Tuna

,
I think you are right about Grigsby's modles but I think that what you are describing appears to occur in real life also. I do think that things tend to snowball as force correlates tend towards greater and greater disparities.
Hartwig,
Trafalgar as a bad example? No, I can't agree. You and Alfred are looking at the realities of the situation we know now ( better British gunnery etc ) and applying them to the battle instead of applying the Lanchester Law model to the situation Nelson found himself in. I'll explain:
1. Nelson found himself going into battle and needed a plan which would succeed. Sure he had superior gunnery etc BUT if I were going into battle I'd try to come up with a plan which would win it irrespective of said qualitative superiority so that IF my assumption was wrong my plan wouldn't fail utterly. If my gunnery was as superior as I thought then it would simply act to reduce my losses once the plan was sound ( this is what actually happened ).
2. Nelson was facing into the battle and what can seem foregone now wasn't then. He came up with a plan to succeed even if quality was, at best, even. That's the way to plan for things. If you have a plan which can succeed in the face of a worst case estimate then you're onto a winner if anything goes your way.
So, let's assume a battle in which 10 RN ships face 10 French ships. You could go 10 on 10 with the end result that both forces would be mutually annihilated or you could split your force vs a portion of the French fleet, seek to destroy that portion of the fleet so quickly that you would be able to turn on the rest of the French fleet before it destroyed your holding force.
Assumption: Square Law applies and forces apply damage in proportion to the square of their numbers. Neither side has a qualitative advantage ( this didn't apply at Trafalgar but is accounted for in the conclusion I will draw... but you'll have to wait for that

).
So, let's look at the interesting things which happen when we split an enemy force:
Unsplit 10 -> 100 adjusted combat power ACP
9/1 split -> 81 / 1 - reduction in ACP of 18%
8/2 split -> 64 / 4 - reduces ACP by 32%
7/3 split -> 49 / 9 - reduces ACP by 42%
6/4 split -> 36 / 16 - reduces ACP by 48%
5/5 split -> 25/25 - reduces ACP by 50%
So, splitting the enemy force 5/5 yields the greatest reduction in ACP it is also pretty difficult to overmass one portion without excessively undermassing the other side. What you're really looking to do is split the enemy and your own forces in such a way that the relative undermassing ( the ratio between your holding force and their main body ) is proportionally less than the relative overmassing ( the ratio between your annihilatory force and their cut off force ).
E.g. splitting the enemy 7/3 and your own force 5/5 results in a 7 vs 5 matchup and a 3 vs 5 matchup.
Matchup 1 ( 7 v 5 ) = 49 vs 25 while matchup 2 ( 3 v 5 ) = 9 vs 25
Assuming that per unit time the forces inflict damage in proportion to their ACPs you can see that in Matchup 2 the 5 ships will inflict 2.5 units of damage ( 1/10th of their ACP ) in the same time as the enemy takes to inflict 0.9 units of damage ). In matchup 1 the 7 ships will inflict 4.9 units of damage while the 5 ships will only inflict 2.5.
The French are inflicting 5.8 units of damage per unit time vs 5 units of damage per unit time inflicted by the RN BUT while in Matchup 1 the French are reducing the British fleet portion at a rate of 20% per round the British are reducing the French fleet at over 30% per round in Matchup 2.
The end result is that the British will finish annihilating the French in Matchup 2 long before the French annihilate the British in Matchup 1 and will be able to switch those 5 ships there in sufficient time to overmatch the French main fleet and overmatch it significantly.
At Trafalgar if you assume that ships would be exchanged on a 1:1 basis then Nelson's fleet division is almost mathematically perfect according to the Lanchester Laws - that's why I say it is the best example... well, that and the fact that we have good sources for it.
Now, some have pointed out that the British had technological advantages also. That's true but I don't think that Nelson took that into account when dividing his force. I think he took a pessimistic view of his ship quality, designed a plan which would work in that worst case scenario and then totally crushed the French when he combined a Lanchester-obedient plan with technological superiority.
If you look at the battle his dispositions follow the Lanchester Laws but his victory and losses don't. I think the discrepance can be explained by the superiority in gunnery etc which he didn't rely on in his pre battle planning ( in which I'm convinced he used the Lanchester Laws ).
So, I don't say the Lanchester Laws explain everything about the battle but I do believe they were used to determine how Nelson split his forces and the splitting succeeded spectacularly and in a manner which all but one history of the battle I've read have failed to really explore.
Now as to Hartwig's view that the OODA cycle and Alfred's view that he took into account command confusion on the enemy side etc... Of course. On the other hand taking it into account doesn't explain the mathematical perfection of his force correlations. The Lanchester Laws do.
Also, I would point out that I was merely explaining a term, not writing a treatise on Trafalgar. If I was writing a treatise on Trafalgar I'd have gone into the other factors but, here, I focussed on the salient point - Nelson's dispositions show how he split what should have been a superior force to allow him to defeat one small portion of it with a locally superior force and then turn on the larger portion with his surviving force which now was stronger than the enemy main body and defeated that in turn - since that sort of operation is relevant to my explanation of future plans.
LoBaron,
1. Aussies vs Amis... I agree, I've linked to it a few posts above as an example of that.
2. Aye, but it doesn't stop people following conventional wisdom even when that wisdom isn't supported by independent analysis and then claiming the game is "broken" when their sub-optimal strategy doesn't magically result in a winning position in 1943. Just because the Allies won doesn't mean that every Allied player is pre-destined to win. If they mess up enough they will find themselves stymied.
3. I disagree with this. I think that anything one can do can be misinterpreted by a poor player. I'm fond of the saying that against a poor strategist one merely needs to wait and allow them to defeat themselves. I've won many chess games etc by just waiting and letting the other person make some monumental blunder they never had to make. Once the opening's there I pounce with all the nicety of a chainsaw attack in a phone box and dismember them. Minutes later it is all over.
I'm interested in playing skillfully and winning with a bit of art. Working myself to death to beat someone who is a poor player isn't appealing to me. If they are prone to serious strategic miscalculation then I'll work to create a situation in which I encourage that and then sit back as the situaiton snowballs and they continue to work hard to continually worsen their strategic position through inappropriate decisions and actions - all with minimal input from me.
So, yes, poor players can misinterpret an over-aggressive strategy but poor players can be relied upon to defeat themselves so long as you aren't even more incompetent than them [:D]. I think it is a bad habit to get into to start doing things which will lead poor players to fall into traps. No, do what will confound a brilliant player and if it all goes over the head of your opponent then that's fine. After all your opponent isn't actually your opponent. Your only opponent is your own expectations of yourself. The person you are playing is merely the vessel by which you test yourself. That's my view in any case... when it comes to games. In real life when lives are on the line obviously one needs to do whatever works and artfulness comes secondary. I think though that playing to the best of your ability is useful as you can never know when you'll run into the next Balck.
Also I would argue that over-aggressive strategy is a hugely misunderstood thing on the forum. Most people here, from what I can see, applaud aggression and view all aggression as being the same. Attacking something is often greeted with laudatory posts which can be summarised as, "Aren't you a great fellow for attacking that. You can always be relied upon to push, push, push." Those posts are actually intended as congratulation and receipted by the AAR writers as such.
In reality I think that those posts are immensely strong critiques of the play and signs of significant flaws. I may attack but I only do so in the pursuit of vital strategic objectives and advantage or as part of a greater plan to gain same. I am never over-aggressive. I'm as aggressive as is necessary to gain the advantage I wish to gain.
I think that players who are aggressive not in the pursuit of suitable strategic gains within the context of an overall logistical goal are, by definition, poor players.
All of the above, however, is a side issue... I'll get back to defining terms over the next day before I get to post the main outline of plans.