Replacement question

[ComradeP]

ComaradeP,

Everything you say is correct. Variability is the basic difference in recovery in terms of whether or not units are broken down. The averages are equivalent mathematically but a higher number of calculations means higher variability in terms of individual results. But I think the calculations for men and vehicles/guns are probably the same. It is just that for men the numbers tend to be larger so the recovery normally relates to more than 1 man, rather than fractions of a man. Although, in all cases they would still need to be rounded to whole numbers.

So, as you rightly point out there is an advantage to being broken down but mathematically it is not huge. Let us take an example of 3 units with a single  tank loss each and assume these units could combine into a single unit. If the recovery rate was 5%, each sub-unit would recover .05 of a tank each turn on average and the combined unit would recover .15 of a tank. In reality they each will recover either zero or 1 tank on a given turn, so what are the chances?

For the combined unit the chance is 15% that it will recover a single tank. For each of the sub-units it is 5% each. So the chance of zero tanks recovered for the combined unit is 85%. The chance that on a given turn all sub-units recover zero tanks is 85.7%, which is roughly the same as if combined (but slightly worse). The chance of the sub-units recovering 1 tank only is 13.5%, of recovering exactly 2 tanks is 0.7% and the chance of recovering all three is 0.1% (or 1 in a thousand). So there is a difference but it is probably not enough to base a decision on whether or not a unit should be broken down. The recovery rate would need to be quite high for the difference to become significant. It is often lower than the 5% I have assumed and so its impact is often very small. Of course I have not seen the code so I am making some assumptions about how it all works.

John

True, for recovery the difference is not particularly significant, but recovery tends to be the icing on the cake unless units are very small or local supply is very poor.

Let's use PzC for the example, as (updated) FWWC titles use fractional numbers in some OOB's that make it difficult to compare conditions between titles. Unlike PzC, Recovery might also be 0 (to prohibit loss recovery for artillery units).

Some PzC titles, such as Budapest '45, feature small battalions compared to other titles. In most cases, infantry battalions will have a strength of 400-600 men or so depending on whether the heavy weapon company is abstracted and added to the regular infantry companies a battalion consists of.

Let's assume the scenario is long enough for results to move towards the average result, removing variability from the examples.

First example: a battalion with a full strength size of 400 Men, and a strength of 300 Men in this situation. A loss of 100 Men compared to full strength.

Recovery 2% at C quality for 2% results in a recovery of 2 Men: 100x0.02=2.


Replacements at 1% (no OOB modification) result in 4 Men being replaced at 50 local supply or higher: 400 x 0.01=4 Men.

The local supply value would need to be 34 or lower in order to be below Men regained by Recovery in this example.
Local supply modifier: (34-20) / 30= 0.4666.
400 x 0.01=4.
4 x 0.04666=1.8664 Men

Bigger battalions regain more strength through Replacements than smaller units regardless of losses suffered, whereas all units of the same quality benefit equally from Recovery. That's also why cutting maximum strength in a Moscow '42 update and decreasing Axis replacements in Kharkov '43 dramatically reduced the Wehrmacht quickly ballooning in size like in the stock versions, for example.

Second example: four non-combinable 20 vehicle at 100% strength Soviet tank companies/"battalions" compared to four combinable 20 vehicle at 100% strength Panzer companies.

Let's assume all companies have 15 runners and let's assume all units are C quality.

The game turns all guns/vehicles into "Men" to determine percentage chances. 1 Gun/Vehicle=10 Men.

Recovery 2%: each company/"battalion" has a 10% chance to recover a Vehicle each turn:
5 Vehicles= 50 Men.
50 x 0.02 = 1 Man or 0.1 Vehicle.

Replacements are also identical for both sides, with a 1% Replacement rate with no local supply modification resulting in a 20% chance to recover a vehicle:
20 Vehicles=200 Men.
200 x 0.01 = 2 Men or 0.2 Vehicle.

In this case, the result is the same, but only because all units are below maximum strength and other conditions are equal.

Third example: Now let's look at a situation where two of the Soviet tank companies/"battalions" have lost 10 tanks, and the others have lost none.

Recovery 2% gives a 20% chance to recover a Vehicle:
10 Vehicles = 100 Men
100 x 0.02 = 2 Men or 0.2 Vehicle

Replacements are as above, with a 20% chance to recover a Vehicle.

Combining and breaking down the German units results in a loss of 5 Vehicles for each company. The results are the same as in the previous example.

The Vehicles regained from Recovery will decrease with each Vehicle that is recovered, whereas the Vehicles recovered through Replacements remain stable as long as the local supply value doesn't change to a value of 49 or lower.

If the two Soviet units that have lost Vehicles move, they can't recover Vehicles. If three out of four German companies move, the fourth can still recover a Vehicle.

The ability to distribute losses between component units and being able to give some units rest whilst others fight on gives a significant advantage over time.