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For example, "offensive power" is probably the most important number on the combat setup screen (in my opinion, I'd love to hear that I'm wrong here). The modifiers are actually quite well documented in the manual and many of them do have tooltips. However, "offensive power" does not appear in the manual anywhere. It does say "the second-to-last icon shows the unmodified attack points per combat round."
What I really want to know is how much offensive power does my armor battalion bring to bear on this infantry battalion, before modifiers. I want to know if this attack even makes sense before I start worrying about modifiers.
But I have no idea how this number is calculated. It definitely is not attack * number of elements which is what I would expect and what the manual suggests. For example, for 20 tanks with 100 hard attack vs. tanks, I would expect unmodified offensive power equal to 20 * 100. Well it's not that. It's some fraction of that. And then that number is further modified up or down based on the various modifiers.
Also, adding units together does not simply add their offensive power together. For example, you might do a regular attack with an armor unit and see an unmodified offensive power of 500, and then add an infantry unit to the attack and see the unmodified offensive power drop to 75! Maybe there is a good reason for that -- maybe the infantry get in the way of the tanks somehow -- but I would expect that to be in a modifier and I would expect the unmodified offensive power to be some kind of sum of the attack (soft or hard) values of the units involved.
So, to summarize, what I think is the most important number in the game can only be determined through trial and error or otherwise guessing. Maybe I'm wrong about this number being so important? If I am, then I'd like to hear how others estimate their attack strength before moving right next to the enemy to see what the setup screen comes up with. If I'm not, then I'd like to know how that offensive power is calculated!
But I will try to address your more specific questions and hopefully this is of some help. The structure of your units is paramount. There is a cohesion factor in divisions beyond just casualties. The chain of command is important. An officer gets a bonus that flows down the hierarchy. His ratio to staff (meaning he is capable of managing that size of staff) affects the effectiveness of the division. The ratio of staff to units also affects the effectiveness of a division/unit/group. The distance of your officers away from their units affect their effectiveness. The % differs depending on the officer. See their percentage and traits. It helps to move your really tired units into higher command (if he has ratio space) and to rest them if you have a good compliment of units. The card bringing in an emergency unit that can come in two can really mess with these ratios if you are not keeping an eye on the ratios.
Readiness is one of the best features I have seen in a war game. It is so realistic, because men were not robots. When they got tired their combat effectiveness deteriorated. So if they are driving across the country and in combat and never being rested their AP will drop. The game designer added a small element of RND too, which I wholeheartedly agree with, because there were instances in the war where elite troops got dominated by superior tactics or where weather or any number of circumstances could change the odds, and these were random sometimes.
Then there is stacking, another very realistic feature in this game. Increasing the size of your attack with numbers hits a threshold where it no longer works in your favour. Also over firing artillery over stacking eventually reduces effectiveness, because the spread is only as big as it is, and dropping x10 the bombs on the same crater won't help. The same applies for AP, sending in more and more tanks in a sq. mile will ultimately reduce effectiveness. Mixing units from different command structures or divisions into one attack can also reduces AP - first of all because you have two chains of command and secondly because there is different rates of readiness. One unit being tired can affect another's performance if they have the same objectives. The same applies to traffic in this game. The more crowded the roads the higher the fuel consumption. Readiness could be recouped while the road is busy, instead of all going at once. This is why in real life outnumbering the enemy just wasn't necessarily going to work for a number of common sense reasons. There were larger battles like Kursk where this wasn't the case, but even then tactics were used that had to consider supplies and the battlefield. Massing your troops has the obvious advantage up to a point. (especially in a heavily wooded area) Look at all the factors including the disadvantages, and this is all reflected in your AP when you give the order to attack. Casualties also affect this, when a unit cohesion drops below a threshold, and these stats show on the units. If a unit took a beating their morale would drop - this also affects their AP. Think of the AP as a scale of moving parts. So elite units have better quality stats, but their AP just starts at a higher point.
More senior officers orders (cards) when timed right can also affects this AP factor. So its not just the immediate officers, but senior officers that can affect that number. Their ratios matter too. The most important part I learned was to use your forces to co-ordinate the balanced quantity with the best quality for attack/defence and resting. The timing of the order cards is important too, and when transferring units from one division to another watch the ratios and be careful not to break divisions down, but rather build them up if the officer ratio allows for it. Marching troops really batters their readiness - if there are trucks pick them up and drop them off. Use nights to rest and recoup.
Slow your roll so traffic is kept down and supplies can keep up. Someone should always be resting to regain readiness. And don't be too eager to bring on all those emergency units and additional divisions via the cards, because all those men want to eat and use up road space and supplies. Some of this differs when playing the allies, and that comes down to tactics and strategy.
So there is no chess move magic number that you can calculate the exact outcome. That in my opinion is what makes this game such a great game. You have to consider all these factors to determine your next move - kinda like it was in real life for generals.
Hey, sorry if I went off the beaten path and perhaps did not address every point/question. Hope I managed to be of some assistance. I haven't played for a while now as BG3 got my attention, but I do love this game, one of my all time favourite war games.
As an example, here's a question I've posted on the Matrix forums which is unanswered as yet. It's about the readiness stat, which I agree is a cool measure, but I give a trivial example in which there are huge readiness penalties applied in a situation where it makes no sense: https://www.matrixgames.com/forums/viewtopic.php?f=10185&t=397122
So while readiness is interesting and important, surely it must be possible to at least understand in broad strokes why the number is fluctuating. I'm not sure what the point of a wargame that applies a 78% (!) attack penalty for no apparent reason is.
With all due humility, I'm sure I'm missing something obvious, but no one has pointed it out yet.
I have not yet looked into the details, but my understanding is that green represents 100% readiness and the height of the bar on the counter represents unit integrity. Looking at your examples in the forum I notice they do not have full readiness/integrity bars.
I have assume the lower integrity affects unit strength and consequently attack value. For example, I had a couple of divisional artillery units with 1/3 green bar and unit strength of 9 at start of battle. I decided not to use them and the unit strength increased to 11 a few turns later. In retrospect, I wish I had checked their attack values over time. Instead I assumed they had been receiving auto-assigned replacements over the previous turns, which contribute to unit strength. The bar didn't go up significantly (or even noticeably). Yet if you look at stronger level units their readiness/integrity bars are higher.
Does integrity contribute to combat readiness? I don't know. Intuitively it makes sense that a unit ready for combat with low integrity (e.g. missing combat roles and equipment) would be penalised going into combat.
I haven't explored this part of the system enough to validate my hypothesis. Perhaps morale is a factor too?
If morale and/or integrity contribute to a readiness penalty, it isn't documented anywhere that I'm aware of. To my knowledge, the only things morale does are related to retreat and panic during battle. The manual honestly doesn't say much about it.
As far as integrity goes, again the manual doesn't say much about it, but I would expect a lower integrity to be reflected in the unmodified offensive power number, not a modifier to some other stat. Why have a separate integrity value in the first place, if it's just going to modify another modifier? But I agree it's plausible.
Undocumented rules in a wargame are tough for me to see past and this game has lots of them.
I just had a look at a Panzer regiment (Panthers) with 100% readiness against an adjacent artillery unit and then against an adjacent infantry regiment. The readiness modifiers on the attack value differed in each case, while the HQ/Staff/Officer modifiers on attack value stayed the same in both cases. Possibly terrain, equipment type and opposing unit type all factor into the readiness modifiers?
Of course this doesn't answer your question.
It seems like you're playing by numbers instead of accepting unit and command dynamics have a level uncertainty. The best part of this game is that it emulates battlefield and unit uncertainty through a dynamic system of modifiers. Not even a real life battle commander could know the exact numerical value of effects that are going to contribute to the outcome of an engagement. I'm bewildered by your idea of accountants leading tactical units in battle.
And honestly, this readiness thing I could live with. But one I can't live with is this one: https://www.matrixgames.com/forums/viewtopic.php?f=10185&t=397321
Call it accounting if you like, but if I can't even approximately estimate my unmodified offensive power, then I don't know what the point is.