Thoughts on Disruption/Broken recovery...

[MisterMark]

From the manual there is a somewhat complex formula for calculating the odds that a unit recovers from disruption/broken status:


A preliminary range test is performed for the unit. If the unit
has an HQ with a Modified Command Range C that is In Command at a range
of R from the unit, then the range test is passed if a randomly generated
number between 0 and 1 is less than C / (C + R).


If the unit passes its range test, it moves to the next test based on Morale. If
the unit fails its range test, then 50% of the time it too moves to the morale test
and 50% of the time the test ends at this point in failure and no change of unit
status.

Otherwise, the current Morale value of the unit is determined based on its
Quality and all applicable modifiers. This is converted into a value between 1
and 6 using the mapping A=6, B=5, ..., F=1. The unit will pass the test and be
recovered from Disrupted or Broken, if a random die roll from 1 to 6 is less
than or equal to the Morale value


Since the chance of recovery is dependent on the distance the unit is from it's parent HQ and that HQ's command range as well as the units moral state, I decided to build a spread sheet to be able to calculate the odds of recovery for different situations.  After playing around with different inputs/variables, I came to some interesting and surprising conclusions...  However before I state those conclusions, I wanted to make sure my math is correct in the spread sheet.

Any of you veterans that are skilled with math and have a good understanding of the above formula want to check my work?  If so, please PM me and I'll give you a link to the spread sheet.

-Mark

[Ricky B]

Not sure I need your spreadsheet Mark, as it seems fairly straightforward - although I just focus on getting the unit as close to its HQ as possible, knowing that the HQ may have a wide area of disrupted units to try and rally - along with supply, helping units spot for artillery at full effectiveness etc.

But my summary would be that if a unit is stacked with its HQ, it has a 100 chance of passing the range test. If it is at max command range for the HQ, it would be at 50%. And anything in between would be between 50 and 100 percent.

If you are looking beyond just the range test to include the variations around passing the morale test, and also including the impact of the range test failing, then although my math would likely help me review your formula for correctness, it is something I have to say I don't want to put any thought into, sorry. It is just too meaningless to me to really care since the only factor I can really control is the actual range.

Rick

[MisterMark]

Not sure I need your spreadsheet Mark, as it seems fairly straightforward - although I just focus on getting the unit as close to its HQ as possible, knowing that the HQ may have a wide area of disrupted units to try and rally - along with supply, helping units spot for artillery at full effectiveness etc.

But my summary would be that if a unit is stacked with its HQ, it has a 100 chance of passing the range test. If it is at max command range for the HQ, it would be at 50%. And anything in between would be between 50 and 100 percent.

If you are looking beyond just the range test to include the variations around passing the morale test, and also including the impact of the range test failing, then although my math would likely help me review your formula for correctness, it is something I have to say I don't want to put any thought into, sorry. It is just too meaningless to me to really care since the only factor I can really control is the actual range.

Rick

Ricky,

Yes agreed, the only factor you can control is the range but in playing with the different inputs (and assuming my math is correct) I found that the range has less impact on the probability of recovering than you might think, especially when outside of the command range and accounting for all the 'forks in the road' in the test.  In contrast moral seems to be the factor with the heaviest weighting when it comes to recovery.  Some examples from my calculations:

A unit with moral of C that is 15 hexes away from it's HQ and the HQ has a command range of 10, the probability the unit recovers is 46.67%.  If that same unit moves to the limit of the command range of 10, the probability will be 50% but it's only a net gain of less than 4%.  If that same unit moves to 5 hexes away from it's HQ the probability improves to 55.56%.  And if the units stacks right on top of it's HQ the probability improves to 66.67%.

In comparison to a unit with a moral of A (and the HQ's command range still 10), the probability of recovery is 70% at 15  hexes away, 75% at 10 hexes away, 83.33% at 5 hexes away and 100% when stacked right on top of their HQ.

I suppose there is no argument in saying that having your unit within command range is better than being outside of that command range when it comes to recovery, but it's only marginally better until you get well within the command range. My conclusion is that there are going to be some situations that it might not be worth retreating several hexes to get into the outer reaches of command range to recover.  Especially if you have high moral units and/or terrain and ground conditions are detrimental to speedy movement, not to mention the potential risks of being spotted in travel mode and taking on an artillery attack or being interdicted.  If it's going to take 2-3 turns to pull back 5 to 10 hexes to get into a command range of the limit or slightly better and another 2-3 turns to get back to the action, it may just be better to pull back a couple of hexes to break contact and wait it out for recovery.

These results might not be surprise to those who have been playing a long time and have a more natural and intuitive feel for it, but it was a surprising revelation to me.

Once again, I'm not 100% certain on my math to make these conclusions confidently so please take my analysis with a grain of salt until I can get them verified.

-Mark

[LordDeadwood]

I would be interested in taking a look at your sheet. PM sent.

[Ricky B]

Based on the rules you captured, including the second item which I didn't know existed, the results you show make sense to me, since no matter what a unit has a 50% chance of checking for recovery, even when 100 hexes away. With that surprise (to me) accounted for, it definitely indicates that that impact of the range test is actually more negligible than fatigue impacts, low ammo, etc that lower current morale, which I do believe is used for the final test.

And rather than reviewing formulas where what you say makes sense, I set up a test scenario with 10 A rated German units, disrupted, with the HQ at quite a distance away. In 7 tests, I got 4 recovered once, 9 at the high end, and in between. The average had to be close to the 70% you show, although not at exactly 15 hexes.

So I am comfortable that your calcs are correct.

[MikeC]

Surprising results, Mark.

My preference would be that there would be more incentive to remain within command range. But I guess supply, artillery effectiveness, along with (minor) recovery effects, all act as incentives to remain in command.

[MisterMark]

I would be interested in taking a look at your sheet. PM sent.

@LordDeadwood - check your PM

[MisterMark]

Surprising results, Mark.

My preference would be that there would be more incentive to remain within command range. But I guess supply, artillery effectiveness, along with (minor) recovery effects, all act as incentives to remain in command.

Mike, yeah I agree that when you consider all the factors, more often than not it's going to be better to be within command range.  But sometimes you can't always be in command range and this is where understanding the impact of the variables can help you make a better choice given the situation.

I'm boiling this down to a doctrine that I will probably follow that assumes units with A or B moral can operate better and longer outside of their command range and won't need to retreat as much to recover from disruption.  And in contrast, I will be looking to keep units with C or worse moral more in command range whenever possible, not push them as hard and pull them back farther when they need a break.

Chances of low ammo/fuel and fatigue will obviously challenge this doctrine but I suppose these are the factors that we all have to balance and weigh out as 'armchair generals'... but nonetheless, these are the sorts of things that make Panzer Campaigns so interesting and engaging.

-Mark

[unonimus]

I did make something like that before:

https://www.desmos.com/calculator/hbxdudmjwt

I don't know if there is some inconsistency between this one and your spreadsheet.

Note that, in PzC, for this calculation, there is a -1 morale penalty for detached units (-2 for Fragile Morale Nationality units if their quality is not A or B.). You don't see it in the unit card because it is just for that calculation. In FWWC, they always have that penalty so it is shown there.

I also have graphs for infantry fire effectiveness, Alternative Airstrike/Indirect Fire Resolution firing compared to the default rule and armour units' real fire value compared to base value.

Edit: It might be possible for the game to check the state of being detached after disruption recovery.

[MisterMark]

I did make something like that before:

https://www.desmos.com/calculator/hbxdudmjwt

I don't know if there is some inconsistency between this one and your spreadsheet.

Note that, in PzC, for this calculation, there is a -1 morale penalty for detached units (-2 for Fragile Morale Nationality units if their quality is not A or B.). You don't see it in the unit card because it is just for that calculation. In FWWC, they always have that penalty so it is shown there.

I also have graphs for infantry fire effectiveness, Alternative Airstrike/Indirect Fire Resolution firing compared to the default rule and armour units' real fire value compared to base value.

Edit: It might be possible for the game to check the state of being detached after disruption recovery.

Oh wow... I didn't realize about the moral hit for being 'detached'.  Thanks for bringing it to my attention.