Ok well, I've been thinking about how a flanking bonus should affect combat strength because you'd think that better tactics from a smaller force should prevail in some way. So i went and parsed the last big battle between Westmoor and Sirion (5 turns 16k vs 22.5k). Some very interesting trends if you do that. *Note - I count a retreat as a full loss of effective CS, hence the trends)
Unsurprisingly the guy with the smaller cs and in this case loser, had exponential losses and the winner after the first round had linear losses that went down with each turn (between 22 and 8% for the winner and 20 to 77% for the loser not including the first round where it was 10% for both).
Incredibly curious to me was the relation between the ratio of CS between the two armies to their losses. For the winner the losses followed a fourth order polynomial (R square of 1, ridiculous I know) The loser followed a exponential decay (R square .9999) though I would love more data points out beyond twice the size to 8 times.
Anyways, I'm still pondering things, but grossly it looks like adding a L R C orientation has certain critical points where things become incredibly non-linear (somewhat unsurprising) I'm incredibly tempted to run some boot-strap simulations of various army dispositions. If I do I'll post the results, but right now it looks to me like the flanks don't change the combat qualitatively because it is so mechanistic. A flank can utterly crumble in a turn if it is outnumbered by roughly 2. It'll suffer 40% losses right around 1.5 Cs ratio and probably collapse the next turn.
In other words for otherwise even armies if you put your values at 50/50/>0 and the other guy is evenly distributed your center line will come in and do ~25% more damage to the center. Your flank will do ~30-35% and will ultimately come out around 70% original strength and will get the bonus to the middle. In fact your middle only needs to hold for at most 3 turns before the flank will join.
So if we do a envelope simulation, where the first flank hits at 50% bonus strength, it'll look something like this (Note I'm assuming that >0 means a single unit or two to tie up the flank for a turn and a side collapses at 60% damage from original, really this should be a full retreat at 90% of CS). Also note this assumes major combat occurs on the first turn in the melee when all units are engaged. In reality this should combined push all combat back by two turns compared to real BM battles. The overall analysis holds I just didn't feel like running it to completion, and if you really want you can try it out yourself. At 60% losses whoever is ahead will get a retreat either the next turn from the enemy or the one following depending on lines units are on, parse your battles and you'll see I'm right =).
Turn 0 : 50/50/>0 33/34/33
Turn 1 : 42/41/0 24/25/33
Turn 2: 37/18.3(~retreated)/0 11.5(~retreated)/49.3/0
Turn 3: 0/47/0 0/36/0
All eggs in one basket could be a definitely bad idea. You lose quickly or you can win spectacularly if your center manages to hold somehow. In all likelyhood the former middle's would've both retreated by the hypothetical turn 3's. This makes the values closer to 32 and 20.5.
A 20/60/20 vs 50/50/>0 works out using the above fun-ness to be roughly an even worse proposition. The flank collapses even more quickly (it takes upwards of 60% damage in the first turn of all out combat), it could in theory try to delay combat there for two turns with dug in troops and take out the middle by turn 2. However, this is extremely unlikely as staggered archers would keep the enemy in for at least another turn and their numerical superiority is small enough that it would take them at least 3 or 4 turns to really win by which point they'd get flanked as they won't reach the real acceleration until turn 3. The flank would come in even more strongly than before and it's effectively game over at that point.
In summary: Because of the exponential damage taken by a flank with significantly less troops if you can hold the middle long enough not to lose (something that would be rather trivial) the best bet is to just mass all your troops on one flank and use only delaying tactics on the other flank. Overall, this would actually make larger armies even more powerful against a smaller foe as the exponential growth in damage taken would only be amplified.
