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RE: Army size limits
Posted: Wed Mar 11, 2009 4:58 pm
by Walloc
ORIGINAL: barbarossa2
A good example of a system which I find fantastic in this manner is AGEOD's Birth of America 2. An older game system would have simply disallowed any movement between December and March. BoA2 allows players to risk marches and campaigns during this time and getting caught in the open. Doing this, especially if hit by very adverse weather conditions and in highly concentrated numbers IS a recipe for disaster. But! If you need to do it, it CAN be done. But is the expected payout worth the gamble? In my humble opinion, putting a cap on your stacking limits is like saying, "no movement from December to March".
Having played AGEODs game alot i agree with u that it works very well in those. Especially taken into consideration the war's it cover.
From a purely historical issue u run into more problems in the Nappy age.
The end of 1805 camapign spills well into dec.
The Eylau part of the 1806-1807 campaign happened during dec-mar. Yes there was lulls and troops going into cantoment, but obviously military operations happened too.
The russo-sweden war of 1808-1809 started in late feb and action in march too.
1809 dec-mar is lull in action.
The end of 1812 and start of 1813 went through dec-march too. Yes losses last part of the retreat in dec was horrible but not so in particular in jan-mar. The dec lossing having more so to do IMO with the conditions concerning the retreat, then purely weather tho if ofc also matters.
1814 campaign happens almost exclusivly in dec-mar
Leaving only 1809 and 1815 and the latter by the nature of it couldnt possibly have happened during dec-mar, as the only campaigns with no action in dec-mar.
Im excluding all the "mediterranean" campaigns where the term winter is argueble from a "bad" weather point of view.
Im in no way saying that weather doesnt play a large role and there shouldnt be penalties. Just pointing out that in the "american" war's, displayed in 2 of AGEOD games, that the no movement in the dec-mar periode seems generally more in line with historical lack of operations. 1861-62 west theater being an obvious exception.
Unlike nappy age where campaigns in that periode of the year isnt that uncommon. Tho spring-summer-fall are ofc prefered for operations.
Kind regards,
Rasmus
RE: Army size limits
Posted: Wed Mar 11, 2009 4:59 pm
by ericbabe
Ahhhh, the ancient debate over battle limits in COG.
In the early days of COG I was implored by many [:@] people telling me just how bad it is that we didn't have battle size limits, and that my game was terrible for allowing every battle to be Leipzig-sized, and that it should only be the very rare battle that was that large. So I did a lot of work adding battle limit rules to make the people [:)], but then after the game came out we had many new [:@] people seeing the game for the first time who didn't want any limits on their battles. At some point, on this issue I rather threw my hands up in the air and moved onto something else, on the principle that if there are roughly as many [:)] / [:@] people on both sides of the controversy, then I've at least achieved some sort of stasis. [:)] Anyway, please feel free to continue the discussion on battlelimits. I just wanted to make you'all aware that we've been over many of the arguments pro- and con- in the game's previous incarnation.
Players do find the battle limit rules for COG:EE confusing, and I almost removed them in COG:EE for this reason alone. "I fought a battle in Switzerland and my guards weren't there" is a question I must have handled in support dozens of times.
What I'd really like to do is have every corps/army have to make a check to see whether it can arrive at the battle on time. The more "stuff" you have in a province, the harder the check becomes (because harder to coordinate many corps than just a couple corps). Units that fail the check enter the battle later, after a certain reinforcement delay. This would give commanders another nice, clear function on the battlefield. It would be an additional layer of complexity, but it would obviate the battlefield limit rules we have now, so it would be replacing one complexity with another, arguably more understandable (and more easily UI-reportable) complexity. Provinces with bad terrain / poor roads would also have harder checks, naturally. This was one of the COG:EE improvements I wanted to do but we just didn't have time/budget for it (and we went way over both time/budget, as it was.)
RE: Army size limits
Posted: Wed Mar 11, 2009 5:26 pm
by Anthropoid
I wonder what the highest concentration of military personnel on Earth ever was? Any ideas?
Stalingrad? Maybe?
Never having served in the military, and not having the kind of detailed knowledge of military history that some might have, I've always wondered about "stacking limits" and the like in games. The contrast between say TOAWIII, and Civilization 4 is an interesting example.
In TOAWIII, a game in which scenarios can have hexes as small as 5 or 10 km or as large as 100km (maybe larger), most scenarios have stacking limits. I seem to recall that for the Barbarossa scenario in TOAWIII, which is Division scale chits (?) you can put about 5 or 6 Div in one hex (scale must be 100km hexes or more?) and then you can keep putting them in there but you suffer as a consequence of doing so, both in terms of supply/attrition and in terms of combat. I always thought that that was one of the most amazingly specific detailed points of TOAWIII: the thing actually does some calculations when you have an 'overstacked' stack and certain weapons (things that go boom, for example) cause _more damage_ to an overstacked stack than a reasonable stacked stack. I mean think about it. If you are shooting at a 10ft wide front, and there 2 guys within range across that front your random chance (even discounting aiming) to hit something is much lower than if you got 4 guys in there, versus if you got 40 guys stuff in there.
I always wonder when I watch these war movies and I see guys all lined up one right behind the other while the enemy is spraying the area with machine gun fire and grenades and such . . . that cannot possibly be realistic!? I mean surely they teach infantry to keep some distance between one another under many circumstances??
Now having said all that: I don't have a freekin' clue what is a reasonable number of guys with guns to allow in any given area of 'space' as abstracted in a computer game . . . but the general idea that there should be 'limit's seems reasonable.
But I think Barbarossa is making a compelling point: the 'limits' should not be manifest as 'caps' but rather as escalating costs for putting more and more guys with guns into a given area . . . Heck! You could apply the same principle to the 'container's themselves! Instead of each 'Walls' infrastructure development level allowing an additional 'unit' of military to garrison in a town, why not change it to be 'allow' in a less rigid sense, meaning:
You can cram as many guys with guns as you want into any container in the game, but be advised that you those toy soldiers will suffer exponentially worse negative consequences the more of them you stuff in over the 'recommended' limits.
Then of course I have to think in terms of the Devs (and testers) perspective on this kinda thing: 'Ah sheeze! It works for Pete's Sake and it is a conceptually valid abstraction of how things work in the real world.' Having players ask for things that are real boogers to implement, or which may result in all kinda unforeseen negative consequences in how the game is balanced must get kinda annoying. But it does raise the question: COULD the game be modded so that the 'limits' for max Div size, max Divs per container, stacking limits per province, etc., were not 'cutoffs' of the sort that Barb and Jim are complaining against, but instead were just levels which, if surpassed resulted in worse and worse attrition, worse and worse supply/economic costs, and/or whatever other negative consequence ensue from stacking too many guys with guns in too small a space?
RE: Army size limits
Posted: Wed Mar 11, 2009 5:31 pm
by barbarossa2
Ericbabe,
I like this idea of the "check" to determine if corps can make it on time! This is a must.
Perhaps you should then also have a "supply" check too. And the more units are present, and the worse the roads, the more likely it is that the unit will have to rely on its own stocks to supply its units and not suffer disproportionately.
But yes. The "march to the guns" check is critical to replicating battle in regions like Switzerland where it certainly could take dramatically longer for corps to gather for battle in certain (but not all) situations.
RE: Army size limits
Posted: Wed Mar 11, 2009 5:38 pm
by Mus
ORIGINAL: ericbabe
What I'd really like to do is have every corps/army have to make a check to see whether it can arrive at the battle on time. The more "stuff" you have in a province, the harder the check becomes (because harder to coordinate many corps than just a couple corps). Units that fail the check enter the battle later, after a certain reinforcement delay. This would give commanders another nice, clear function on the battlefield. It would be an additional layer of complexity, but it would obviate the battlefield limit rules we have now, so it would be replacing one complexity with another, arguably more understandable (and more easily UI-reportable) complexity. Provinces with bad terrain / poor roads would also have harder checks, naturally. This was one of the COG:EE improvements I wanted to do but we just didn't have time/budget for it (and we went way over both time/budget, as it was.)
That would be excellent. Especially if the forces can in over a 2-3 day period allowing some kind of movement to contact to occur initially with say a cavalry corps stumbling into an enemy defensive position and then the rest of the Corps in or moving into the province to "move towards the sound of the guns" over the next couple days before the main engagement.
ORIGINAL: Anthropoid
But it does raise the question: COULD the game be modded so that the 'limits' for max Div size, max Divs per container, stacking limits per province, etc., were not 'cutoffs' of the sort that Barb and Jim are complaining against, but instead were just levels which, if surpassed resulted in worse and worse attrition, worse and worse supply/economic costs, and/or whatever other negative consequence ensue from stacking too many guys with guns in too small a space?
For one thing I can guarantee it would smell god awful. Especially if it was too many French guys with guns in too small a space.
[:-]
RE: Army size limits
Posted: Wed Mar 11, 2009 5:59 pm
by barbarossa2
So the way it is now, do all of the units in a region when the shooting starts get to participate? If so, then this may be part of the problem of having "unrealistically" large "battles".
However, there are two kinds of "battles" revelant to a game like CoG:EE...
Battle Type 1) a tactical struggle over 1-3 days in one relatively well defined geographical location not stretching over 10-14 miles in any direction (during the Napoleonic era)
and
Battle Type 2) an operational struggle for a area of land approximately the size of a region in CoG:EE, lasting one month (or however long a turn is in CoG:EE).
If your "battles" in CoG:EE represent type 2 above, then it would be odd not to have large "battles/struggles" for provinces. The number of troops present at these type 2 battles would not jive* with what most players know as normal type 1 "battle" sizes. CoG:EE battles MUST be of type 2 if there is only ONE CoG:EE battle resolution per month in any region. I can't think of any campaign which had ONE type 1 battle per month per region or anything like it...in fact most of the battles were small affairs which most of us never hear of. So a CoG:EE "auto-resolve" battle resolution must be a type 2 battle with several smaller engagements rolled into it. There were at least five battles with 5000 or more deployed on each side in the campaign for Ulm, but I am almost sure no one reading this can name them. So it seems that an "autoresolve" CoG battle should be of type 2 and have a good chance of involving most of the units present to some extent or another.
If CoG:EE is modelling type 2 battles, the numbers involved in these CoG type 2 "battles" WOULD seem large compared to "battles" of type 1 of the time--if those are the numbers players are complaining about when there are no limits. But in a simulation of the kind CoG:EE is, the modelling of large struggles for a region of type 2 would be necessary!
When Napoleon marched on Ulm in 1805, he had 230,000 men. NONE of the engagements were large ones (I lived close to most of them and visited them all). They were relatively speaking, small affairs. The size of the battlefields is nothing like that of Waterloo or the decisive Hohenlinden (1800) for instance (which feels --and is-- massive in comparison). Yet, in a game like CoG:EE, the struggle for the region of SW Germany would have to take these 230,000 men into account. It would HAVE to be a large CONFLICT of type 2. So, unless your system has multiple small battles, which go into determining the control of a region in any one turn, and you want to stick with one battle resoltution, I am not sure that you need to "march to the guns", but there should be effects for a unit's variable contribution to the effort depending on leadership, its supply state, its morale, the road network, command style, over all plan (envelopment, frontal assault, guerilla war, defensive). A lot of the Ulm campaign was won with maneuver and encirclement and I don't know if "marching to the guns" captures the effects of what other corps could even be up to. However, I would have to think about that more.
IMHO, I think the designers of COG:EE need to decide on if each "battle" represents a conflict of type 1 or of type 2. And then design from there.
*to jive with: (that's 1970s USA pop talk for "to correspond with")[:'(]
RE: Army size limits
Posted: Wed Mar 11, 2009 6:49 pm
by barbarossa2
A report for the "Operational Struggle" for the provence surrounding Ulm in one turn, might look like this...
***********
230,000 French troops under the command of Napoleon are struggling for the provence of Baden-Wuttemberg this turn.
They have fought 3 minor battles and 2 medium battles for the region.
They have suffered 5,600 losses.
They have inflicted 10,000 losses on the Austrian armies present.
They have captured 40,000 Austrians, including the Austrian General Mack.
***********
Of course, if you let players think that they have 230,000 men of theirs present at a single type 1 battle again and again and again, they will complain and say it is unrealistic.
I think it is a mistake to lower "stacking values" in a region to give players what they expect in terms of "battle size".
IMHO, go with type 2 battles for your Automatic Resolution and then let players pile in the troops to their own detriment. It won't take long for them to realize there is a healthy medium for troop density. Just as I quickly learned to disperse my troops and put them in many settlements during winter in AGEOD's fine Birth of America. Punish the player adequately and they will learn quickly. And the system will be a much better simulation.
On the other hand, you also have "tactical resolution" of battles, which really makes this complicated. For that you might see if each unit can "march to the guns" of the player controlled battle and then actually resolve other minor battles in the region automatically (the player doesn't control these) and mix the results together to determine what happens in the region.
RE: Army size limits
Posted: Wed Mar 11, 2009 7:22 pm
by Mr. Z
I would say that COG battles are definitely intended to model the major battles of the Napoleonic Wars. Hence the fact that tactical battles tend to last only a matter of a few days at most. (And that tactical turns are on the order of 1 hour each!)
We simply disregard the minor battles as either being uninteresting or simply not able to fit into the engine's system.
Turning combat into operational affairs would require a major rewrite of the quick combat and hexwar code. That's unlikely to happen.
If players would rather imagine them as large-scale operational affairs, they are free to use the Instant Resolve system.
Not that the above ideas aren't interesting ideas, of course! We encourage discussion of them [:)]
RE: Army size limits
Posted: Wed Mar 11, 2009 7:25 pm
by barbarossa2
Cool. Of course, I actually agree that it is more interesting for players to think that each engagement is a battle of type 1.
Mr. Z, doesn't this mean though, that you are assuming that most of the troops in a region end up in the "major battle" most of the time? In my humble opinion, I think this is where your system has made a mistake. (NOTE TO ALL READERS: THIS HAS BEEN CONFIRMED TO WORK DIFFERENTLY IN A POSTING BELOW)
It seems that this assumption (that most forces in a region end up in the same battle--the "MAIN" battle) results in unrealistically large battles on a repeated basis, and that you are then compelled to come up with mechanics which force capping of stacking limits artificially to give players what they want in terms of the size of battles.
Which is why, perhaps, you appear to have to spin in circles on this. IMHO, it would be worth considering changing the combat model for your next release, CoG:EE2 [&o] so that you can give players both accurate battle sizes AND realistic stacking limits. At the moment, based on some decisions you have made which I cannot question (after all, I am the armchair computer game designer and you are the real designer), I think you are hamstrung into providing them with one or the other. Or a mix which is unrealistic for both issues.
But I think with sufficient recoding, you can offer the players the "zoom in battles" and give them a more realistic type 2 battle model as I mentioned above. Let them have their "zoom in" battles and see if units march to them in time. This can be the "major" engagement of the struggle for the region. Then auto-resolve the rest of the conflict in the region around it. And mix the results together. Just an idea.
RE: Army size limits
Posted: Wed Mar 11, 2009 10:08 pm
by barbarossa2
Anthripoid (cool name and great icon),
You ask above what the highest concentration of troops has ever been in a "battle". I guess it depends on the size of the space you are talking about.
One candidate MIGHT be the town of Blenheim in the critical and decisive battle of Blenheim (also near Ulm along the Danube--another amazing battlefield to visit...just oozing with history). It was 1704 during the Spanish War of Succession. Primarily fought by the British forces under Marlborough against the French and their Bavarian allies. One of the French generals thought it would be a good idea to secure the village of Blenheim on their right. In a classic example of "too much of a good thing" is too much, the town was crammed with French to defend it.
This is the wikipedia account...
"Although the Allies were again repulsed, these persistent attacks on Blenheim eventually bore fruit, panicking Clérambault into making the worst French error of the day.[56] Without consulting Tallard, Clérambault ordered his reserve battalions into the village, upsetting the balance of the French position and nullifying the French numerical superiority. "The men were so crowded in upon one another", wrote Mérode-Westerloo, "that they couldn’t even fire – let alone receive or carry out any orders."[56] Marlborough, spotting this error, now countermanded Cutts’ intention to launch a third attack, and ordered him simply to contain the enemy within Blenheim; no more than 5,000 Allied soldiers were able to pen in twice the number of French infantry and dragoons.[57]"
Other accounts I have read in lengthier books on the matter make it sound even worse.
Again, this is an example of the type of error players should be allowed to make on their own. Stacking limits would have prevented this and actually keep players from reenacting the battle of Blenheim. Or its critical moments.
I say let players cut their own throats and let them put 700,000 troops into a region if they demand it, then punish them for it. There should be some benefits. But the benefits should be outweighed by the negatives more and more the higher you go.
RE: Army size limits
Posted: Thu Mar 12, 2009 12:31 pm
by sol_invictus
I was one of those players who was howling about the massive battles in COG. They ruined the game for me because any sense that Napoleonic warfare was being depicted went right out the window. In a game such as this that strives to replicate the factors that made Napoleonic warfare what is actually was, I think it is critical to either include very complex rules to reflect the limiting factors that controlled the size of armies that could be brought to the field of battle or to use some less complex but sensible limit to approximate those limiting factors. Whichever path is chosen, the end result should be that massive sized battles don't occur as soon as the game begins and not every battle approaches Leipzig sized proportions.
It seems that a happy medium course; leaning toward limits was chosen; which is fine with me. I could demand a "better" way to achieve the reasonable outcome, but since I don't have to code it I will leave that to the judgement of others. I will say that since battles are limited, I will certainly end up buying GOG: EE in the near future and that if the old system that allowed massive armies was still used, I would not even consider purchasing it. I have Empire: TW and the inevitable Napoleonic expansion to tickle my mood for a fantastical romp through history, but COG: EE need to meet my expectations for a much more believeable depiction of warfare in this era.
RE: Army size limits
Posted: Thu Mar 12, 2009 12:51 pm
by ericbabe
ORIGINAL: barbarossa2
So the way it is now, do all of the units in a region when the shooting starts get to participate? If so, then this may be part of the problem of having "unrealistically" large "battles".
No.
Mr. Z, doesn't this mean though, that you are assuming that most of the troops in a region end up in the "major battle" most of the time? In my humble opinion, I think this is where your system has made a mistake.
It doesn't work this way.
RE: Army size limits
Posted: Thu Mar 12, 2009 12:56 pm
by barbarossa2
Dear Mr. Z and Ericbabe, [&o]
Well, I am VERY happy to announce that I have just purchased the incredible looking and playing (so I am told) CoG:EE (though am having problems downloading from Digital River, whose server keeps having "internal errors" and their customer service hasn't responded yet)! I will withhold further comment on this battle issue then, until I have acquainted myself with this problem better! Within a week, I should be able to stop speaking out of my ass on this subject.
However:
I was lying in bed awake last night wondering about this problem. It seems that there are 5-6 requirements which need to be met for "realism" and marketing purposes:
1) For marketing purposes, CoG must offer battles for tactical resolution which offer "Type 1" battles.
2) This system should not result in giving players a "Leipzig" sized battle more than 1-4 times in every Napoleonic Campaign (1805-1815)
3) Stacking limits for a region should be realistic
4) Players should be able to auto resolve every conflict in a region at the click of a button
5) Turns should represent 1 month spans or so and that historically, 1 month turns could have many small, medium, or many large battles for a region
6) Regions the size of those in CoG:EE could hold up to 250,000 troops historically. But only on the rarest occassions would they all make an appearance at any single battle
It seems that what you could do is use the type of "Type 2" battle system I have proposed, but when generating the files for the turn's conflict in a region, the computer would also determine how many Type 1 LARGE battles would be fought. If a player is auto-resolving this, not much would change (but it would list the number of small, medium, and large battles fought during the turn for control of the region). If the player prefers tactical resolution of the large battles, the computer would work out which units could appear at the first (and perhaps only) large battle. This could then be fought. If it was then determined that there was a second large battle, and control of the region was still not decided, there may be a second large battle (again determining which units (or which commands) could participate). The results for these would be stored and mixed together with the rest of the auto-resolved conflict. So, theoretically, you could lose a region even though you won the "large battle" or even both. But the odds would be low for the first case, and close to zero for the second case.
Perhaps you could let players select if they want to tactically resolve all of the small, medium, or large battles on their own--giving them an option as to how much they want to do (I personally, WOULD be interested in gaming battles the size of Elchingen, a critical mid-sized engagement in the campaign for Ulm in 1805 where Ney earned his Marshall's baton). Though it would take a while to resolve 1-2 large battles and 1-3 medium battles a turn, maybe some people want to game medium battles. However, if not every battle were of "Leipzig" proportions, these battles wouldn't take as much time on average. And the Leipzig battles would be mostly dropped.
You could even add a "massive battles" category and let players game only those when they popped up--leaving large, medium, and small battles for the auto-resolve system.
RE: Army size limits
Posted: Fri Mar 13, 2009 11:54 am
by Erik Rutins
ORIGINAL: barbarossa2
Well, I am VERY happy to announce that I have just purchased the incredible looking and playing (so I am told) CoG:EE (though am having problems downloading from Digital River, whose server keeps having "internal errors" and their customer service hasn't responded yet)! I will withhold further comment on this issue then, until I have acquainted myself with this problem better! Within a week, I should be able to stop speaking out of my ass on this subject.
Send me an e-mail with your order info if DR doesn't respond, or contact our Help Desk please.
RE: Army size limits
Posted: Fri Mar 13, 2009 8:50 pm
by Tanaka
ORIGINAL: Arinvald
I was one of those players who was howling about the massive battles in COG. They ruined the game for me because any sense that Napoleonic warfare was being depicted went right out the window. In a game such as this that strives to replicate the factors that made Napoleonic warfare what is actually was, I think it is critical to either include very complex rules to reflect the limiting factors that controlled the size of armies that could be brought to the field of battle or to use some less complex but sensible limit to approximate those limiting factors. Whichever path is chosen, the end result should be that massive sized battles don't occur as soon as the game begins and not every battle approaches Leipzig sized proportions.
It seems that a happy medium course; leaning toward limits was chosen; which is fine with me. I could demand a "better" way to achieve the reasonable outcome, but since I don't have to code it I will leave that to the judgement of others. I will say that since battles are limited, I will certainly end up buying GOG: EE in the near future and that if the old system that allowed massive armies was still used, I would not even consider purchasing it. I have Empire: TW and the inevitable Napoleonic expansion to tickle my mood for a fantastical romp through history, but COG: EE need to meet my expectations for a much more believeable depiction of warfare in this era.
Instead of limiting units wouldnt it just make more sense to make units more expensive, rare, and special? I wish more games were made this way for some reason most games are made to spam lots of everything. Micro-management nightmares!
RE: Army size limits
Posted: Fri Mar 13, 2009 8:55 pm
by barbarossa2
Actually, I am with you on this Tanaka,
I am curious as to why there are "mobilization limits".
Shouldn't units just be more expensive to keep people within "realistic" limits?
This kind of punishes players who ran their economies differently so that when they needed the armies "for a rainy day" they would have them.
I think it is entirely feasible that a player may run his economy entirely differently than the power of the day and then be able to field more units in a time of crisis.
Is there a way to turn off mobilization limits in games? (I wish units could be made more expensive too then I suppose, though I don't have a feel for the game yet, so I can't say).
RE: Army size limits
Posted: Fri Mar 13, 2009 9:13 pm
by ericbabe
The mobilization limits are meant to model factors beyond economic expense. Even the most extremely mobilized nations during the Napoleonic wars only had a few percent of their people under arms. The Royal Navy could raise the revenue required to buy many new ships of the line, but even with draconian feudal-style impressment of manpower, they were hard-pressed to recruit even the minimum number of lubbers they needed to man them all.
In the advanced economy, we can model this with our population rules -- which we could have made much tighter for this purpose. However the simple economy does not have this layer of complexity, so we needed a rule that could limit the level of units a nation can field without making units unrealistically expensive.
RE: Army size limits
Posted: Fri Mar 13, 2009 9:35 pm
by barbarossa2
Ah! So in the advanced economy there are no such hard and fast mobilization limits?
RE: Army size limits
Posted: Fri Mar 13, 2009 9:53 pm
by theonlystd
ORIGINAL: barbarossa2
Ah! So in the advanced economy there are no such hard and fast mobilization limits?
I still see the mobilization limit thing with the advanced Econ on.. I think he met you cant really hit it in the advanced econ game without totally screwing up your Econ. Which from what i've seen and did is most likely true. I know i couldnt
RE: Army size limits
Posted: Fri Mar 13, 2009 10:01 pm
by ericbabe
Remember that we also have a "Unit Cost Increase" parameter that models the effects of scarcity, inflation, and war-weariness. However I don't think that mobilization limits were primarily a matter of economic scarcity. It would be weird if Britain were able to give Prussia double its normal national income, and that this would allow Prussia to field 12% of its population. Historically, Britain could have given Prussia this much, but there's just no way that Prussia could have mobilized anything beyond the 6% it already had in the field -- at some point, money just wasn't the limiting factor.