I had earlier come up with an approximation of the stacking penalty via in-game testing of the 1939 scenario as Germany with all leaders removed to avoid the coordination bonus. I recorded the number of brigades and the stacking penalty for a wide range of combats. The resulting correlation was pretty good, but not great.
I assumed the stacking penalty was based on the number of brigades as per the manual:
L2.0-
There is a Stacking Penalty which penalizes each side for
each Brigade they have in either the Front or the Reserves. It
becomes difficult to coordinate so many Units, but effective
Leadership can counteract that.
Also,
L5.1 Stacking Penalty
The more Divisions involved in a combat, the harder it
is for them to effectively coordinate. A skilled Theatre
Commander may add to this ability, avoiding the penalty.
This is basically a stacking penalty. Certain Doctrine
Research and Tech Advances can also help. The Stacking
Penalty is approximately 1% per brigade, even if it is not
in combat (reserve), and there will be a 1% reduction for
every skill level of the Theatre Commander. As a result of
this Penalty, an army comprised mostly of Support-heavy
Divisions (i.e. only one Combat Brigade) may face problems
with coordination.
It was recently suggested that perhaps it is the number of divisions and not brigades that determines the stacking penalty. This would explain the variation in the data that I observed. I therefore re-ran some tests tonight and kept track of number of divisions, brigades and the stacking penalty for a number of combats.
The results are below:
Even a quick perusal verifies that it is not brigades that affect the stacking penalty. To further solidify this conclusion I created two graphs and fit some regression curves to them.
First is the number of brigades versus the stacking penalty with a linear equation. The equation is close but there is significant variation.
Next is the same with the number of divisions. Using a second order polynomial the fit is perfect.
The definitive equation for stacking penalty is therefore:
Penalty = -0.1069*(# Div)^2 + 5.9502*(# Div) - 22.066
(Note that this should only be used >4 divisions)
The only assertion in the manual, that the stacking penalty depends on all of the units in the province and not just those involved in combat, is also erroneous. I performed several tests by initiating combat with all the divisions in one province and then with only part of them. The stacking penalty only depended on the number of divisions actually involved in combat.
I believe this definitively proves that the manual is incorrect in this particular. It's possible they will update the calculation in a future version, but I would guess that it is a low priority.
What implications does this have on how to play? There is no penalty to packing in as many brigades as possible into each division. Additionally, there is a clear incentive to stuff more support brigades into each division such that more brigades can be involved in combat simultaneously.
I assumed the stacking penalty was based on the number of brigades as per the manual:
L2.0-
There is a Stacking Penalty which penalizes each side for
each Brigade they have in either the Front or the Reserves. It
becomes difficult to coordinate so many Units, but effective
Leadership can counteract that.
Also,
L5.1 Stacking Penalty
The more Divisions involved in a combat, the harder it
is for them to effectively coordinate. A skilled Theatre
Commander may add to this ability, avoiding the penalty.
This is basically a stacking penalty. Certain Doctrine
Research and Tech Advances can also help. The Stacking
Penalty is approximately 1% per brigade, even if it is not
in combat (reserve), and there will be a 1% reduction for
every skill level of the Theatre Commander. As a result of
this Penalty, an army comprised mostly of Support-heavy
Divisions (i.e. only one Combat Brigade) may face problems
with coordination.
It was recently suggested that perhaps it is the number of divisions and not brigades that determines the stacking penalty. This would explain the variation in the data that I observed. I therefore re-ran some tests tonight and kept track of number of divisions, brigades and the stacking penalty for a number of combats.
The results are below:
Even a quick perusal verifies that it is not brigades that affect the stacking penalty. To further solidify this conclusion I created two graphs and fit some regression curves to them.
First is the number of brigades versus the stacking penalty with a linear equation. The equation is close but there is significant variation.
Next is the same with the number of divisions. Using a second order polynomial the fit is perfect.
The definitive equation for stacking penalty is therefore:
Penalty = -0.1069*(# Div)^2 + 5.9502*(# Div) - 22.066
(Note that this should only be used >4 divisions)
The only assertion in the manual, that the stacking penalty depends on all of the units in the province and not just those involved in combat, is also erroneous. I performed several tests by initiating combat with all the divisions in one province and then with only part of them. The stacking penalty only depended on the number of divisions actually involved in combat.
I believe this definitively proves that the manual is incorrect in this particular. It's possible they will update the calculation in a future version, but I would guess that it is a low priority.
What implications does this have on how to play? There is no penalty to packing in as many brigades as possible into each division. Additionally, there is a clear incentive to stuff more support brigades into each division such that more brigades can be involved in combat simultaneously.