Tag Archives: Schwerpunkt

Schwerpunkt: Calculating the Optimal Point of Attack

MATE’s analysis of Blue (Union) position at Antietam. NB: Unable to outflank Red’s position, MATE has calculated the Schwerpunkt, or optimal point of attack on Red’s lines. Click to enlarge.

The holy grail of military science is an algorithm that calculates the optimal point of attack upon an enemy’s lines. In German, the word is Schwerpunkt and is commonly translated as “the point of maximum effort.” I have written extensively about Schwerpunkt previously in this blog, in academic papers and in my doctoral thesis.

MATE (Machine Analysis of Tactical Environments 2.0, the AI behind General Staff: Black Powder) is now able to calculate Schwerpunkt to a new, substantially greater, degree of accuracy. There are a number of reasons why this is now possible, but the primary cause must be the ability to analyze the battlefield in 3D and to accurately map where every unit on the map can project its force. Indeed, for many years now I have looked at the problem of computational military reasoning (AI for tactical situations) as a force projection problem.

Below, is a visual representation of the total force projection of all units at Gettysburg, Day 3 (July 3, 1863 0600 hours):

Visual representation of the total force projection (Range of Influence, or ROI) for all units at Gettysburg Day 3. Note: normalization and alpha values affect color output. Also, note how the terrain (woods, depressions, hills) shape the projection of force. Also, all projections are independent of unit facing. Click to enlarge.

If we ask MATE to determine the Schwerpunkt for the Confederates in the above situation, it responds with:

MATE’s selection (labeled OBJECTIVE) for Red Schwerpunkt. Click to enlarge.

And adds the following commentary (edited for brevity, the numbers are the Premise Statement ID#s. This is basically a logic trace of MATE’s thinking):

8|∴ The enemy does not need to capture more Victory Points.
9|∴ The enemy will be on the defensive.
22|The enemy's flanks are anchored.
23|[9] + [22] ∴ Frontal assault is the only remaining option.
25|COA: Battle Group #1 (Mixed) assigned objective Weak Point Calculated by ROI coords: 551,232
33|Red Battle Group #1 is opposed by Blue Battle Group #6
34|Red Battlegroup # 1's strength = 21,663
35|Blue Battlegroup # 6's strength = 13,635
36|Red Battlegroup # 1 has a numerical advantage of 8,028. Red has a 1.59 / 1 advantage over Blue Battle Group #6.
37|Distance to objective is 1,029.86 meters.
38|The maximum slope along the line of attack will be on an upward slope of 3.64%.
39|The attacking avenue of approach will be in enemy ROI for 541.18 meters.
40|The greatest enemy ROI along the avenue of approach is: 1,276.00 .
41|There is an unrestricted avenue of attack.

In other words, MATE has found a path to its objective that encounters the least amount of enemy projection of force. MATE would much prefer to flank the enemy position but it has calculated that this is impossible (#22, above).

ROI (Range of Influence) is calculated using values set up for each unit in the General Staff Army Editor and running a 3D Bresenham line algorithm to ensure that there is direct Line of Sight (LOS) to that point.

Screen shot of the General Staff Army Editor showing the interface for entering values for a typical artillery unit. Note that the accuracy curve is user editable (there are also default curves for various common weapons). Click to enlarge.

It is because every unit has an accuracy curve attached to it we can exactly map out the overlapping fields of fire (see above) and we can precisely calculate how long each attacking unit will be under fire and its intensity. That is how MATE chooses the optimal attack point: the path where its troops will be under the least amount of fire.

When MATE is presented with a tactical problem it first determines what it needs to do to win; is it on the offense or defense? On the offense, MATE will next check to find the enemy’s open flank and, if there is one, are there any crucial choke points on the flanking route? If MATE is unable to ‘fix and flank’ the enemy, and it has determined that it must be on the offensive, MATE then calculates Schwerpunkt (above). With this new Schwerpunkt algorithm the last big piece of the offensive AI puzzle is in place. Ironically, much of MATE’s defensive calculations involve first figuring out how to attack itself and then countering what it determines are its own optimal moves against itself (see this blog).

As always, please feel free to contact me directly with comments or questions.


I first encountered the German word Schwerpunkt in Major General F. W. von Mellenthin’s Panzer Battles many years ago. The word has a number of definitions but, for our purposes, we’ll use, “the point of maximum effort;” or the point where we should hit the enemy’s lines with all our strength. For von Mellenthin it was the point where his panzers would smash through the Allied lines in the 1940 Western Front blitzkrieg.

Many years later, when I was working on my doctoral research on tactical AI, I realized that calculating the Schwerpunkt was crucial for any offensive algorithm (it’s also a good thing to know your weak points when planning a defense). On every battlefield there is at least one Schwerpunkt but calculating that point first involves numerous algorithms to analyze the terrain, elevation, unit positions, 3D Line of Sight (3DLOS) and range of influence (ROI) of these units.

TIGER1)Tactical Inference GEneratoR was the program created from my doctoral research that performed battlefield analysis. Later, with a DARPA grant, it was expanded into MATE 2)Machine Analysis of Tactical Environments. One problem, that was discussed in my last blog post, was that after analysis MATE would come to the conclusion that some forces should not attack in specific situations (for example, Lee at Gettysburg). However, for General Staff,  we need an AI that will attack when we want it to.

My solution was to create the General Staff AI Editor (this may be rolled into the General Staff Scenario Editor for convenience) which allows the scenario designer to specify objectives for each army’s battle groups.

Screen shot of Antietam with battle groups, range of influence and objectives displayed. Blue indicates areas within Blue forces Range of Influence (ROI); meaning that their weapons can fire on these locations. The darker the color the more firepower they can concentrate at that location. The same is displayed for Red forces. Note that areas under both Red and Blue ROI cancel each other out (based on accuracy and firepower). Click to enlarge.

This output is just for debugging and won’t be displayed during the actual game but you can see how MATE made it’s decision to place the Schwerpunkt for Blue Battle Group #1. MATE starts by making a series of statements. These are  similar to predicates used in predicate logic but every statement is known to be true. MATE then constructs hypothetical syllogisms by combining these statements. In the series, below, MATE identifies the opposing force that must be dealt with to achieve its assigned objective, does strength analysis of the two opposing forces, determines if the defender has anchored or unanchored flanks, calculates the slope of the attack, etc., and then calculates the Schwerpunkt after analyzing the enemy’s flank positions, supporting forces and if the attacker has an unrestricted avenue of attack.

Screen shot of the output from the General Staff AI Editor showing the analysis for Blue Battle Group #1 at Antietam. The top section, “Statements about the tactical situation,” are the results of MATE algorithms that analyze unit positions, strengths, 3D Line of Sight, etc. The bottom section, “Tactical Analysis,” are conclusions drawn from the above statements. Click to enlarge.

The Schwerpunkt for Blue Battle Group #1 is displayed on the map as a blue square.

Screen shot from the General Staff AI Editor showing the location of Blue Battle Group #1s schwerpunkt (marked by a blue square). Click to enlarge.

I have written before 3)https://www.general-staff.com/antietam-ai/ about the American Civil War battle of Antietam and I frequently use it as a ‘baseline’ for my AI work. This is because I am very familiar with the battlefield having walked it numerous times, as well as having studied it in depth. So, I know the area that MATE has indicated where Blue Battle Group #1 (Union I and XII corps) should concentrate their attack: west of the West Woods at J. R. Jones’ Confederate Division’s exposed left flank.

The original caption, “Photograph shows four Union soldiers looking at dead Confederate soldiers on Miller Farm, looking toward the west woods on September 19, 1862.” From the US Library of Congress. Click to enlarge.

Many years ago I had an accountant who would apply what he called, ‘the Reasonable Test’, to Profit & Loss statements. He would look at the P&L statement and ask out loud, “does this look reasonable?” Is this a reasonable number for income? Is this a reasonable number of expenses? So, I ask, “is this a reasonable place for the Union I Corps to attack at Antietam?” And, I have to conclude, yes, it is. I can’t mathematically prove that this is the best place to attack; but I think it’s pretty good. In general, MATE will always attempt to outflank enemy positions and, I think, this is a very solid approach to offensive tactics. Indeed, I’m reminded of Wellington’s comments about Napoleon’s tactics at Waterloo, “Never did I see such a pounding match. Both were what the boxers call gluttons. Napoleon did not manoeuvre at all. He just moved forward in the old style, in columns, and was driven off in the old style.” 4)“Wellington: The Years of the Sword,” p, 488 Longford, Elizabeth For MATE, pounding is a last resort. This is the case at Burnside’s Bridge:

MATE analysis for Blue Battle Group #4 (Union IX Corps) at Antietam. Note that MATE recognizes the choke point (Burnside’s Bridge) and orders up an artillery barrage before the assault. Click to enlarge.

In the Tactical Analysis section (above) look at statement #8: “Blue Battle Group #4 has a severely restricted Avenue of Attack (Bridge).” MATE recognizes that there is no way to maneuver around to the objective (Snavely’s Ford is not on this battle map so there really isn’t any other option except over the bridge). Frontal Assault is MATE’s maneuver of last resort. Consequently, MATE first orders up the artillery to positions within distance (> 50% accuracy as set in the General Staff Army Editor for these units) and with a clear Line of Sight (3DLOS) of the target. MATE will order the artillery to bombard enemy forces that control the bridge for an hour before ordering an infantry assault).

Let’s look at MATE’s analysis of First Bull Run:

Screen shot from the General Staff AI Editor showing objective set for Union forces at the battle of First Bull Run. The Union Schwerpunkt is the blue square to the west of the Confederate left flank. Click to enlarge.

Here Blue Battle Group #2 (Heeintzelman’s and Hunter’s Union divisions) are assigned the objective of capturing the Henry House Hill (historically accurate). MATE set’s their Schwerpunkt to the west of the Confederate left flank. This is very close to Union commander McDowell’s original strategy. Again, MATE will attempt to outflank strong positions rather than attack them directly. MATE is not a pounder.

MATE’s analysis for the Union’s right flank: they have an unrestricted Avenue of Attack and Red’s left flank is unanchored. Click to enlarge.

MATE recognizes that the Confederate’s left flank is unanchored and is a perfect target for an envelopment maneuver and places the Schwerpunkt at the end of Red’s line appropriately.

I still have work to do on MATE’s ability to construct defensive lines and that will be the next thing to add to the AI. But, as you can see, great progress has been made. I believe that the MATE tactical AI is unique and I know that there is nothing similar even among the wargames used by US and NATO allies. As always, please feel free to contact me directly if you have any questions or comments.


1 Tactical Inference GEneratoR
2 Machine Analysis of Tactical Environments
3 https://www.general-staff.com/antietam-ai/
4 “Wellington: The Years of the Sword,” p, 488 Longford, Elizabeth