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Thread: Force Ratios and the 3:1 Rule Debate

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    Default Force Ratios and the 3:1 Rule Debate

    The 3-1 rule of land combat is a military aphorism rooted in operations research that states that an attacking force should have a 3 to 1 advantage over a defending force in order to succeed. The reason the attacking force must be so large of course, is to account for losses that can occur when assaulting a fortified position. A smaller attacking force often assumes much greater risk by not having enough soldiers to create and exploit a breach; likewise, choice of terrain, cover, level of preparedness, area denial, distance to resupply, distance to reinforcements, and home field advantage (morale) is usually on the side of the defender.

    1986 survey of 600 land battles from 1600 to 1973 by the U.S. Army Concepts Analysis Agency.


    Statistics above (though arguably vague) suggest that the 3:1 rule is not always necessary for an attacking army to win (the attacker still won close to 50% when facing 1:1 odds). However the 3:1 rule might still be a good rule of thumb when planning offensive operations. When an invading army numbered over 3:1, they succeeded 74% of the time.


    My critique and questions for researchers:

    How valid is the 3:1 rule in the first place? (ex successful offensive operations led by Nazi Germany, but then their failure against the Soviets).

    Does the 3:1 rule apply to all offensive ground operations, or only in cases of frontal assaults when facing a peer competitor?

    Is mass and concentration of forces a fitting refutal to the 3:1 rule? Or is it an extension?

    How does airpower alter the 3:1 rule?

    As a general rule to land combat, what is the most effective force multiplier (tech, terrain, mobility, supply, firepower, coordination of forces, or actual numbers)?

    When attempting a breakthrough, should you ever divide your forces? And what are the major risks?
    Last edited by Dick Cheney.; January 15, 2017 at 03:13 PM.
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    Default Re: Force Ratios and the 3:1 Rule Debate

    It's five to one against a prepared, alert and dug in defender.
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    Default Re: Force Ratios and the 3:1 Rule Debate

    This theory has a couple of problems:
    - A force three times larger than its opponent should usually win a battle (given both sides are on par in technology), regardless of stance.
    - A seriously weaker force tends to stack on the defensive, even though military unwise, in which case the question who was attacker doesn't have to be reason for the other to win
    - The strength of the defensive is very much depending on the strength of defensive fire-power versus offensive military means. This was dramatically stronger only the period of mid-19th to early 20th Century. If you would exclude these battles from the survey you would get a complete different image (IIRC, in the Seven Years Wars all battles were either a draw or won by the attacker, for example)

  4. #4

    Default Re: Force Ratios and the 3:1 Rule Debate

    That's where force multipliers come in; you can extend the range from where artillery can be concentrated on one spot, and add a third dimension with air support.

    Then you can add in interdiction to the rear area, isolating the objective and cutting off resupply and reinforcements.
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    Default Re: Force Ratios and the 3:1 Rule Debate

    I thought the 3-to-1 ratio referred to concentration of force on a tactical scale, rather than operations on a strategic scale. Even the statistics you posted are a study of battles, as opposed to campaigns. So, it's not really applicable to the operations of Nazi Germany versus the Soviets, for example, as the scale is totally different there.
    Last edited by Charerg; January 15, 2017 at 10:24 AM.
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    hellheaven1987's Avatar Comes Domesticorum
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    Default Re: Force Ratios and the 3:1 Rule Debate

    Technically it means you can safely push your opponent by attack its front and both sides; however I remember the three-units modern system was created to ensure the minimum amount of men to create a push (technically one front, one flank, one reserve). It was notable that three-units system was not common before and during WWI, and was created as more a maneuvering unit instead a direct approach unit (hence many WWII commanders felt uneasy to command a three-units system).
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    Default Re: Force Ratios and the 3:1 Rule Debate

    A mate of mine in the Australian forces told me "if we don't have 3-1 local superiority against a like foe then we don't attack", essentially that's a tactical doctrine hedged about with the usual qualifiers (eg "like foe", in Vietnam two or three companies of Aussies took on an NVA division at Long Tan and chewed on them for a couple of hours, leading to a standing order to not engage our units).

    The table posted by OP explicitly notes this is engaged forces not national army totals. This is very much a tactical doctrine applying to a specific battle scenario, dislodging an entrenched opponent. A quick Google revealed this: http://mearsheimer.uchicago.edu/pdfs/A0013.pdf

    It seems the 3:1 rule is a pre WWI Prussian infantry doctrine, those guys did heaps of theory an gaming around dynamic as well as prepared battles and were probably to most thorough and experienced military in Europe at the time. So its c. 1900 military rule of thumb.

    Not sure how relevant it is in the days of asymmetric warfare. Even WWII is a stretch. The classic example of the Nazi forces in WWII is their air force ran close interdiction and support allowing tank breakthroughs, in the period 1939-1940 creating non "like-force" ratios (pinned and unsupplied formations) against armies who lacked large air forces or even interdiction and independent armour doctrines.

    My own guess is the German army also enjoyed tactical superiority through a higher degree of professionalism than most French, and nearly all British Russian and US formations: they generally weren't fighting like formations. Once air superiority was denied German forces saw catastrophic defeats (usually when orders or enemy air dominance interdicted movement) but were still able to lash out on occasion.

    This sort of force requitement and force multipliers are represented at an operational (corps-army-front) level in games like Totaler Krieg (a fine board game) by starting with your force ratio (3:1 is usually a winner) then sliding the odds through other factors: extreme terrain -1 or -2 (favours the defender), supplied or unsupplied defenders, armour and air forces present, Paras (could be significant even at the corps and army level) etc. the game featured a "blitz" factor as well, if the army had been supplied with the extra resources to undertake breakthrough/deep operations which gave an extra shift in the odds.

    This explain why its so easy to find exceptions t the 3:1 rule. There's always some genius commander or stupid CiC messing the odds, some material or materiel advantage, and just plain coincidence.

    I recall an analysis of battles in the War of the Rebellion which demonstrated an odd anomaly: when numbers were roughly equal (or at least within the expected range, 2:1-1:2) the battle usually went to the defender (as you would expect) except when the forces were between 20-40,000 a side, when a huge proportion of victories went to the attacker. I'm pretty sure this is just coincidence, but its one that would drive a theorist looking for a pattern crazy.
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  8. #8

    Default Re: Force Ratios and the 3:1 Rule Debate

    There have been cases where three brothers or one berserker holds the bridge against all comers.

    Or three hundred tourists against one million illegal immigrants taking the Balkan route.
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    Default Re: Force Ratios and the 3:1 Rule Debate

    Quote Originally Posted by Charerg View Post
    I thought the 3-to-1 ratio referred to concentration of force on a tactical scale, rather than operations on a strategic scale. Even the statistics you posted are a study of battles, as opposed to campaigns. So, it's not really applicable to the operations of Nazi Germany versus the Soviets, for example, as the scale is totally different there.

    From what I can tell, the 3:1 rule appears to have a lot of different meanings.

    Can we expect a defending force for instance, by default, to usually be three times as effective in combat as any attacking force? And what would happen to the defender's 3:1 martial advantage if he is forced to spread out and defend more ground than his small numbers typically allow. Does our rule still apply?

    And while I agree that the 3:1 rule does seem to apply more to the tactical realm of dislodging a dug in defender than the actual campaign map. What does apply strategically, and must still be considered in any grand strategy and battle plan is the defender's initial advantage and then each army's disposition of forces; which are of course, theoretical foundations for the 3:1 rule.


    Operation Downfall-1945
    Need More Troops?


    US Forces: 5,000,000
    Japanese Defenders: 4,000,000 - 35,000,000 (Projection)

    https://en.m.wikipedia.org/wiki/Operation_Downfall
    Last edited by Dick Cheney.; January 15, 2017 at 10:20 PM.
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    Default Re: Force Ratios and the 3:1 Rule Debate

    All things being equal.

    Patton mentions getting there fastest with the mostest, so momentum counts.
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    Default Re: Force Ratios and the 3:1 Rule Debate

    Quote Originally Posted by Dick Cheney. View Post


    From what I can tell, the 3:1 rule appears to have a lot of different meanings.


    Indeed.

    The rule is an historical artefact, from a period when Europe had a balance of power and wars were planned down to the nth detail over the same patches of dirt they'd been fighting over since the Romans pulled out. Its sounds technical and cool I guess, but like a lot of technical jargon it has a specific meaning they is often ignored as it is bandied around to make some fat mouth sound smart.

    I recall a British "military expert" commentating just before the start of Desert Storm that "Saddam has half a million soldiers and we need three soldiers for each one of his to kick him out of Kuwait", utter tripe when you give even a moments thought to the matter. Most of the army was back in Iraq, and they didn't need to be fought all on the one day, but hey, talking heads gotta talk.

    Quote Originally Posted by Dick Cheney. View Post
    Can we expect a defending force for instance, by default, to usually be three times as effective in combat as any attacking force? And what would happen to the defender's 3:1 martial advantage if he is forced to spread out and defend more ground than his small numbers typically allow. Does our rule still apply?


    Of course not, the doctrine is a tactical one and would apply to (I imagine) a formal engagement at perhaps divisional or lower level (front warfare not having been considered at this point) in a typical European theatre, stressing elements like dynamic mobility and field officer initiative. Campaigns such as North Africa in WWII demonstrate the importance of manoeuvre and supply over force concentration (although a little more force concentration at Tobruk in the various sieges there might have altered the campaign somewhat, the matter was decided by superior allied supply capacity).

    One side light is to this discussion is force fatigue and refit. Wehrmacht units were highly regarded for their ability to continue fighting across extended periods and even after taking heavy casualties. I believe the Israeli army has used "tank showers" and deodorant when refitting damaged armoured vehicles as it improved refit time turnarounds (apparently the mechanics find the smell of charred corpses off-putting), getting tanks back into the fight faster: the various Arab Iraeli wars have been determined by swift strikes from Israel against the piecemeal advances of their widely separated opponents. US cavalry units use choppers to get boots exactly where they are needed to apply local superiority, and leave again if necessary.

    Logistics and doctrine are a huge part of achieving local force superiority. Napoleon utilised his staff of brilliant aides-de-camps to send specific instructions and respected inspirational leadership to the point on the battlefield it was needed, and allowed rapid redeployments on the grouhd when the enemy commander would have a "chain of command lag", and tried to retain a hard handful of troops to fling at the critical point. The Nazi forces sent armour and dive bombers to crash into and through the enemy line, something no one else was doing at the time (pace Tukachevsky who was dead by this point) in the period 1939-1942.

    Quote Originally Posted by Dick Cheney. View Post
    And while I agree that the 3:1 rule does seem to apply more to the tactical realm of dislodging a dug in defender than the actual campaign map. What does apply strategically, and must still be considered in any grand strategy and battle plan is the defender's initial advantage and then each army's disposition of forces; which are of course, theoretical foundations for the 3:1 rule.


    Absolutely, elements such as speed and manoeuvrability of both forces and supply, air and sea support, local terrain, weather etc are all critical when considering Downfall especially (I'm sure you know about the "Downfall typhoon").

    Quote Originally Posted by Dick Cheney. View Post
    Operation Downfall-1945
    Quote Originally Posted by Dick Cheney. View Post


    US Forces: 5,000,000
    Japanese Defenders: 4,000,000 - 35,000,000 (Projection)

    https://en.m.wikipedia.org/wiki/Operation_Downfall
    Yep, nukes, vastly superior industrial and scientific capacity, complete air dominance and naval control are all force multipliers.
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    hellheaven1987's Avatar Comes Domesticorum
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    Default Re: Force Ratios and the 3:1 Rule Debate

    Quote Originally Posted by Cyclops View Post
    "if we don't have 3-1 local superiority against a like foe then we don't attack"
    Quote Originally Posted by Cyclops View Post
    A mate of mine in the Australian forces told me
    It is Australian/British military, and we all know caution is major point of British modern military doctrine, so not a surprise here.
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    Default Re: Force Ratios and the 3:1 Rule Debate

    Quote Originally Posted by hellheaven1987 View Post
    It is Australian/British military, and we all know caution is major point of British modern military doctrine, so not a surprise here.
    Indeed, small professional armies with an "overseas mission" (former colony intervention/peacekeeping) posture. However the doctrine itself is Late Second Reich Prussian military (mass land warfare/destruction of other mass armies) so I guess the surprise is its such a robust doctrine that it would be embraced to the point of being a shibboleth over a century after it was formulated.

    OP's point is sound, while the doctrine itself has a specific useful application it is subject to all the caveats and qualifications one might expect: I think it has acquired a certain amount of "tacticool" and I have heard it deployed by people trying to sound smart as well as sensible professionals discussing their trade.
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    Default Re: Force Ratios and the 3:1 Rule Debate

    It's really circumstantial; if the the Germans had run into a fresh, in tact, dug in British Expeditionary Force, they would have lost at least one army, and would have been forced to outflank, encircle that, before they could Schlieffen around Paris.
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    Default Re: Force Ratios and the 3:1 Rule Debate

    Quote Originally Posted by Cyclops View Post
    However the doctrine itself is Late Second Reich Prussian military (mass land warfare/destruction of other mass armies) so I guess the surprise is its such a robust doctrine that it would be embraced to the point of being a shibboleth over a century after it was formulated.
    I would rather say it was independent evolution, as both Soviet and Japanese also adopted the same ratio after WWI; Japanese did it more because they found it easier maneuvering with less units but recognized 3:1 was not enough in a brutal frontal assault operation.
    Quote Originally Posted by Markas View Post
    Hellheaven, sometimes you remind me of King Canute trying to hold back the tide, except without the winning parable.
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    Default Re: Force Ratios and the 3:1 Rule Debate

    Quote Originally Posted by Condottiere 40K View Post
    It's really circumstantial; if the the Germans had run into a fresh, in tact, dug in British Expeditionary Force, they would have lost at least one army, and would have been forced to outflank, encircle that, before they could Schlieffen around Paris.
    Certainly the "rule of 3:1" is not a hard an fast or universally applicable one. The Schlieffen plan was of course specifically designed to avoid having to make specific breakthroughs, intended rather to bag the entirety of the French armies in a Super Cannae. First Army was the tip of an encircling tentacle, not a schwerpunkt, and achieved tremendous strategic surprise. It took another marvel of manoeuvre by Joffre to cobble a "remnants and latecomers" force including the handful of Brits across the path of the German advance to stall them.

    Quote Originally Posted by hellheaven1987 View Post
    I would rather say it was independent evolution, as both Soviet and Japanese also adopted the same ratio after WWI; Japanese did it more because they found it easier maneuvering with less units but recognized 3:1 was not enough in a brutal frontal assault operation.
    The Prussian army was the model for the Japanese army and I imagine the Soviets were well aware of German effectiveness also, continuing a tradition of looking to Germany for military culture going back to Peter the Great ( eg Trotsky developed military cooperation and exchanges with Weimar Germany in the "wilderness years"), so its hardly independent evolution that those forces should adopt this notion about force ratios.

    I would argue that since 1870 the Germans have provided the model of military organisational and doctrinal (but sadly not moral) excellence, outperforming all opposition and really only finding themselves on the losing side because of political factors (specifically unsound supreme leadership). Repeated operation successes against greater odds, durability in the field, successful and often groundbreaking doctrinal development etc etc all make the German Army's performance one of the factors giving the lie to the idea the "3:1 rule" is some absolute truth.
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    Default Re: Force Ratios and the 3:1 Rule Debate

    The Wehrmacht had some sort of major organizational renaissance once they realized they bit off more than they could chew, after Barbarossa, which was basically that they realized thirty guys had the same amount of force as fifty, and that most fighting was done within three hundred metres.

    Before that, they had to water down their divisions so they could stretch them across a really wide front.
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    Default Re: Force Ratios and the 3:1 Rule Debate

    What about adding estimated skill of the officers and potential shifts/surprises in diplomatic grounds (to not say supply lines)? Germany in WWI invading a France without allies (such as UK and Belgium) could've allowed Germany win the later equivalent of battle of Verdun.
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    Default Re: Force Ratios and the 3:1 Rule Debate

    Quote Originally Posted by fkizz View Post
    What about adding estimated skill of the officers and potential shifts/surprises in diplomatic grounds (to not say supply lines)? Germany in WWI invading a France without allies (such as UK and Belgium) could've allowed Germany win the later equivalent of battle of Verdun.
    This is Dick Cheney's point I think, there are so many variables in determining success and the actual 3:1 doctrine is only really applicable in a fairly restricted sense, its not some universally applicable verse from the "Art Of War".
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    Default Re: Force Ratios and the 3:1 Rule Debate

    When it comes to battles themselves I would be more interested in figuring out whether the terrain was actually conducive to the use of that 3:1 superiority. But I disagree with the very idea of 3:1 ratio. The numbers exactly are what matters. 10,000 men in a large open area will have a hard time against 30,000. 100,000 men would have an easier time against 300,000 regardless but with the appropriate terrain it could still have an even easier time. Usually though it is hard to beat 3:1 odds in general. The difference is too vast.
    Last edited by Lord Oda Nobunaga; January 18, 2017 at 06:58 PM.

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