Shannon V. OKeets
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Joined: 5/19/2005
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Here are some excepts from the current AIO design document about the value of hexes. Because they are pretty obvious in Russia, I have omitted related sections about which types of units to produce and how to deploy them into the frontlines. Also missing is my preliminary analysis about cutting supply lines, since that is not in a coherent form yet. Note this is all a work in progress and comments, suggestions, and criticisms are always read seriously.
P.S. I know this is long but in my opinion, handling the tactics of land combat is the most essential element of getting the AIO to play well.
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2.9 Hexes
The ultimate goal is to be able to evaluate the risk of losing units in combat versus the gain of capturing hexes close to enemy capitals, resources and factories. There has to be very strong motivation in terms of combat values (CVs) for the AIO, playing Germany, to drive on Paris and Moscow and to contemplate invading Britain. Victory cities only play a role in the Grand Strategist decision making.
All of this leads to the value of land hexes. Now in and of themselves, hexes usually have no value. The exceptions are some specific hexes (capitals, resources, factories, rail lines, and victory hexes) and to that list we can add sources of supply when supply is hard to come by. But even the most mundane of hexes can rise in importance when the battle lines draw near. It is as part of a front line that hexes achieve their primary importance. Looking at Germany versus France in 1940, Germany versus the USSR in 1941, and China versus Japan in any year, the outstanding characteristic of the land combat is where the front lines are. What exactly is the value of a hex in the front line?
When on defense, we can count hexes defended by rivers as worth double “the average CV for the front line” since they effectively double defensive strength. We can count forest hexes as half the enemy’s average tactical air CV since they cut ground strikes and ground support in half. We give cities a bonus for forcing the enemy to use the assault table. We penalize clear hexes if the enemy has armor capable of overrunning our weaker units. And there are similar adjustments for other types of hex and hexside terrain. But when on the attack, all of these change in importance. It is better to attack weak hexes and force the enemy to abandon strong ones because of the threat to his lines of communications.
For both attackers and defenders, maintaining a continuous line is very important. Only under unusual circumstances can the goal of maintaining a continuous line be put aside.
8.25 Estimate land combat odds and losses
Weather, action choice/activity limits, and initiative affect likely CV losses. Those calculations can be done under the various conditions and probable losses (weighted by the probabilities for the weather et al) figured out. There are two ways to go here: (1) take the straight probable losses, or (2) take the minimal losses under the worse conditions.
8.26 Choose attack hexes - normal; s.11.16 (4)
Primary tactical stance
The FM receives information from the JCS which includes whether he should be on the offensive or defensive against the countries opposing him.
Front lines
Assuming that the primary tactical stance is offensive, the FM determines where his front line is (front lines are) for each enemy country. For example, at the start of the Global War scenario, Germany has one front line facing France and Great Britain and a second facing Poland. Against France and England, Germany is strongly defensive and against Poland, going in for the kill. Note that the front line includes coastal hexes that can be invaded and hexes behind the front line proper that can be attacked using paradrop and glider units.
Attacking units
Focusing on a single front line, the FM determines the land units he has available with which to attack. That is, the units are face up, in supply, and can reach an enemy zone of control this impulse. Sorting these units by combat strength and separating the corps from the divisions, he creates hypothetical stacks of 3 units per hex, again arranged from the best through to the worst. This is just a first pass for estimation purposes, since the units may or may not be able to actually form up in those groups because of their positions in the line. What he now knows is the highest number of combat factors that he can bring to bear on 1, 2, 3, or more hexes.
Defending units
Switching over to the enemy front line, he examines each hex that is in the ZOC of an enemy unit and sees if he can move units into it. Since being able to move into an enemy unit’s ZOC means you can attack the enemy unit, this determines which enemy hexes he can attack. Paradrops and invasions are slightly different, but a comparable procedure is used. For each attackable enemy hex, he calculates the defensive strength of the hex. As part of this calculation, he includes in the defensive strength the number of shifts (because enemy units are disrupted or there are forts present), the number of units in the hex, and the hex’s susceptibility to the use of any special units the FM has available. For instance, whether using armor or an engineer might have an effect.. Lastly, this calculation looks at the effect of terrain on the combat (e.g., assault table mandated) and counts the number of hexes from which the FM can attack this impulse (an attack across a river would count as half a hex).
Weak and strong points
For each hex that might be attacked, the FM makes a crude estimate of the odds he can achieve if the best possible units were to reach ideal positions for the attack. These estimates let the FM rank the hexes according to their vulnerability. Basically, the enemy weak points and strong points have been determined.
Disruption status
One of the subgoals of the FM during a turn is to turn all of the enemy units face down. Though this achieves only a temporal advantage, it can be decisive during long summer turns. The following items relate directly towards achieving that subgoal.
At the beginning of each impulse, the FM makes assessment A1 for each of his frontlines and records for each side the number of: (1) face up/down corps, (2) face up/down divisions, (3) face up/down tactical bombers, (4) face up/down strategic bombers (re: carpet bombing), (5) face up/down fighters, (6) face up/down ATRs, (7) units capable of immediate paradrops, (8) units capable of immediate invasions, and (9) offensive chits available. In addition, the FM identifies which units are out of supply, and the supply lines for units that are in supply. Other needed information is the likely number of impulses remaining i the turn, likely weather for the rest of the turn, and reinforcements available to both sides.
Tactical mode
What the FM needs to determine is which of 4 modes of attack to use: (1) destroy enemy units this impulse, (2) disrupt enemy units this impulse so they can be destroyed in a later impulse (or turn), (3) maneuver so better attacks can be made in the future, or (4) push the enemy back. Maneuvering can change supply status for friendly and enemy units, increase the number of hexes from which to attack an enemy hex, and improve the selection of hexes from which to attack. In situations where the enemy has the ability to counterattack, maneuvering can improve the FM’s resulting defensive line at the end of his impulse.
The calculations of estimated results provide the expected changes (for both sides) to the front line. This includes kills and disruptions. In addition to disruptions, units can also become face down because they were committed during the impulse (e.g., air units). And face down units might be reorganized. When the impulse is over, the FM makes a new assessment, A2, for each front line., and compares it to A1.
By extrapolating the change from A1 to A2 over the remaining impulses in the turn, the FM judges whether disruption is a viable tactic for the current turn. It works if the enemy units are mostly face down with no reorganization capability left while the FM still has a viable attacking force face up.
Direct attacks to kill enemy units is usually the best tactic but it might cause too many friendly casualties or disruptions. Or, if the FM limits attacks to only those with excellent odds, it might be too slow. Yet again, maneuvering is rarely fast and there might not be enough impulses in the turn to use the disruption tactic. The FM must be willing to accept that none of the modes will work as well as he would like and simply go with half measures, or no attacks at all.
4.3.8 Field Marshals
Based on the assessments and estimates of land units only, decide on your situation: (1) desperate defense, (2) strongly defensive, (3) somewhat defensive, (4) balanced, (5) somewhat aggressive, (6) attacking, or (7) going in for the kill. To some degree the 1st and 7th will depend on the proximity of objective hexes to the front line.
I will ignore paradrops and invasions for the moment. They need to be analyzed separately and from two perspectives: (1) opportunities to attack and (2) need to defend against possible attacks. For now, I will assume that the only units involved in an offensive are coming by land.
The value of a hex, and of a front line in general, depends on the tactical balance in the theater of operations. This is true both for attacking and defending.
...
1. Hexes that have direct value in CVs define what we are trying to defend (or capture from the German point of view).
2. The relative strength of land forces in the theater of operations tells us whether we are attacking or defending.
3. When defending we look for other units that might come to our aid, be they our own units from other theaters or from our allies. Actually, we might look for other units to help even when on the attack.
4. We calculate the length of the frontline we need to hold, and the average number and defensive strength of units we can put in each hex.
5. We decide whether to hold every hex, every other hex, or every third hex depending on the strength we can muster per hex for each possibility.
6. We worry about overruns.
7. We choose hexes with good defensive terrain.
8. We try different placements protecting the more valuable hexes first.
9. We perform post evaluations of placements critically, looking for weaknesses that the attacker might exploit.
10. We reduce the number of valuable hexes we are trying to defend if the post evaluations find too much fault with the placements.
...
Here is how I think the AIO should analyze the position for France in 1940.
(1) France is in a Somewhat Defensive position numerically. It would be worse except that the front line is short and every hex is behind the Maginot line. France can get about 14 strength points in each hex, which are tripled behind the fortified line to 42 points per hex. The weakest part of the line is Strasbourg because it can be attacked from 4 hexes but the Germans probably can’t get more that 18 points per hex which only gives them odds of 2:1 on the assault table at the very best. That assumes that air units are contributing a lot to the attack odds. The French units might be disrupted, but still, with extra units in the rear to replace lost units and participate in counter attacks, the French defensive line looks very solid.
(2) The major risk is having to defend the borders with the neutrals to both the left and right of the Maginot line.
(3) Switzerland looks like a tough nut to crack. It only has 2 hexes on the German border, both are mountainous, and the Swiss have 6 corps with which to defend (average strength of 4.5). Even if Italy gets involved, the Swiss only have to add one hex to their defensive line. The Swiss defensive strength is 10 per hex doubled for mountain, with the mountain unit tripled. That comes out to about 22 strength points per hex. The Germans are only attacking from 3 hexes at best, for 2:1 odds. It looks very similar to the Maginot line. In a worse case scenario, Germany would get an open hexside on the end of the Maginot line which isn’t very much gain for a lot potential casualties.
(4) Belgium is vastly weaker. Their 4 corps average 3.5 strength points each and they have 4 border hexes to defend against a German invasion. Two of those hexes are clear and susceptible to being overrun. With one unit in each frontline hex, the Belgian defensive strength is only 3.5 per hex and the Germans can get excellent odds against any hex they choose. The German air force can really help out here because the French and British can’t assist Belgium during the impulse that war is declared and the German Stukas can increase the odds with a couple of shifts all by themselves. Even more distressing is that once Belgium falls, the French frontline becomes extended by 6 hexes, 5 of which are clear hexes with virtually no good defensive terrain between Belgium and Paris.
(5) Therefore, France should ignore its border with Switzerland and set up units to defend against a German declaration of war on Belgium. That means France needs to defend 10 hexes of frontline from Calais to the border with Switzerland.
(6) The British can help out here by defending Calais and maybe even Lille if they are being generous with land units in continental Europe. That leaves 8 hexes for France to defend. 1231 and 1232 are the weak points because both of them are clear terrain and the Germans can attack from two hexes. France is hard pressed to get two units in every hex with divisional units on top to take losses. Even optimistically, they can only expect to get 12 strength points per hex.
(7) Given that Germany will be able to put 18 points per hex, that gives them 3:1 odds on the Blitzkrieg table. Since there is clear terrain in almost all the hexes behind the frontline, advance after combat looks like a serious threat.
(8) As soon as Germany declares war on Belgium, France goes over to a Strongly Defensive posture. Once Germany gets within 2 hexes of Paris, France goes to Desperate Defense.
(9) If possible, France should move into Belgium because that shortens the frontline by a hex. In general, France should press their frontline right up against the Germans because that increases the number of hexes between the Germans and almost all the valuable hexes France is trying to defend.
(10) We are getting closer to where the value of hexes comes into play. Let’s start by examining the 2 die 10 land combat table. The important numbers here are expected attacker losses, expected extra attacker losses due to terrain or weather, expected defender losses (excluding shattered units), and the probabilities that the defensive hex will be left empty if it holds 1, 2, or 3 units.
Odds A losses A+ losses D losses Empty 1 Empty 2 Empty 3
1:2 Assault 1.32 .38 .31 25% 3% 1%
2:1 Assault .93 .40 .81 67% 21% 15%
5:1 Assault .42 .25 1.59 97% 72% 64%
Increasing the odds from 1:2 to 2:1 reduces the attacker losses by .39 and increases the defender losses by .50. The chances of taking out a 3 hex stack so the attacker can advance into an empty hex increases by 14%. Similar calculations can be done for other changes in the odds on the assault and blitzkrieg tables.
(11) In combination with the CV of individual units, we can now calculate the expected CV loss of a hex at various odds levels, for both the attacker and the defender. Putting in our knowledge of the terrain, we can see the effect terrain has on expected CV losses inflicted and received. We can also compare the Assault table to the Blitzkrieg table for expected losses and probability of having the defended hex vacated.
(12) All together, we now can compared the defensive value of 1132 (a clear hex) with 1131 (a woods hex half defended by a river). Eh, viola! We have a relative value for a hex in the frontline measured in terms of expected CV losses.
(13) We can examine each hex in the front line, assuming the attacker focuses maximum pressure on it, to determine expected CV losses. When we have done them all, we can then assign a value to each hex in either absolute CVs or as a ratio when compared to the best defensive hex in the line. Let’s go with the absolute value by simply subtracting the change in attacker CV losses from those of the defender. One of the CV loss values will be negative so you can think about this number as the net change to the two engaged armies. To summarize, hex 1131 is X number of CVs better than 1132. Alternatively, we could do this as a ratio and say that hex 1132 has only Y% of the defensive value of 1131. This loses the CV measure but it provides a direct measure of the relative worth of the hexes.
(14) One of the neat applications of this analysis is measuring the value of a hex adjacent to an intrinsically valuable hex. For example, going back to Poland, we can measure the improved odds Germany achieves by having an extra hex from which to attack Warsaw. That gives us the change in expected CVs and the value of the additional adjacent hex. In this discussion about France in 1940, we can apply it to evaluating the advantage of getting an extra hex from which to attack Lille or even the resource hexes 1232 and 1030. The value of hexes adjacent to valuable hexes can now be calculated in CVs.
(15) Indeed, if we have to give up one of two hexes, both of which are adjacent to a valuable hex, then we could use the ratio measure to determine which is better/easier to hold.
(16) A frontline is only as good as its weakest hex. Therefore we can use the hex CV measure to try out different placements of units to maximize the strength of the weakest hex.
(17) We can also examine different possible frontlines and perform the same assessment. This will let us decide whether to pull out of Belgium (1234 and 1233) if we lose 1232 and defend in France proper instead. The advantage is going to be that Lille is a city so the assault table has to be used. Both Lille and Calais are attackable from fewer hexes (3 to 2 and 2 to 1) than the hexes in Belgium. It should also let us measure the benefit of a shorter frontline since the average strength point per hex is likely to increase.
(18) However, pulling back means we are letting the Germans get closer to valuable hexes, Paris in particular.
(19) Time is another factor that needs to be considered when choosing a defensive line. If we can cause the attacking units to be disrupted, or at least increase the probability that they will, then that reduces the number of units the attacker can use to attack in the next impulse. Of course we should always be measuring the enemy’s ability to reorganize units with the goal of reducing that number to zero by either using ground strikes, keeping fighters available to intercept ATRs, or disrupting so many enemy units that the opponent depletes his reorganization capability.
(20) While on the subject of time, we should look ahead 2 or 3 turns to predict what the future has in store in the way of reinforcements for both sides. This is perhaps most crucial as we approach the end of a turn. Typically by then, during a major offensive, many units will be disrupted and the enemy’s ability to attack severely impaired. Most of his air units will have flown missions too, so he is unlikely to be able to put together more than one solid attack per impulse. Our evaluation of the defensive prowess of our frontline might be overly optimistic. We evaluate how feeble our opponent is with all those disrupted units and think about resting on our laurels. That is very dangerous, for if the opponent ends the turn (has the last impulse in the turn) and then gets the initiative for the next turn, we can be looking at all face up enemy units with his full complement of air units while our reinforcements have yet to arrive and our frontline irregularly formed after the opponent’s last attack. This possibility has to be considered very seriously and contingency plans made. It only takes one bad turn to transform a good defense position into a lost cause.
(21) It should be fairly easy to calculate how many attacks the enemy can make in the next impulse. There might be several numbers, such as 2 at very good odds, plus 1 at ok odds, plus 1 other at poor odds. From the defensive point of view we want to know probable CV losses for each side, the probable number of disrupted units for each side, likely defensive hexes left vacate, likely advance after combat hexes (including blitzkrieg advances), and likely retreats. We would do this for 2, 3, and 4 attacks (using the immediately previous hypothetical).
(22) Post analysis (look ahead) after pessimistic, likely, and optimistic results should be done. That lets us evaluate how bad things might be when we next get to move. Here is where we should worry about the turn ending and the opponent gaining the initiative for the next turn - and having to face the dreaded two impulses in a row.
(23) Comparative post analysis of different frontlines would let us choose between them. What we want to take into consideration is the attrition that inevitably occurs during combat. If we start out at a slight numerical disadvantage and equal casualties/disruptions are taken for a serious of impulses, the opponent usually ends up with units left to move while we have none. How many impulses remain in the turn becomes a crucial question. How many reinforcements both sides are going to receive also becomes crucial information for making good decisions.
(24) It would be nice to continue doing look ahead for several turns but that is a red herring. The probabilistic outcomes make looking ahead more than 1 impulse silly. We should rely on first principles of what constitutes a good defensive line instead. The incremental gain in information versus the cost in CPU time (and programming time) makes looking ahead more than 1 impulse not worth the effort. What we might do as a half measure is extrapolate from the previous impulse through to the expected end of turn. For example, we might have lost one hex of the frontline (Germans occupy what had previously been held by French units) and had so many casualties and disruptions on each side. If that continues for 3 more enemy impulses, then we will be back an entire hex row (closer to Paris).
(25) Looking back at the Poland example, we could expect to lose so many units/hexes during the first German impulse. A post analysis after pessimistic, likely, and optimistic results will let us predict if the second impulse will be about the same, better, or worse. Figuring out how long it will be until Warsaw falls should be doable. Applying a similar analytical process to the French frontline, the eventual fall of Paris can be crudely estimated.
_____________________________
Steve
Perfection is an elusive goal.
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