I may be presumptuous in saying this, but I think the 10,20,40,80 requirement is what I call a mutable requirement. "Let's put something out there and see how it works." The idea here is that we will make it a tailorable parameter and tweak it in based on more experience with the implemented system. The fact that it has stood without challenge for this long is testimony to the fact that it was a pretty darn good point of departure. Recently, I think the general conclusion is Axis corps are less useful than they ought to be (maybe not - the designer may be very intentional about this impact).
As I wrote in the post about the probability of failing the initiative check - the intent of the designer is key.
So if we were to frame this as a requirements statement, we might have for the "Probability to Pass Leader Check" requirement:.
The game should reinforce traditional corps-army command structure by ensuring that in typical situations, the leader checks are more likely to pass when a corps is in the chain of checks then when one is not. The typical situation should be considered a corps commander with an effectiveness of 5 and an army commander with an effectiveness of 7.
If that is the the intent, this post takes the notion to the next level of refinement. Applying my handy dandy speadsheet (PM me if you want it), there are two ways to achieve this:
1. Improve the effectiveness of the corps commander.
2. Reduce the effectiveness of the army commander if it is the first level in the chain.
A third alternative is to make the command checks continuously variable based on the command scope. In other words, a corps commander with six points has a greater probability of success than a corps commander with eight points. My impression is that the designer has firmly rejected that approach. It remains an option with many variations. The current design is continuously variable down to the default command scope then constant.
For the requirement as stated and using whole numbers for the base, for option one we get seven as the base for corps in the first position. The base for the army in the first position remains ten. This implementation improves the effectiveness of corps commanders in all situations.
For option two, we leave the corps base at ten but change the army base to thirteen if it is in the first position. See the next post for the exciting details. This option reduces the effectiveness of army commanders in the first position so primarily effects the Soviets unless the Germans are deleting corps commanders.