Clausewitz on odds

[JasonC]

I was reading this today and thought others here might find it somewhat interesting. I consider it sound. I note that considerably departures from it occurred in WW II eastern front German thinking and planning. Consider this an elucidation of past threads about Russian views on the importance of odds and attrition, vs. too great a faith in the effect of maneuver factors.

Note that he clearly conceives lopsided quality cases ("Marathon") and scans for them, and reasons from their empirical absence. The rest is von C -

If we strip the combat of all modifications which it may undergo according to its immediate purpose and the circumstances from which it proceeds, lastly if we set aside the valour of the troops, because that is a given quantity, then there remains only the bare conception of the combat, that is a combat without form, in which we distinguish nothing but the number of the combatants.

This number will therefore determine victory. Now from the number of things above deducted to get to this point, it is shown that the superiority in numbers in a battle is only one of the factors employed to produce victory; that therefore so far from having with the superiority in number obtained all, or even only the principal thing, we have perhaps got very little by it, according as the other circumstances which co-operate happen to be so, or so.

But this superiority has degrees, it it may be imagined, twofold, threefold or four times as many, etc., etc., and every one sees, that by increasing in this way, it must (at last) overpower everything else.

In such an aspect we grant, that the superiority in numbers is the most important factor in the result of a combat, only it must be sufficiently great to be a counterpoise to all the other co-operating circumstances. The direct result of this is, that the greatest possible number of troops should be brought into action at the decisive point.

Whether the troops thus brought are sufficient or not, we have then done in this respect all that our means allowed. This is the first principle in strategy, therefore in general as now stated, it is just as well suited for Greeks and Persians, or for Englishmen and Mahrattas, as for French and Germans. But we shall take a glance at our relations in Europe, as respects war, in order to arrive at some more definite idea on this subject.

Here we find armies much more like one another in equipment, organisation, and practical skill of every kind. There only remains still alternately a difference in the military virtue of armies, and in the talent of generals. If we go through the military history of modern Europe, we find no example of a Marathon.

Frederick the Great beat 80,000 Austrians at Leuthen with about 30,000 men, and at Rosbach with 25,000 some 50,000 allies; these are however the only instances of victories gained against an enemy double, or more than double in numbers. Charles XII., in the battle of Narva, we cannot well quote, the Russians were at that time hardly to be regarded as Europeans, also the principal circumstances even of the battle, are but too little known. Buonaparte had at Dresden 120,000 against 220,000, therefore not the double. At Collin, Frederick the Great did not succeed, with 30,000 against 50,000 Austrians, neither Buonaparte in the desperate battle of Leipsic, where he was 160,000 strong, against 280,000, the superiority therefore considerably less than double.

From this we may infer, that it is very difficult in the present state of Europe, for the most talented general to gain a victory over an enemy double his strength. Now if we see double numbers, such a weight in the scale against the greatest generals, we may be sure, that in ordinary cases, in small as well as great combats, an important superiority of numbers, but which need not be over two to one, will be sufficient to ensure the victory, however disadvantageous other circumstances may be. Certainly, we may imagine a defile which even tenfold would not suffice to force, but in such a case it can be no question of a battle at all.

We think therefore, that exactly in our relations, as well as in all similar ones, the superiority at the decisive point is a matter of capital importance, and that this subject, in the generality of cases, is decidedly the most important of all. The strength at the decisive point depends on the absolute strength of the army, and on skill in making use of it.

The first rule is therefore to enter the field with an army as strong as possible. This sounds very like a common place, but still is really not so.

In order to show that for a long time the strength of forces was by no means regarded as a chief point, we need only observe, that in most, and even in the most detailed histories of the wars, in the eighteenth century, the strength of the armies is either not given at all, or only incidentally, and in no case is any special value laid upon it. Tempelhof in his history of the Seven Years' War is the earliest writer who gives it regularly, but at the same time he does it only very superficially.

Even Massenbach, in his manifold critical observations on the Prussian campaigns of 1793-94 in the Vosges, talks a great deal about hills and valleys, roads and footpaths, but does not say a syllable about mutual strength.

Another proof lies in a wonderful notion which haunted the heads of many critical historians, according to which there was a certain size of an army which was the best, a normal strength, beyond which the forces in excess were burdensome rather then serviceable.

Lastly, there are a number of instances to be found, in which all the available forces were not really brought into the battle, or into the war, because the superiority of numbers was not considered to have that importance which in the nature of things belongs to it.

[Philippe]

Marathon is a funny battle. I don't pretend to know what really happened there, but there are a couple of things to keep in mind about it that probably have a bearing on the "lopsided quality" issue.

Because they lived in small city states, most ancient Greeks knew how large each national army was, and what proportion of their 'national guard' had been sent to fight in a given battle. Add to that the fact that most Greek city-states used pretty much the same tactics and formations, and you can be pretty sure that if an experienced Athenian was present at a battle between Athenians and Boeotians, his estimate for the number of troops involved on both sides was probably pretty good. He would know what his side showed up with, and he could tell at a glance if the enemy line overlapped his, and/or if they had more men than that length of battle line would suggest because of how they were deployed (looser or deeper).

And I'm not even going anywhere near the problems that ancients had with large numbers, or the hash that manuscript transmission makes out of such things.

The problem comes when a Greek has to fight someone who doesn't use Greek tactics and formations. I've got x number of men, shoulder to shoulder with locked shields, eight deep, and my formation fills most of the plain from the foothills to the seashore. Not sure what he's got, but he overlaps me on both flanks and it looks like his army is three or four times as deep as mine. Guess he probably outnumbers me two or three to one.

Guess again.

Phalanxes fought in tightly packed shoulder-to-should formations, but the Persians used something much looser. The result was that a Persian formation would tend to give way on impact, not because of any difference in valor or moral superiority, but because of the dynamics of a concentration crashing into a more dispersed formation.

I'm sure the first few times the Athenians fought the Persians they were uncertain about the numbers they were facing because they were unfamiliar with their opponents' formations (not totally clueless, though, because the Ionians had been having military contact for several years). So the bottom line is that it is not entirely impossible that the numbers on the two sides were roughly equal, or that, perhaps, the Persian landing party was actually outnumbered even though it had a bigger footprint.

Any way you cut it, it was a lopsided battle. The fact that the Persians gave the Athenians as much trouble as they did is a testimony to their fighting prowess, not to any supposed superiority in numbers.

[Guest Mike]

vC's analysis based on numbers is, of course, dependant upon what he know of numbers ar the time.

for Marathon he was relying upon Herodotus and other ancient authors mostly sourcing information from Herodotus.

Much depends upon the size of the Persian fleet, and how many were transports carrying perhaps 300 men, and how many were trireme warships carrying about 200, and how many of those would actually fight on land. Trireme crews would include about 170 rowers who would usually be minimally equipped for land battle, so only 30 "real" soldiers. Transport crews would be much smaller, and hte majority of people on board would be soldiers. Transports were also required to carry horses for cavalry - typically 15-20 I believe.

so Herodotus's 600 triremes would only carry some 18,000 fuly-armed fighting men maximum, and no cavalry.

Greek hoplites did not fight shoulder to shoulder tho - they fought chest to back - turned more-or-less side on to the enemy with their shields resting on their leading shoulder - you cannot rest the hoplon on your shoulder if facing the enemy!

[Sgt Joch]

Common sense tells us that between armies of equal quality in terms of leadership, officers/NCO's effectiveness, weapons, in theory the larger army should prevail.

In the history of modern warfare over the past 150 years, however, there have been many instances when armies which were numerically inferior and even had inferior weapons consistently beat larger foes, for example:

1-Lee's Army of Northern Virginia vs. the Army of the Potomac, 1862-64;

2-Rommel's Afrika Korps vs. British Eighth Army, 1941-42;

3-German Army vs. Soviet Army, 1941-42;

4-Ridgway's Eighth Army vs. Chinese Army, 1951;

5-IDF vs. Egypt, Jordan, Syria, 1967;

6-IDF vs. Egypt, Syria, 1973;

Therefore, I would venture to say that the quality of the leadership of an army at all levels from the NCOs up to the commanding general is a better indicator of success than the quantity of bodies.

[JasonC]

1-3 all lost to attrition processes eventually, and any skill edge just postponed the result.

4 was a draw, and largely driven by a far more capital intensive army holding off a more numerous but far less equipped one. Yes Ridgeway was good, far better than Mac, who was losing due to odds alone. But Ridgeway didn't hold because he was studly, but because he had 2000 combat aircraft including heavy bombers, 5 times the artillery park, and more like 20 times the tank fleet and logistic thruput.

5-6 were maneuverist wins, no question. They resulted from air and armor superiority in desert fighting, with yes a large edge in skill and doctrine. But they are clearly exceptional, not the rule.

[undead reindeer cavalry]

Originally posted by JasonC:

Now if we see double numbers, such a weight in the scale against the greatest generals, we may be sure, that in ordinary cases, in small as well as great combats, an important superiority of numbers, but which need not be over two to one, will be sufficient to ensure the victory, however disadvantageous other circumstances may be. Certainly, we may imagine a defile which even tenfold would not suffice to force, but in such a case it can be no question of a battle at all.

i don't know if the cause was the change in equipment at all levels and thus change in the nature of warfare, or horibbly incompetent warmaking, but WW2 saw a great number of battles where odds well above 2:1 did not ensure victory.

Heinrici considered that against a good defender the attacker would need at least 6:1 odds.

[JasonC]

URD - largely a scale issue. 2 to 1 odds on a strategic scale were perfectly sufficient to exceed 6 to 1 on choosen attack sectors. Proper application of an odds edge does involve some skill certainly. But the Russians were able to defeat the Germans consistently with overall theater odds around 3 to 1, usually won tactically with that much, and the western allies never lost when full sector odds exceeded 2 to 1. The ratio may have been nearly equality in the later Napoleonic period due to the evenness of tactics, sure.

My main point in quoting von C on the subject, though, is his logic, not the 2 times figure he arrived at considering wars of his time. At some point odds will outweigh everything else, the effects of the other aspects he allows for are bounded. That is all the logic of strategic attrition needs to "go through".

He clearly shows the same reasoning in his discussion of battle and its goals, and his insistence that destruction of the enemy armed force outweighs ancilliary issues. He considers the effects of momentary dislocation quite clearly and regards them as ephemeral, and the whole point of e.g. envelopment is to cash the momentary fall in morale and cohesion of a successful battle, for a hard, lasting edge in destroyed enemy forces.

I am substantiating that von C and the German tradition handed on from Napoleonic times was focused on annihilation battle with a strategic attrition wrapper, with odds vital. The later idea that maneuver factors outweigh all others and render odds superfluous, was considered and weighed by the founders of that tradition and rejected as unsound.

Yes one can find lots of other stuff in von C on the overwhelming importance of energy in commanders and the like, but he never let it blind him to the brute power of odds. He notes that Napoleon's skill usually manifested itself in a superior force being present for a major battle, and when he did not have that he usually lost (with Dresden the sole exception - of course Davout did it too, twice).

I also wanted to show he understood that this principle was flat missed by earlier traditions (his comments on military history before his time, which thought there was an optimum size due to march issues and sustainable expense etc), and that it is quite possible to simply fail at it through lack of appreciation of its importance. Which of course is key to my own diagnosis of Germany in Russia in the first 18 months

[Sgt Joch]

Originally posted by JasonC:

1-3 all lost to attrition processes eventually, and any skill edge just postponed the result.

4 was a draw, and largely driven by a far more capital intensive army holding off a more numerous but far less equipped one. Yes Ridgeway was good, far better than Mac, who was losing due to odds alone. But Ridgeway didn't hold because he was studly, but because he had 2000 combat aircraft including heavy bombers, 5 times the artillery park, and more like 20 times the tank fleet and logistic thruput.

5-6 were maneuverist wins, no question. They resulted from air and armor superiority in desert fighting, with yes a large edge in skill and doctrine. But they are clearly exceptional, not the rule.

If you look at 1,2 and 3, the turning point came about when the opponent's leadership/army was improved, for example Grant or Montgomery taking over in 1864 and 1942 respectively.

for example, the overall odds in men and weapons between AK and 8th Army did not change that much between may and october of 1942. In both cases Rommel was outnumbered, yet in May, he routs the British and in October he is beaten, numbers alone do not explain the different result.

The eastern front is another example, in both 1941 and 1943, the German army had less men/weapons than the Soviets and the overall odds were not that different, yet in '41 they consistently won driving up to the gates of moscow while in '43, they were consistently driven back (despite having cooler tanks). What explains the diference other than the improvement in the leadership of the Soviet Army.

[JasonC]

On 1, Lee lost to Meade, who was a mediocre general. Yes it took Grant to finish him, but the war was lost in the west long before anyway.

On 2, yes odds mattered at El Alamein, not mere leadership. DAK simply could not be supplied sufficiently at that distance, and the tank fleet dwindled to less than half the Brit figure. The Brits also had over a hundred Shermans that outclassed the Axis fleet, hopelessly. Their edge in artillery and ammo was largely still. Also, Montgomery was a mediocre commander who stuffed up numerous subsequent battles.

On 3, the Russians went from an unprepared mech arm that evaporated on contact, to a tank fleet a third the original size in front of Moscow. Armor strength down dramatically. In the course of 1942, higher production not only replaced lower losses but built a fleet of 20,000 AFVs, with 40% of them heavy modern types. That is the period in which the Russians got their lead in armor odds, which they never lost.

What explains it is that the Russians were adding forces flat-out while the Germans were simply not doing so. Germany had as high an AFV production potential as Russia, as is proven by their actual production achievement in 1944. But they did not turn it on until years after the Russians did. As a result, the Russians got a much higher integral of tanks produced, out of the same peak rate.

Were the Russians also learning operationally? Sure. The Germans were also getting radically stupider. German strategic direction from the fall of 1942 on is clearly inferior to Russian. It is not surprising there was a change, as the Germans sacked most of the men responsible for earlier victories.

But the reason for those cashierings, dumb as they were, was the failure of the Russians to fold under the earlier blows. Which was a direct function of a higher replacement rate from the same industrial base - and a far higher than 2 to 1 manpower stream from twice the manpower base (if that, after losing the Ukraine to occupation and considering Axis minors etc).

Why was the Russian reinforcement rate so much higher than the German, to the point where the Russians built relative strength while the Germans were inflicting more losses than they took themselves? Simple, because the German replacement rate was practically in the "off" position. The Germans barely matched their own losses in their period of victory, because they discounted the importance of odds, and gambled on rapid victory.

They did not pull out the stops on industrial mobilization until after Stalingrad, and they didn't pull out the manpower stops until the collapses of 1944. Doing so let them hold after losing White Russia and France and 2 army groups in as many months, and reveals the depth of manpower still untapped earlier.

In other words, at the strategic level the Russians correctly appreciated the importance of odds and consider the whole affair a total war to be decided by attrition processes, and the Germans gambled that they could avoid that doctrinaire Clausewitzean truth. Well, they could not.

[Sgt Joch]

We may be talking apples and oranges, certainly in an attrition/total war scenario, overall numbers matter since if you throw enough stuff at the other side, you should eventually win, but how many of those have there been, U.S. civil war, WW1, WW2?

On an operational/tactical level, however, there have been numerous examples from Thermopylae to the Yom Kippur war when a smaller, less well equipped but better led force has beaten a bigger, well equipped but poorly led force, so you cannot say it is all a numbers game and leadership does not matter.

[bitchen frizzy]

Did you mean Marathon?

[Sgt Joch]

Originally posted by bitchen frizzy:

Did you mean Marathon?

Actually I meant Thermopylae since I recently saw "300" for the 1st time, but come to think of it the Persians won in the end, so Marathon is a better example.

[Philippe]

Please note that the Spartans lost the battle of Thermopylae, and, as a result, the Persians were able to burn the Acropolis of Athens, pretty much at their leisure. Greek hoplite armies were good at doing one thing only -- moving directly towards the enemy in a straight line that tended to drift to the left. Persian armies were good at maneuvering and making outflanking marches in the mountains, which is how they defeated the Spartans at Thermopylae.

It should also be noted that you can't, in fact, pile on as many troops as you want in unlimited numbers -- sooner or later disease and starvation will lay you low if your army is too big. Herodotus' figures for the size of the Persian army that invaded Greece are impossibly unrealistic (the tail end of the army would probably have still been crossing the Hellespont during the battle of Thermopylae), but he also notes that Xerxes took much (most?) of his land forces with him when he left Mardonius camped out in Boeotia. The reason usually mentioned is the difficulty of keeping a larger army supplied after losing the naval battle at Salamis.

Having more men than you can feed or control usually does more harm than good.

The Judas Maccabeus factor is another question, though.

[JasonC]

Sgt Joch - the point is not that maneuver or quality multipliers do not exist, but that they are generally bounded in size, and frequently also limited in time. Maneuver edges are particularly fleeting.

If you can "cash" them for lasting odds in the period when they are sizable and in your favor, great. But relying on them is a strategy with an absolutely abysmal track record.

Good commanders show their ability less by beating superior forces with smaller ones, than by ensuring they bring superior forces to a decisive point, in the first place. Or at least roughly equal ones in conditions of much larger than normal advantage from other factors.

Why do they remain bounded or disappear?

Because leading states are generally able to copy or counter each other's methods.

Because solid professionalism can get well within half of anything genius can do, even if outright foolishness does not.

Because poor doctrines are noticed by professionals and adaptations occur.

Because a long conflict equalizes skill levels by training the less able and by attriting the more able and diluting them with replacements.

Because momentary maladjustments of forces can be borne and overcome readily by rallying and repositioning etc, if they are survived without serious permanent loss in an odds sense.

Because forces in being over long periods are set more by replacement or mobilization rates than by stocks of initial forces or the results of single battles.

Can you find cases of technological mismatch so extreme they are nearly fights between armed men and disarmed men? Yes, but they are usually not between leading contemporary states (they are typically one of those vs a backwater) and they do not last indefinitely. Weapons and methods diffuse.

It takes a continual stream of new revolutionary methods to maintain any given multiplier. The usual thing, therefore, is to see a momentary displacement as one of them appears, followed by a gradual reduction in the scale of edge it confers. If in the meantime a permanent odds edge is achieved through its use, the effect may be lasting. Otherwise, it drops out as a critical determinant of outcomes and odds come back.

By all means seek such advantages. But do not rely on them - they are not as solid or permanent, of their very nature, as the sheer scale of forces. Use them to change the scale of forces - by eliminating enemy forces or their means of mobilization or both. "Cash" them for odds. Bank every advantage you can muster, for odds. And strain for odds the while, because all the rest are supplements only.

Is a greater proof of this needed than the first 6 months of the Russian campaign? The Germans inflicted losses of 15 to 1 against an opponent twice as large, which is about the largest achieved ratio ever seen between leading states. But at the end of that period, their own force was weaker than at the start of it, while their opponent was as strong in fielded forces as it had been at the outset.

Why? Because the Germans neglected their own side replacement stream, and were thereby outmatched by the Russians in mobilization by enough to outweigh their success in the field. Why did they let that happen? Because they placed insufficient emphasis on turnings their initial quality edge into a lasting odds edge.

The same thing happens within wars, in individual operations. It happens grand tactically, as well. Robust deployments, adaptation, temporarizing to neutralize momentary enemy advantages, focus on attrition efficiency to reduce the enemy force, employment of all available combat power oneself, and at the critical points rather than dispersed on secondary objectives - these work at every level of conflict.

[JasonC]

Philippe - I deny it. This is the position von C ridicules as the idea of a best size of force, in the military historians of the pre Napoleonic period. Napoleon neutralized it by inventing the army corps. It is a poor commander who cannot find profitable ways to employ double the force.

Yes one can "overstack" a logistical route and therefore wreck a large army. This is an unforced error of planning, not a reason to avoid numbers as such. The idea of the corps was to have a force small enough to be readily supplied "off the land", taking up a limited enough space on roads to be march maneuverable in hours, strong enough to sustain combat against a major force for limited periods. If one has 4 extra corps one may need to spread more to march, that is all. If the total logistic limits of a theater have been reached, then one can employ strategies that strain it for the enemy, including use of your additional forces elsewhere.

A general who can see no use for an addition of say 50% to the size of his force, is a general who does not understand his own tools.

[undead reindeer cavalry]

Originally posted by JasonC:

URD - largely a scale issue.

i agree and see the merits of the whole idea of odds. it's clear that all things being equal, odds will dictate the result.

what i suspect is that advancements in various technologies have pushed the scale up considerably, up to the point where it's become difficult to achieve the required scale.

[undead reindeer cavalry]

what comes to Soviets and Germans, i don't think there was such a huge difference in reality.

i think the idea of fundamental difference is most of all a mental fabrication born out of human need for tales and myths. showing the errors contained in these mythical ideals is noble, especially if these ideals are tainting the thinking of this day, but i think one needs to be clear whether one is attacking a mythical idea or presenting a historically incorrect claim.

[Philippe]

Not sure I follow you, JasonC. I wasn't thinking about the concept that there might be an optimal force size as much as the concept that there might be a force size that was inherently sub-optimal. Don't pile on more troops than you can feed, don't try to maneuver with more units than you can control (unless you can hit the pause button). If the stack in a hex gets too high you'll always be in trouble, even if you don't have long-haired cats with bushy tails.

Overstacking can cause a logistical and health catastrophe as well as loss of command and control. Napoleon's first two months in Russia may or may not be your overstacking health catastrophe, as for the loss of command control, I think that the tripping-over-your-own-feet factor was at work with Napoleon in 1813 generally and especially at Leipzig, and with Darius at Gaugamela. You can only control x number of corps if you have two or three times that many moderately intelligent ADC's who have a modicum of initiative and plenty of changes of horses. Or a lot of really inspired and insightful corps commanders who aren't constantly complaining that their #@$&&! of a boss is trying to get them all killed before they can retire.

A contributing factor to the Roman defeat at Cannae was probably that the Romans had too many men and couldn't control them effectively. [Another factor is the confusing account of the battle -- still don't know which side of the river it was fought on]. So there seem to be two kinds of overstacking going on here -- beyond your logistical capacity (hello typhus) and beyond your command capacity.

As an aside, the Roman defeat at Carrhae was inflicted by a Parthian army that was a third or a quarter the size of the Roman army. But that had more to do with bad preparation and tactics coming up against good preparation and insight than tripping over one's own feet (though Crassus may have done a bit of that too).

[JasonC]

Philippe - having a force of size X does not force you to overstack all of X in two square miles. Unforced errors of overstacking are not caused by having a large force but by not knowing what to do with it. For any given helpfulness of a limited force size, you can deploy the larger force so as to achieve all those benefits, and other ends as well (reserves, depth for engagement in sequence, feints at other objectives, etc, etc).

Cannae is ridiculously hyped as a brilliancy, it was just the natural result of winning the cavalry battle. The Romans always had deficient combined arms, relying on allied auxiliaries for most of their cavalry and virtually all of their light troops. Hannibal just wasn't someone to let them get away with it, and had a far superior cavalry.

It won rapidly while the infantry engagement was still going on, and the rest followed for exactly the same reasons later seen at Adrianople. It was also a case of cashing a momentary edge for more lasting odds. It was also strategically a case of a quality edge being insufficent in the long run (Hannibal was clearly the better general, but he lost the war).

Carrhae was an extreme case of this, a virtually cavalry-less army fighting on a plain entirely suited to it against a nearly pure cavalry army. Nor was this an undiscovered failing (read the Anabasis), the Romans were just quite bad at it and that particular emperor more cluelless than most.

It is also quite silly that such cases have to be reached for trying to sustain the thesis. In modern war between leading states, momentary multipliers are not decisive. In fact, the only other serious contender alongside attrition odds processes as a decider of modern wars, is political disunity and its proper exploitation. Compared to both, lasting results from maneuverist superiority can be counted on one hand. Plenty of temporary advantages, certainly.

[Guest Mike]

cf the fate of Mark anthony's expedition with that of Crassus - MA actually lost more troops than Crassus, but took a much longer campaign to lose them and actually captured Ctesiphon. He never fought a pitched battle.

Vendetius defeated the Parthians 3 times IIRC, killing several of their leading generals and a Roman turncoat fighting with them.

[undead reindeer cavalry]

WW2 contains a good number of overstacking cases.

Operation Barbarossa perhaps being the biggest one, with almost total break down of German logistics that was quite near of causing a German defeat already during the first winter. they survived only because Soviets failed to utilize their superior odds.

another good case of WW2 overstacking is Winter War, where Soviets got both logistical problems and unability to utilize their superior odds, which lead to some of the worst warfighting seen in modern times.

you can have too many troops, so that infrastructure, transportation and logistics cause problems. it's not just a question of how you use all your troops, since reseve troops are useless if you can't transport them where you need them, or worse still - you are not able to use them at all due to supply and service shortages.

having great odds is not enough in itself, and in historical perspective it's perhaps likely to lead to inefficient execution, perhaps because of command push (e.g. army level isn't too interested about or even aware of regimental realities).

nevertheless it is clear that odds are crucial and it's quite possible that theory of odds is often neglected. i can't remember reading any worthwhile game theory studies about odds. it would be very interesting if anyone could point out some modern studies about proper application of odds in combat.

[JasonC]

URD - Russian doctrine calls it "correlation of forces" and writes about it extensively, right up through modern times.

US force design and warfighting planners did as well, through the early 1980s or so. Computer modeling of combat led to reckoning of forces and deployment schedules in "ADEs" - armor division equivalents. As a rule of thumb, mech forces were counted as 2/3rds of armor and light as 1/3rd, etc. Definite odds and force to space ratios were though necessary to stop potential Warsaw Pact attacks and therefore to deter them, etc. It was a standard part of army thinking.

[undead reindeer cavalry]

apologies for horribly slow reply, i've been quite busy with other stuff.

i'm familiar with standard CES procedures - relative combat power, minimum planning ratios and such, but these deal with specific tactical/operational situations. i'd be interested to read more theoretical studies on military application of odds. something that deals with more abstract properties (e.g. "loss regeneration ratio") and aims to construct algorithms.

do you know any good works worth reading?

[pamak1970]

Originally posted by undead reindeer cavalry:

apologies for horribly slow reply, i've been quite busy with other stuff.

i'm familiar with standard CES procedures - relative combat power, minimum planning ratios and such, but these deal with specific tactical/operational situations. i'd be interested to read more theoretical studies on military application of odds. something that deals with more abstract properties (e.g. "loss regeneration ratio") and aims to construct algorithms.

do you know any good works worth reading?

I guess you want to read theoritical studies of "military operation research".

I am not sure if you are familiar with the above.

In case you are not ,i will point a few things.

Sinjce you want application of the theory for constructing algorythms, you need to know math of the highest level.

Still even if you have a background in computer engineering or programming is not enough.

I have a background in mechanical engineering and i frequently have trouble to follow the authors,since they use a wide range of various branches of higher mathematics.

For example ,i had elementary knowledge of "set theory" ,not to mention that i had to recall knowledge i gained 15 years ago.

The second thing is that most of these books are very expensive.If i recall well we are talking about $150-200 each.

The third thing is that there is no definite answer to your quest.

There is saying "all models are wrong but some are useful".

Finally,if you think you have a very good mathematical background and it is worth to spend effort and time,here is one suggestion.

J.S Przemieniecki

"Mathematical methods in defence analyses".

I have the third edition,but there might be a newer one.

I strongly suggest you go to a bookshop and have a look at the book inside before you spend money to buy it.

Try also amazon if it let's you look inside .

Here are some topics

Scientific methods in military operations

includes subcategories like, theory of combat, decision theory, linear programming, Queuing theory, network analysis, game theory, differential games, and so on

Deterministic combat models

Lanchester models, Markovian attrition rates, Helmbold models, battle disengagement,forced break points, casualty exchange ratio, variable attrition coeficients and so on,

Probabilistic combat models

many on many engagements,uniform and random assignment of targets, sequential and continuous combat duel and so on

Strategic defence

Layered defence, two-person zero sum game-pure and mixed strategies, optimal pentetration routes, and so on

Theater missile defence

Tactical engagements of heterogenous forces

Reliability of operations and systems

Target detection

Optimization methods

Linear and non linear programming among others

Modeling

and finaly some appendixes with mathematical charts

AND software with applications of programming based on the previous chapters.

[pamak1970]

I looked into my archives about a typical monograph regarding odds, force ratios and "force to space ratios" in theoritical form .

I am sure you can google it,find and download it

The level of math used is high but "logical".

You face it basically in the second half of the monograph.

The good thing is that there is plenty of text that everybody can read and understand.

The first half can actually be read by everybody

The book i recommended before depends much more heavily in math and it is much more difficult to read it.

The level of math is also higher.

Find in internet the following monograph to get a "feeling" of theoritical mathematical studies

"Defence at low force levels

The effects of force to space ratios on conventional combat dynamics"

Stephen D. Biddle ,Project leader.

[ October 04, 2007, 12:40 PM: Message edited by: pamak1970 ]