wrote, with a simulation BGs in 4 win 55% of times and BG in 8 only 45%. I can exhibit the program wrote in Java with a Open Source program (NetBean)

I would expect a little more humility from you, not because I'm a graduated engineer, but at least because when you blamed me sometime ago to have made wrong calculation (do you remember? a post about fighting impact with a narrow front give better chance to spear BG against impact BG) I took 5 minutes to demonstrate your excel formulas where wrong and my calculations were right. I never got public excuse for this.

[marioslaz]

Something else to consider in melee - if you are fighting against an opponent that has POA advantage on you, [...]

Out of scope. I confronted BGs of same kind troops. I haven't time to alter my program to see what happen if...

Re. shooting, if you consider instead of Achaemenids or similar the opposition is instead 2 ranks of LF/LH or Cav/MF/HF with only a second rank of shooters then the calculations change.

Excuse rounding to nearest integer in the following! Let's assume even POAs, obviously the probability values change if shooting at - POA, but I think the "shape" of the results should be similar.

Against a 1x8 BG there will be 4 dice. 3 hits needed to cause a test. Chance of getting at 3 hits is 4/16, 25%. To cause a -1 on the test 4 hits are needed, 6% chance. So overall chance of causing a test, with or without the additional -1, is 31%.

Against 2x4 BGs, 2 hits on either with 2 dice each is needed to cause a test. Therefore 1/4 chance in each case to cause a test. To cause only one of the two BGs to test, chance is 37%. To cause both to test, chance is 6%. To cause a test on at least one of them is 44%.

So considerably more chance of causing at least one test vs. the 2x4 BGs. And when they do test, it is always going to be with the additional -1. So much more likelihood in this situation of the shooters affecting cohesion.

Set against this:

a) If the 1x8 BG does have to test and fails, the effect of the cohesion loss is greater than if one of the 2x4 BGs tests and fails.

b) There is no chance of causing base losses to the 2x4 BGs, whereas there is to the 1x8 (I make it 7.5% chance).

On balance, I'd prefer to be the owner of the 1x8BG in this situation.

There is just a certainty: we have different opinion! The motivations you listed as "Set against this" for me are enough to stronger my opinion on favour of BGs in 4. Simulating the advance of a BG against a shooter opponent and the subsequent melee is too much for the few spare time I can dedicate to this kind of curiosity, so I suppose we will remain each one on own opinions.

[ShrubMiK]

Out of scope? Well, maybe it is to you, but when you are deciding what troops to pick in your army and what size BGs you want to deploy them in, perhaps it really should be in scope? Especially if the opposition you expect to be facing consists of very different types of troops to your own

Don't get me wrong, I'm not saying I prefer the 1v8 block in all circumstances. Take the battle I was referring to. I chose to deploy my 8 bases of average MF auxilia as 2v4, whilst the major part of my infantry (16 bases of poor, undrilled, protected, HF, LS+Sw) were deployed as 2v8. Why? Well. I had in mind very different roles for them. And given that I was fairly confident the HF would lose against anything decent that came their way, I wanted them to provide a smaller percentage of my total BGs so I could lose them with less chance of the army breaking. Plus it is easier and cheaper to provide rear support for this mass of crap when it is divided into only 2 BGs. By 1 of the 2x4 BGs of auxilia, for example.

So what I'm saying is that making these arguments by concentrating on a limited set of interactions is always going to fall short. If you want to convince people that the small BGs should cost more or be penalised in other ways you need to present a case that they are overpowered - i.e. more [powerful than average in a large majority of circumstances, not just a few (possibly carefully selected) ones.

If you expect us to review your simulator for design correctness, it would be easier if you described in some detail what it does One thing that does spring to mind is: how does it decide where to remove bases from, in cases where there is a choice? As I suggested above, I think my opponent gained some advantage by being clever in this respect. There may be other choices we as humans would make intelligently that are harder to build in to a simulation. 55% vs. 45% isn't a huge difference in results, it would be easy to imagine a fairly small error or incorrect assumption tipping the balance, so being confident that the simulation is producing the right sort of result is harder.

[marioslaz]

Out of scope? Well, maybe it is to you, but when you are deciding what troops to pick in your army and what size BGs you want to deploy them in, perhaps it really should be in scope? Especially if the opposition you expect to be facing consists of very different types of troops to your own

Sorry for the misunderstanding. I omitted an important point. When I was talking with friends in our local club about this argument, we agreed that perhaps it could be the case to reintroduce the cost per BG that has been lost with DBM and the subsequent games with bases instead of miniatures. (ARMATI could be an exception, due to standardized BGs, but it's not a ruleset used for tournament). Our thought is little BG are at present better because they fight better (I didn't make the simulation, but if 2x4 are better than 1x8 with even PoA, I expect they perform better also in other conditions; don't misunderstanding what I mean: I don't want to say 2x4 with -PoA can win against a 1x8, but that 2x4 against an opponent with which they have -PoA can be better than 1x8 against the same opponent; I hope to have been clear) and because they grant an higher Army Breakpoint.
I add also that we are interested in some mechanics of play because we planned a big convention in October and we want to host a FoG tournament too, but as player we are moving toward other games. So, mechanics of games for us are interesting about game balancing, a factor for satisfaction of tournament players.

Don't get me wrong, I'm not saying I prefer the 1v8 block in all circumstances. Take the battle I was referring to. I chose to deploy my 8 bases of average MF auxilia as 2v4, whilst the major part of my infantry (16 bases of poor, undrilled, protected, HF, LS+Sw) were deployed as 2v8. Why? Well. I had in mind very different roles for them. And given that I was fairly confident the HF would lose against anything decent that came their way, I wanted them to provide a smaller percentage of my total BGs so I could lose them with less chance of the army breaking.

This is absolutely true. But in my post are not in discussion the tactical choice, only the improvements (better chance in melee, greater army breakpoint, etc.) you can get only due to the difference in size of a BG. If you want to talk about tactical choice, in my limited experience with FoG I like BGs in 6 for HF spear and 4 for Cav. Since I like a lot armies as Carthaginian, with a lot of cav and the bulk of army made by spears, or even phalangites as for Macedonian armies, I found that is very useful to keep some BG with a formation 2x3. They are more solid, since losing of a base doesn't provoke losing of any dice, and you can combine 2 such BG to strike a blow in a point of opponent's formation.

[grahambriggs]

Some other points to consider Mario, which may be difficult to model:

In favour of the 8 BG:

- generals as others have mentioned. It is likely that the 8 will have a general fighting. Will you risk two generals with the 4s? If I have 3 8s fighting 6 4s I will fight with 3 generals. The 4s cannot have 6 generals.
- the 8 might be able just to fight one of the 4s if you are clever (example: the 4s charge screening LF and one rolls + for variable move)
- if the 8 kill one 4 they probably kill both 4s. So 4 Victory points. If the 8 loses only a loss of 2 Victory points (but the army with 4s may have more BGs)

In favour of the 4s:

- 2 4s can be in two places. perhaps one fights the 8 frontally and one hits the flank?
- 4s are more manouverable than 8s.


I think this may be an fight where the small example (1x8 vs 2x4 no generals) suggests on result but the large example (3x8 vs. 6x4, 3 generals each) might be different. Is it possible for you to model that Mario? Unfortunately, I don't have your modelling skills...

When using my Early Persians I found that four units of 8 armoured troops (2 hoplites, 2 Immortal) plus 4 generals surprised opponents will their ability to kill. The factors don't look like it should happen but the generals make a big difference on 32 dice and enemy are under pressure when overlaps appear.

Regards

Graham

[hammy]

While the odds are that both sides will get 4 hits it is actually quite likely that one of the 4 base BGs will end up losing and then all your calculations go out the window.

I didn't make calculation, but only examples. As I wrote, with a simulation BGs in 4 win 55% of times and BG in 8 only 45%. I can exhibit the program wrote in Java with a Open Source program (NetBean)

I would expect a little more humility from you, not because I'm a graduated engineer, but at least because when you blamed me sometime ago to have made wrong calculation (do you remember? a post about fighting impact with a narrow front give better chance to spear BG against impact BG) I took 5 minutes to demonstrate your excel formulas where wrong and my calculations were right. I never got public excuse for this.

My experience is that there is no significant advantage to 2 BG of 4 fighting 1 BG of 8. I can't look at your code so if it is correct then I have to assume it is and say I am surprised at your findings.

Off hand I do not remember the previous discussion in detail but I am confident that the calculations in my spreadsheet are correct although they are simplistic in that they do not fully factor in cohesion tests and such.

I agree that there is a higher chance of the BG of 8 losing a base if it draws or wins but I suspect that the actual chance of one of the BGs of 4 losing a base is catually quite likely as well because of the different distribution of hits from the BG of 8.

I know that last weekend a BG of 8 superio protected spear with a commander made short work of two of my BGS (one of 8 and one of 6) of average armoured spears. It didn't feel right but it clearly happened.

With the 2 BGs if one of the pair does badly the other will quickly be in trouble as well. Does your program factor in subsequent rounds of combatr?

You quote 55% and 45% but what are these refering to?

[marioslaz]

I think this may be an fight where the small example (1x8 vs 2x4 no generals) suggests on result but the large example (3x8 vs. 6x4, 3 generals each) might be different. Is it possible for you to model that Mario? Unfortunately, I don't have your modelling skills...

Not a so great skill... just a basic knowledge of programming (I graduated as IT engineer, but as professional I work as electrical engineer and I think my programming skill can be beaten easily) and a lot of patience to teach to a stupid PC all the steps in a FoG melee
Anyway, your opinion is very interesting, but I don't think a similar modelling could be useful. I have no doubt that 3x8 against 6x4, each with 3 generals reverse the odds, and the bigger BGs would now be in advantage. Remember the point from which I started: confrontation between 8 bases of the same troops in one case grouped in a big BG, in the opposite case in 2 smaller BGs. What is the goal of discussion? (which I guiltily miss to mention when I started the discussion) Making a thought about the convenience to introduce a cost per BG, like command points in old rules.

I think we can summarize the opinions so far expressed like so:

Pro smalls

• it's harder they suffer casualties
• they are better manoeuvrable
• they grant an higher army breakpoint

Pro bigs

• they absorb better casualties
• a general influence more bases

I intentionally didn't mention the better chance in a single melee, the point from which I started, because I think this is comprised in "it's harder they suffer casualties" (better, is a consequence). Anyway, at this point in the discussion, I think "it's harder they suffer casualties" it's slightly more important of "they absorb better casualties" because in an isolated melee 2 smalls vs 1 big (a very difficult case to obtain) the 2 small have better chance. I didn't mention even shooting, because it's difficult to assess to whom to recognize a pro (but I'm still convinced smalls could claim this as a point in their favour).
Looking to the list I'm still in my though that a little cost per BG would be opportune. Of course this is just my opinion.

[marioslaz]

With the 2 BGs if one of the pair does badly the other will quickly be in trouble as well. Does your program factor in subsequent rounds of combatr?

You quote 55% and 45% but what are these refering to?

Full melee (as long as one side breaks)

[hammy]

With the 2 BGs if one of the pair does badly the other will quickly be in trouble as well. Does your program factor in subsequent rounds of combatr?

You quote 55% and 45% but what are these refering to?

Full melee (as long as one side breaks)

Interesting.

My gut feel is that the moment the 4 base side ends up with one of its BGs losing a fight they are in big trouble. If both sides inflict 4 casualties then yes there is a 33% chance that the 8 base BG will lose a base but there is almost a 50% chance that one of the 4 base BGs will have lost and taken 3 or 4 hits so for the 4 base side you end up with a roughly 25% chance of losing a base and a 30% or so chance one of the 4 base BGs will disrupt.

I know that in for example a Santa Hermandad army where spears can be in BGs of 4-8 bases I would always choose the 8s. I have never seen an army based around 4s do well in comps and would expect to easily beat one if I faced it. Perhaps I am wrong.

[ethan]

It is an interesting result. I suspect mostly it will come from the death rolls. The 8 accumulates more hits so when it wins it is more likely to lose a stand as the +2 modifier on the death roll is static - this is a clear advantage to small BGs. Basically a BG of 4 won't take more than four hits in an even melee so if doesn't lose the worst death roll is a 2. An eight stand unit can in theory take 8 hits and not lose leading to an automatic death.

Consider in that siuation in which every die hit the two four stand BGs lose on average 2/3 of a stand and the eight stand unit on average loses a stand. Possibly an argument that 8+ stand BGs should get +3 on the death roll if they win or something but that is a different discussion.

That said I am not sure the 45-55 swing isn't terrible as the 8 stand unit has a number of advantages in other areas. As has been much discussed it is better for generals and it is much better against shooting as more hits are requied to force a test.

I suspect it comes down a bit to a design issue and both are valid choices, which is good. What is bad is that I have a feeling that FoG as an overall design wanted to make more meatier units attractive and right now a lot of things in the game seem to be pulling it back towards lots of small units. This analysis showing that there isn't a combat advantage, the obvious maneuver advantages, and the BP advantages...

[philqw78]

I have never seen an army based around 4s do well in comps and would expect to easily beat one if I faced it. Perhaps I am wrong.

I think you are definately well off the mark there Hammy. Think before you type.

[nikgaukroger]

I have never seen an army based around 4s do well in comps and would expect to easily beat one if I faced it. Perhaps I am wrong.

I think you are definately well off the mark there Hammy. Think before you type.

Is the Dom Rom swarm so quickly forgotten

[marioslaz]

That said I am not sure the 45-55 swing isn't terrible as the 8 stand unit has a number of advantages in other areas. As has been much discussed it is better for generals and it is much better against shooting as more hits are requied to force a test.

I don't agree about shooting. If you keep a battle line of some such small BGs, your opponent must divide shooting dice. As for a previous post, smalls test less but always with -1, bigs test more often, but less times with -1. IMO in this category pro and against are balanced.
More, I never said 45-55 it's terrible, I said smalls are in advantage instead to be at even. If you read my last post, I didn't included in pro for smalls the advantage in melee because I think this is only due to the lesser chance they got a casualty.

[marioslaz]

Is the Dom Rom swarm so quickly forgotten

Excuse my ignorance, but what is Dom Rom swarm? I suppose something like Dominate Roman with a lot of small BGs, but what happened with this army and what relation there is with the present discussion?

[madaxeman]

I have never seen an army based around 4s do well in comps and would expect to easily beat one if I faced it. Perhaps I am wrong.

I think you are definately well off the mark there Hammy. Think before you type.

Is the Dom Rom swarm so quickly forgotten

Nope. Its evolving into the Principate Rom Swarm and planning its next outing as we speak.