New firing procedure at built-up areas

One of the main issues we wanted to fix at the 4th Edition is the Built-up area's combat outcome. As a first approach we began with the firing procedure related with built-up areas. We felt that the outcome when firing at built-up areas was unrealistic because a deployed brigade could be rejected, using only fire combat, from his position too easily. This issue had been a recurrent topic at the forum and Bob Coggins agreed that it should be fixed, hence we began to work on it since the beginning of the project.
The goal was to harden the survival chances of a deployed unit in a built-up area if the damage was only caused by fire and also force an assault in order to clean a built-up area from deployed enemy units. First we developed some statistical approach in order to find the initial outcome curve and then after some analysis make the corrections at the rules until arriving to the desirable outcome curve.
With the aim of simplify the difficulty of the math associated with the problem, we have made some assumptions that must be taken into account. We have eliminated the defender's fire. ie, curves represented here are upper bounds on the success of the attack. This is not a problem if interpreted correctly, and it is accurate in many possible configurations for the attacker. The bonus used is the total bonus of the attacking unit after applying all the necessary modifiers. It is not taken into account the option of setting built-up areas on fire, but the probability is low and we will take it in account later.
Next you will find some graphics related to the "old" firing procedure at built-up areas.
One attacker (-2 final bonus) Vs defender (Disorder=2, Rout=4, Dispersal=8) using NBIII
This graphic corresponds to modelling one attacker with a final bonus -2. This could be an infantry brigade or an artillery battery firing without any special modifier, only the -2 for 'vs cover'
As you can see at the graphic, one lonely infantry brigade or artillery battery has almost 50% probability of causing more than 4 casualties to the defending unit after only 2 combat hours (8 round of fire). This allows players to disperse (or nearly) a medium size and moral unit after only 2 hours of bombardment, and take the built-up area without an assault. And we stated that one single battery or unit could not do that. It could take hours (if possible) to dislodge a whole brigade from a built-up area with this procedure.
If we analyze the same subject with two attacking units (one could be an artillery battery and the other an infantry brigade ) with the same -2 bonus, things go worst.
Two attackers (-2 final bonus both) Vs defender (Disorder=2, Rout=4, Dispersal=8) using NBIII
As it could be expected in this situation the 50% probability of 4 or more casualties arrives after only one hour (4 rounds) and this time after 2 hours (8 rounds) the defender has 90% chances of 4 or more casualties, including more than 60 of rout or dispersal. This leaves, for instance, that one artillery battery and one infantry brigade (which are not necessarily of high quality) could destroy a deployed unit in a couple of hours only using distant fire, without close combat.
As we feel this is an unrealistic output, we have changed the firing procedure, and after testing various solutions, we have chosen the one that combined with a slightly change at the combat procedure related to built-up areas almost bans the attacker from dislodging a deployed unit without an assault.
With the new rules the firing probability curves at the Marechal edition are like this.
One attacker (-2 final bonus) Vs defender (Disorder=2, Rout=4, Dispersal=8) using NBIV
This case could represent an average French infantry brigade, a light artillery battery firing from medium distance, or heavy artillery firing from greater distance.
As you can see, at the new edition, a single battery or brigade may not dispersal or rout an average deployed brigade only by firing. Then with the Marechal edition changes it is almost worthless to fire in this situation, and probably it is a waste of time and resources. If the defender chooses stand and do not make a sortie, they could resist the whole day without getting dispersed or routed.
Two attackers (-2 final bonus both) Vs defender (Disorder=2, Rout=4, Dispersal=8) using NBIV
As you can see at the graphic, combining two units heavily rises the success chances for the attacker. Anyway the probability for the defender unit to get dispersed is almost negligible against the nearly 45% of the NB III edition after 2 hours (8 rounds)
Testing the rule at Marengo
As an example, we present a little historical analysis of the fighting for Marengo. Since the beginning of the austrian attack the austrian batteries from Hadik and Kaim divisions fired against the french defenders.
Assuming these batteries could be represented by two 3# batteries firing from a range of 4 inches to 6 inches, in order to avoid defender's fire and assuming also that the defender is a 16FrLN brigade. The firing probability curves are these:
With the "old" III Edition Rules, two Austrian 3# batteries could easily dislodge a deployed 16FrLN brigade. As you can see at the graphic, these light batteries, even not firing at close range, have a 55% probability of causing four or more casualties or dispersal or rout, after 3 hours (6 rounds). And more than 70% after 4 hours (8 rounds), so Marengo would be untenable, and although French casualties where heavy they resisted for more than 6 hours before evacuating Marengo without being routed or dispersed in NB terms.
With the IV Edition Rules, it is a waste of time, firing with two 3# batteries from a large distance against Marengo. The rules force a good player to get close (risking the batteries, but getting a -1 or +0 modifier) and (if possible) fire against the French supports at the flanks of Marengo (they are not under cover), and a wait the assault opportunity that the batteries may give you with the new rules.
As a brief summary, at the Marechal edition you will find a new firing procedure against built-up areas that makes built-up areas less vulnerable to distant fire and forces the attacker to assault in order to dislodge a deployed unit (This involves changes at the combat at built-up areas, but this topic will be covered in next articles).
Here you have a few graphics about the analysis.

More detailed articles will be posted at the web once the rules are published, this is just an introduction to show the type of background analysis we have made.