BG sizes and scaling issues (was various other topics)

[lawrenceg]

The chance of one of the 4 base BG's losing is I think significantly higher than an 8 base loosing but the chance of both 4 base BG's loosing is going to be lower than that of an 8 base one loosing.

The real problem with 4 base BG's is that once they lose a single base they are 25% down which is a different subject.

Yes, e.g. for 0 POA if there are two 4-base then the chance of (At least one 4-base loses) is about 60% compared to 40% chance for a single 8-base to lose.

The point about lost bases throws up another issue however.

4-bases each expect to take half as many hits as an 8 base. When it comes to death rolls, 4-bases have a much higher chance of passing the test. This is particularly noticeable if they win or draw (or for shooting hits) because two 4-base BG benefit from two lots of +2 on the death roll.

For example, distribute 4 shooting hits at random on two 4-base. The expected bases lost is 0.125
Do the same shooting hits on a single 8-base. The expected bases lost is 0.333

To avoid this kind of scale effect I would like to see the +2 replaced by "ignore 1 hit per 2". This would give about the same relative lethality overall (compared to losing close combat hits), but the scaling would be much smoother (i.e. relative lethality is not so much affected by the size of the BG).


There is a similar scaling issue for the "At least 2 more hits received than inflicted in close combat" in that it is difficult to get an absolute difference of 2 with a small number of dice, but very easy with lots of dice. I suggest changing that to "difference between hits received and inflicted is at least 1HP4B". In that case to get the -1 on cohesion test you need:
4-base, difference of 1 hit
6 and 8-base, difference of 2 hits
9, 10 and 12 base, difference of 3 hits.

These two proposals would remove some of the advantages of 4-bs BGs, but they have plenty. The ony disadvantage at present seems to be the losing 25% once one base is lost. I'm not sure how significant that is. Hammy mentions it a lot, but from what I've heard, most people with a choice of 4 or 6 bases for knights always choose 4.

[hammy]

To avoid this kind of scale effect I would like to see the +2 replaced by "ignore 1 hit per 2". This would give about the same relative lethality overall (compared to losing close combat hits), but the scaling would be much smoother (i.e. relative lethality is not so much affected by the size of the BG).

I think that is a nice idea, it is one of the areas where things sometimes feel odd.

Code: Select all

There is a similar scaling issue for the "At least 2 more hits received than inflicted in close combat" in that it is difficult to get an absolute difference of 2 with a small number of dice, but very easy with lots of dice. I suggest changing that to "difference between hits received and inflicted is at least 1HP4B".  In that case to get the -1 on cohesion test you need:
4-base, difference of 1 hit
6 and 8-base, difference of 2 hits  
9, 10 and 12 base, difference of 3 hits.

Another interesting idea but it might be a bit complicated. It would also mean that a BG of 4 bases that drops to 3 from a casualty would roll at -3 (1 HP3B, 25% and beaten by 1) whenever it lost a combat

These two proposals would remove some of the advantages of 4-bs BGs, but they have plenty. The ony disadvantage at present seems to be the losing 25% once one base is lost. I'm not sure how significant that is. Hammy mentions it a lot, but from what I've heard, most people with a choice of 4 or 6 bases for knights always choose 4.

Knights and shooty cavalry are troops that I would pretty much always use in 4's (although I have used knights in 6's from time to time). Infantry though I generally like to have in 6's or more.

The real killer with BG's of 4 is trying to rally them when they have lost a base. To be honest it is simpler just to ignore them as the odds of getting them back are very small.

[lawrenceg]

Another interesting idea but it might be a bit complicated. It would also mean that a BG of 4 bases that drops to 3 from a casualty would roll at -3 (1 HP3B, 25% and beaten by 1) whenever it lost a combat .

Perhaps count knights, chariots and elephants as 2 bases for this calculation (as they fight as effectively 2 bases anyway). This makes it a little bit more complicated, but far from intractable. It shouldn't be too hard to remember that bases which have 2 or more combat dice in melee count as 2.

[spikemesq]

A quick flip through the army lists suggests another potential angle for the 4bs-BG.

As I reveiwe the parameters for including elite mounted (e.g., French Knights, Companions, Parthian Cataphracts, etc.) the amount of troops available is limited by number of total bases (e.g., 6 - 24) and size of BG (e.g., 4-6, 4-8). Thus, a player is free to include 6 x 4bs-BGs in many cases.

What if the army lists also imposed a max number of BGs as well?

Thus, the French player's current range of choice:

Men-At-Arms Knights/Superior/Undrilled/Hvy Armour/Lancers/Swordsmen : 4-6 bs-BG : 12-24 total bases

becomes

0-4 BG Men-At-Arms Knights/Superior/Undrilled/Hvy Armour/Lancers/Swordsmen : 4-6 bs-BG : 12-24 total bases

This would at least force a decision point for players seeking to use more than 16 bases of french Knights and tempers and eliminates the use by min/max types of buckets of penny-packet mounted BGs.

It also might help to tailor certain armies by permitting more and smaller units along the same lines of DBx armies that could obtain a 4th reg general.

Thoughts?

Spike

[lawrenceg]

Another interesting idea but it might be a bit complicated. It would also mean that a BG of 4 bases that drops to 3 from a casualty would roll at -3 (1 HP3B, 25% and beaten by 1) whenever it lost a combat .

I've now done some sums for a few cases of average BG's fighting at 0 POA:

For single-dice bases, the proposal would convert a -2 (existing system) to -3 about 25% of the time.
For double-dice bases a -2 bcomes a -3 about 20% of the time.

The extra -1 changes the CT result in 8/36 or 22% of the time.

The 3-base BG would therefore be worse off (i.e. lose a cohesion level that they would not have previously lost) only about 5% of the time under the new proposal.

Next I had better look at the effect on a 4-base BG to see if the scale effect was signficant in the first place.

[shall]

Hammy in Picts vs Romans wrote:
The chance of one of the 4 base BG's losing is I think significantly higher than an 8 base loosing but the chance of both 4 base BG's loosing is going to be lower than that of an 8 base one loosing.

The real problem with 4 base BG's is that once they lose a single base they are 25% down which is a different subject.

Yes, e.g. for 0 POA if there are two 4-base then the chance of (At least one 4-base loses) is about 60% compared to 40% chance for a single 8-base to lose.

An therefore the odds of 8 bases losing as 2 bg of 4s is roughly .6 x .6 = 36% which is very similar to the 40%.

When I last simluated it it was almost identically equal in fact overall as a simulation throguh to conclusions. 1 8 man is more resilient but goes as whole.

Si
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[lawrenceg]

Hammy in Picts vs Romans wrote:
e.g. for 0 POA if there are two 4-base then the chance of (At least one 4-base loses) is about 60% compared to 40% chance for a single 8-base to lose.

An therefore the odds of 8 bases losing as 2 bg of 4s is roughly .6 x .6 = 36% which is very similar to the 40%.

When I last simluated it it was almost identically equal in fact overall as a simulation throguh to conclusions. 1 8 man is more resilient but goes as whole.

Si
[/b]

Actually that 60% already includes the case where both 4-base BGs lose, which is only about 13%. The other 47 % is made up of one or other of the two 4's losing on its own. It is however true that 1 8-base is more resilient but goes as a whole and it is encouraging that this matches Si's simulation (although it's not clear to me from his post what is identically equal to what )

[shall]

For what its worth we tried 2 x4 vs 1 x8 about 5000 times through a simulation with different troop types at it was so close to equal in end result that it was hard to call. IIRC Bruce Brown did his own version of it and found a similar thing.

This came in part form the absolute 2 gap to create the second - which the larger one is vulnerable too more than the smaller ones due to size, but also less vulnerable to it due to spread (i..e if you rolled 1000000 dice the restults get pretty averaged out). To simulate it you haev to do the complete tree of impact, CTs, melee, CTs until, one side break and loses everything. So its a bit tricky to do.

I expect that is why those of us who played a lot have given up on trying to pick our BG sizes for some sort of mathemaqtical reason and instead choose them on the basis of an expected tactical utilisation...surely a good thing

Si

[lawrenceg]

For what its worth we tried 2 x4 vs 1 x8 about 5000 times through a simulation with different troop types at it was so close to equal in end result that it was hard to call. IIRC Bruce Brown did his own version of it and found a similar thing.

This came in part form the absolute 2 gap to create the second - which the larger one is vulnerable too more than the smaller ones due to size, but also less vulnerable to it due to spread (i..e if you rolled 1000000 dice the restults get pretty averaged out). To simulate it you haev to do the complete tree of impact, CTs, melee, CTs until, one side break and loses everything. So its a bit tricky to do.

I expect that is why those of us who played a lot have given up on trying to pick our BG sizes for some sort of mathemaqtical reason and instead choose them on the basis of an expected tactical utilisation...surely a good thing

Si

(after more sums...)

It turns out that an 8 is more likely to suffer a -2 than a 4 is (by a factor of about 1.6 unless they have a POA). The exception is fighting at ++ where a 4 is more likely to have to test at -2, but this happens less than 2% of the time anyway.

The situation in an overall fight is complicated because it is possible to break one of the two 4's before the other one. When this happens, the 8 will have a significant advantage over the remaining 4. So I suspect that two 4's are not as good overall as they look on paper.

The probabilities indicate:

If you have a + or ++ in combat, then two 4's are marginally worse than one 8. However, with a + or ++ you will probably win the fight overall, so you won't notice the difference. I predict that in simulations, two 4's with advantage tend to be more battered than one 8 when they have won the overall fight.

If you have a - or -- then two 4's are better than one 8 (makes a difference 5-10% of the time). This may be compensated for by the possibility of one BG breaking early. You will probably still lose the overall fight, so won't notice the difference.

If you have 0 POA, two 4's appear to be marginally better than one 8. This may be compensated for by the possibility of one BG breaking early.

Changing the -1 for 2 hits difference to -1 for 1 hit difference per 4 bases makes the small + and ++ BGs even worse, but largely cancels the paper advantage of small BGs at 0, - or --.

Given the simulation results quoted above, which indicate no effect of BG size on overall results, it seems there is no need for a change. All the different scaling and rounding effects cancel each other out in practice.