Empirical tests of combat effects: The mortar (Full Version)

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springer -> Empirical tests of combat effects: The mortar (5/23/2011 9:40:19 PM)

I was looking over the discussion in the Your "Templates" forum and saw that the ratio of mortars within units seemed to vary a bit. In addition, Victor's much-appreciated comments on the use of mortars caught my interest too.

I was curious: What are the strength and weaknesses of mortars (MTR)? How do infantry (INF) numbers impact I decided to run a few of my simple simulations to get a handle on this. In this test, I just looked at the effect of the INF/MTR ratio.

What I didn't do is examine in much detail how INF quality and experience can modify how support weapons, such as mortars impact a battle. I had already taken a look at this issue in a previous empirical test. (Though they were done in AT, I think they probably still hold for ATG.)



springer -> RE: Empirical tests of combat effects: The mortar (5/23/2011 9:53:28 PM)

To test the impact of Mortars, I create three levels of units for the attack:

1. The 40INF-5MTR unit (40/5 unit).
2. The 40INF-2MTR unit (40/2 unit).
3. The 30INF-4MTR unit (30/4 unit).

I picked these levels for the following reasons
1. The 40/5 unit represents the template that tweber uses in the 6th Army campaign. It's a solid unit. With the addition of 5MG, it achieves a 50 stack size, which is a good size when having two units attack one from adjacent hexes (i.e., two 40/5 units attacking side by side don't create an overstack.). This unit has an 8:1 INF-MTR ratio

2. The 40/2 unit represents a similar unit but examining the effect of reducing the MTR punch. This unit has a 10:1 INF-MTR ratio.

3. The 30/4 unit represented a unit that costs the same as the 40/2, but sacrificing INF for more MTR. This unit had a 7.5:1 INF-MTR ratio.

Here's one way I thought about the comparisons:
The 40/5 vs. 40/2 comparison shows the impact of extra mortar fire power
The 40/2 vs. 30/4 comparison more directly reflects the relative merits of production commitment
The 40/5 vs. 30/4 comparison shows the impact of unit size on the ratios.





springer -> RE: Empirical tests of combat effects: The mortar (5/23/2011 10:08:03 PM)

In addition to varying the INF-MTR ratio and unit size, I also played with the following parameters:

1. MTRs at 40XP vs. MTRs at 80XP. My idea was pretty straightforward here. I figured the effect of MTR XP would be proportional to the ratio of MTRs. The more MTRs, the more XP effects. INF XP was kept constant at 40XP throughout the tests. (As mentioned, the impact of INF XP had been done previously.).

2. Both INF I and INF II was tested. The reason for this is that the previous tests had shown that INF upgrades can have a big effect on support weapons like MTRs (those these effects are greatest at high levels of INF XP)

3. Defender retreat % was tested for both 50% and 100%. (Attacker was kept to 50%). The reason for this will be discussed with the findings.

To simplify the analysis, only the percentage (%) of victorious attacks out of 200 (sometimes 400) were measured (i.e., number of attacks that successfully dislodged the defender).
Though I'll discuss losses at the end of this test, the effect of losses was relatively constant across situations. % of victories seemed the easiest tool for measuring the effectiveness of an attack.


By the way, the defender was always the same: 40INF-5MG-5MTR at 40XP.



springer -> RE: Empirical tests of combat effects: The mortar (5/23/2011 10:09:18 PM)

Here is the standard situation for the tests, showing both 3-1 and 2-1 attacks.
(This example shows 40/5 attackers)

[The units that are stacked with the attackers were not used in these tests...]

[image]local://upfiles/31842/645DBCCCD82D4C72B7EA9C073EB2F9D7.jpg[/image]



Ande -> RE: Empirical tests of combat effects: The mortar (5/23/2011 10:56:55 PM)

Considering the amount of interesting data trials such as this can generate and the difficulty to display that data, I'm toying with the idea of creating something of a AT simulation toolbox for Matlab. It would be neat to run all sorts of optimizing on unit composition and to be able to display all data in convenient graphs.



henri51 -> RE: Empirical tests of combat effects: The mortar (5/23/2011 11:29:18 PM)

This is very interesting. My intuition tells me that the optimum is near 50/4, but of course I could be dead wrong.What could be historical values? 40/2?

To make things more complex, another consideration is cost, i.e. let us say that adding another mortar ALWAYS increases the effectiveness, but does the ratio of cost/effectiveness go up or down? When is it optimum?

Henri



springer -> RE: Empirical tests of combat effects: The mortar (5/23/2011 11:52:42 PM)

Hi Henri,

Great questions.  One of the reasons I compared 40/2 and 30/4 was because the production costs were equivalent.  But this only answers a small part of the question.  It's hard to figure out cost/effectiveness because a highly experienced mortar unit can keep paying back high dividends, even when paired with a green unit, as long as it is well-stocked with troops who will hold the front line.   I'll post my results and try not to comment for a bit.  (Maybe others will have insights...)



springer -> RE: Empirical tests of combat effects: The mortar (5/23/2011 11:57:57 PM)

Here are the results: (3-1 at 50% retreat; and 2-1 at 100% retreat are probably less meaningful as the results often wind up at the ceiling (around 100%) or the floor (around 0%), respectively.

The percentages are the % of victories in 200 or 400 simulations (rounded to the nearest whole number)
(Corrected error on 5/24/2011)





[image]local://upfiles/31842/393936D52E1346B5A5AC00AE04DE6DEA.jpg[/image]



springer -> RE: Empirical tests of combat effects: The mortar (5/24/2011 12:00:33 AM)

AT with MATLAB... That's a wild idea, Ande.



Frido1207 -> RE: Empirical tests of combat effects: The mortar (5/24/2011 12:32:21 AM)

Another great test, springer. Thx for sharing. Would it be possible to run another test with a 20/6 composed unit, although i guess it would only confirm the tendency of the results running the 40/2 & 30/4 composed units.

Aside: If you continue with your several tests Vic will soon also need a scientiwiki page. [;)]




Barthheart -> RE: Empirical tests of combat effects: The mortar (5/24/2011 2:24:31 AM)

Great work springer.... here's something that might help you work things out faster!
There is a function built into AT:G (well and AT as well) that helps you see the results of different combat situations really fast.
It's called "Combat Sim". You can turn it on by going to the System Option screen (small computer looking button near lower left).
This will cause your first attack in any scenario to be run 200 times! and then put out the results and average win/loss info.

To use it to it's best, edit yourself a small 10 x 10 map and put the units you want to test on the map. Then run the scenario and set the Combat Sim check box.

Hope this helps your study. [8D]


[image]local://upfiles/13114/5810D92EC1274265AE564D11C6FB89E3.jpg[/image]



springer -> RE: Empirical tests of combat effects: The mortar (5/24/2011 3:34:38 AM)

Thanks Bartheart,  That's the tool I use!  (It was probably either you or tweber who taught it to me the first time.).  But it's good to post the diagram so that others can play with it too.

It's a great tool.

(And thanks for the comment too, th1207 .  I do find analysing the game as fun as playing it [:)].)



springer -> RE: Empirical tests of combat effects: The mortar (5/24/2011 3:52:27 AM)


For 3-1 attacks, losses varied a bit for each unit type.
I found that for the 40/5 combination with INF I attacking at 3-1 odds, attacker losses averaged about 32 INF out of 120 INF attacking (26% loss). 
However, for the 40/2, loses climbed to about 40 INF out of 120 INF attacking (33%).  My guess is that the increased losses partly reflect decreased likelihood of victory.
However, the 30/4 combination wracked up about 37 INF out of 90 INF attacking (41% loss). 

For 2-1 attacks, the losses for all combinations was between 34-37  INF ( I suspect because they are mainly defeats). 

The higher losses for 30/4 units is interesting.  Three 30/4 units attacking a 40/5 UNIT is really attacking at 2.25:1 odds in terms of INF (not 3:1 as with 40/5 or 40/2). But even these relatively poor odds have a good chance of taking the ground, especially if the mortars have experience.  However, the relative price will be higher than a proper 3:1 attack.  A unit that participates in such an attack will not have much left in terms of battle effectiveness afterwards.





Jeffrey H. -> RE: Empirical tests of combat effects: The mortar (5/24/2011 4:11:26 AM)

SO, what would be an optimum grunt to mortar ratio ?, It's fairly obvious that 8 to 1 is much more effective than 20 to 1. Even when the production cost is factored in, the "basis point" increase in effectiveness appears to more than offset the production cost. The question I have is, what about say 4 to 1 and 2 to 1 grunt to mortar ratio ?



springer -> RE: Empirical tests of combat effects: The mortar (5/24/2011 4:41:42 AM)

th1207,

Simulations with 3-1 attacks with  20/6 units were tested out.  This is an attack at 1.5 to 1 odds.  
When Mortar XP was 40, the attack had an 80% chance of succeeding with the defender at 50% retreat and a 46% chance of succeeding with the defender at 100% retreat.
When Morter XP was 80, the attack had a 96% chance of succeeding with the defender at 50% retreat and a 68% chance of succeeding with the defender at 100% retreat.

Unfortunately, casualties tended be high in all simulations (around 30 out of a total of 60 INF, or 50% casualties).  Defeats tended to result in the loss of upwards of 5 MTRs.

It seems that if they are used properly,  experienced mortars can be important ground-taking units.
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springer -> RE: Empirical tests of combat effects: The mortar (5/24/2011 4:46:52 AM)

Jeffrey H.

Here's my guess (though I suspect the real ATG grognards have even better ones)

I think the answer lies somewhere in balancing absolute unit size with the INF to Mortar ratio. A 8 to 1 ratio with about 1/2 of stacking points in INF balances the ground-taking power of the mortar with tolerable casualty percentages for the infantry that leave the units battle effective for another round.

If the size of the unit is too small, a "successful attack" can fall victim to a counter-attack that wipes out the mortars to.

Of course, if the unit is too big, overcrowding will raise casualties too.

That's my thoughts, anyway...




Twotribes -> RE: Empirical tests of combat effects: The mortar (5/24/2011 5:20:13 AM)

I never use just mortars. My units are always with MGs and if I have the tech bazookas. As my tech increases I add inf guns and AT and flak.

So before bazooka I have a 50 stack, after it climbs to include 5 bazooka, 2 inf guns, 1 AT gun and 1 Flak.



springer -> RE: Empirical tests of combat effects: The mortar (5/24/2011 8:24:05 PM)

Very true TwoTribes, few players use pure units.  The use of INF and MTR only is primarily a simplifying assumption.  On the offensive, inclusion of other INF types, such as bazookas and machineguns, shouldn't impact the results.  Of course, the more auxilaries, you add to a unit the higher the stack.  But the stack limit of 50 is not an ideal, I would think the ideal is a 2:1 from adjacent hexes tries to avoid go over 100 (i.e. a 70 stack in one hex and a 30 in the other) to keep the casualties manageable.  (Of course, in a real situation all these norms can be cast to the wayside.  And sometimes, an overstack may be what is needed to take a hex...)



Ande -> RE: Empirical tests of combat effects: The mortar (5/24/2011 8:52:20 PM)

It might be interesting to see exactly when overstacking becomes inefficient. I can imagine that little bit of overstacking doesn't hurt if it means that you deal more damage and as a consequence recieves less. I think "breaking through" is determined by if a particular unit was targeted in the last few combat turns and a unit that has broken through is much more effective than a unit that hasn't. So if you bring enough units, you're bound to have some breaking through, nevermind the hords of units you'll loose.



springer -> RE: Empirical tests of combat effects: The mortar (5/24/2011 10:00:51 PM)

Ande,

Since I have it set up, and have the time (for just a bit longer), I thought I could do a quick analysis of the over stack effects for one situation, just upping the INF. The defender is at 50% loss retreat. (The number for 40/5 unit's victory is slightly different than the early chart because it is a different set of simulations.)

All numbers refer to the attacker, not the defender, since the defender's losses will remain relatively constant (approximately 50%).

I think it is important to note that the loss results are not quite accurate as they mix both victories and defeats. Defeats are probably much more expensive.



[image]local://upfiles/31842/06B8480E7D264DE28533952FAA09E864.jpg[/image]



Ande -> RE: Empirical tests of combat effects: The mortar (5/24/2011 10:29:46 PM)

Very nice of you to do this indeed. I guess the interesting number here is the victory ratio. It is maxemized at 40 points overstack when defending unit is half the stacklimit. If I had my matlab simulation toolbox, I would try to plot victory percentage and it's variance over a couple of other variables. The first would be defending stackpoints and the second entrenchment.



henri51 -> RE: Empirical tests of combat effects: The mortar (5/25/2011 1:42:57 AM)

I could be wrong, but my experience is NEVER attack at odds lower than 5:1 (as indicated by the numbers on the units). This seems to be somewhat confirmed by the high losses that you obtained for 2:1 and 3:1 odds. Even if the defender is practically annihilated, attacking losses of 20% or more for each attack will 1) rapidly whittle down your units to useless; 2) prevent them from getting any significant experience.

An interesting statistic would be the odds required WITH and WITHOUT mortars to ensure attacking losses less than 10%, which IMHO is what would normally be considered acceptable losses (does anyone remember the real number?). Correct me if I am wrong, but in WW2, for Western armies, losses of 30% were considered a terrible disaster ( the famous bombing attack on Germany that resulted in the complete stoppage of daylight bombing of Germany comes to mind - the Allies figured with those kinds of losses, they would soon have no bombers left to bomb Germany). The soviets with their almost unlimited manpower were a different story: as Halder noted in his diary, "...we destroy a dozen Soviet divisions, and they just replace them with another dozen."

Henri



springer -> RE: Empirical tests of combat effects: The mortar (5/25/2011 8:58:47 AM)

I totally agree that it is important to preserve INF. I also agree that good concentric (i.e., multi-hex) attacks at overwhelming odds are the best.

The problem is that INF saving can be very hard especially with low-tech attacks.
I think what the sims consistently show is that pure infantry attacks, even with support weapons are going to cost casualties. (Even the best 3 unit 40/5 attacks with 100% chance of victory cost about 32-35 INF I and 25-28 INF II ( ~28% and ~22% losses, respectively). I think what saves the infantry best is technology: armor, planes and artillery. But what does one do if the hex is a vital one but on terrain that negates technology?

In these low tech situations (e.g., situations when the terrain negates technology) The question becomes one of "how badly do you want that hex?" Is it really worth 49INF loss in a single assault?


You also raise a great issue about casualty rates over time. In terms of losses through consecutive attacks, I think ATG does a good job of giving a sense of historical flavor. For example, in the Sixth Army AAR from a year ago tweber and I discussed how the casualty rates some American divisions suffered nearly 200% casualties from D-day to V-day (tweber cited Ambrose's Citizen Soldiers and I mentioned the charts at the end of Peter Manoor's The GI Offensive in Europe: The Triumph of American Infantry Divisions in Europe.). That's nearly 20% loss of original strength per month. So even units that are treated well can expect to have their strength eroded if they are regularly used.






phatkarp -> RE: Empirical tests of combat effects: The mortar (5/25/2011 4:34:34 PM)

In response to Henri's general 5:1 rule, I would state the (obvious) point that sometime soldiers just have to die for the greater good.  This is especially true in PBEM games, where desperation is the constant companion of a beleaguered army.  More than once I've sent unready, understrength armored divisions to dash themselves on the tip of the enemy spear in hopes of blunting and slowing it. 



henri51 -> RE: Empirical tests of combat effects: The mortar (5/25/2011 7:39:19 PM)


quote:

ORIGINAL: phatkarp

In response to Henri's general 5:1 rule, I would state the (obvious) point that sometime soldiers just have to die for the greater good.  This is especially true in PBEM games, where desperation is the constant companion of a beleaguered army.  More than once I've sent unready, understrength armored divisions to dash themselves on the tip of the enemy spear in hopes of blunting and slowing it. 



I don't disagree that there are cases like that - there are always exceptions. But what I do when I really really want a hex (say an enemy city protected by a big stack) is to hit it with as much artillery and air power as I can spare more than once if necessary, which will usually reduce it to low values. If that doesn't work, one can also surround the hex and starve it (but that is not always possible - for example an enemy port when one does not have a navy to blockade).

I also agree that in real life as well as in the game there will be units that take maybe 200% casualties over the game, and it probably happened in my AAR although I did not take count. But if the US had taken 200% casualties over its whole army, it would have run out of manpower[X(].

Henri



springer -> RE: Empirical tests of combat effects: The mortar (5/25/2011 11:15:25 PM)

Hi Henri,

I suspect I might be wandering far from the topic, but it might be worthwhile to compare ATG results to real-life.
(And you piqued my interest!)

Using the data from Army Battle Casualties and Nonbattle Deaths in World War II. I did a quick bit of calculating to see what the average % casualties were like for US Divisions in the ETO.

For all 42 US Infantry Divisions in the European Theatre of Operations (ETO) the average casualty rate across the entire duration was 64% if one assumes a standard strength of 14,000 (including both combat and support units). Looking at the half of the divisions (21 divisions) that took the most casualties, losses are an average of 102%. (It's certainly not 200%, but it is surprisingly high!)

Of course, many of the casualties were due to non-combat causes. In addition, about 45% eventually returned to duty in the ETO. Still, the total casualties (troops not returning to combat) are about 210,000 soldiers.




CSO_Talorgan -> RE: Empirical tests of combat effects: The mortar (6/13/2011 5:46:33 AM)


quote:

ORIGINAL: springer

AT with MATLAB...


What is "MATLAB"?



henri51 -> RE: Empirical tests of combat effects: The mortar (6/13/2011 2:36:15 PM)


quote:

ORIGINAL: CSO_Talorgan


quote:

ORIGINAL: springer

AT with MATLAB...


What is "MATLAB"?


Matlab is a high-level programming language.

Henri



CSO_Talorgan -> RE: Empirical tests of combat effects: The mortar (6/13/2011 3:00:32 PM)

Why are people enthusiastic about the idea of linking ATG and MATLAB?



springer -> RE: Empirical tests of combat effects: The mortar (6/13/2011 5:43:32 PM)

I think the reference to MATLAB is more of a joke about how one can turn ATG into an exercise in mathematical testing.

MATLAB is used to test various mathematical equations and combinations with many variables.  The Analogy is to these tests, where we look at the interaction of factors in ATG (odds, SFT, terrain, supply, moral) and see how small changes interact just like scientist use MATLAB to see how small variable changes can change the performance of mathematical systems. (Interestingly, though it doesn't look like it at first glance, ATG is a complex mathematical system too.)


As an aside, I think that anyone who can program the editor in ATG could probably do a good job programming in MATLAB as well.  IMHO, they both make similar syntactic demands.



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