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"Three to one" Topic

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Comments or corrections?

goragrad19 Jan 2012 1:29 p.m. PST

Discussion on attacker/defender ratios for a successful engagement came up during the 'How many Shermans to Kill a Panther' thread. Got me to thinking and I wondered if this might be it?

Coming from a work of fiction, I am not sure of the accuracy of the following (wasn't able to find another source on the web) -

In 'Killer Angels,' Micheal Shaara has a passage on Longstreet and Pickett's Charge. In it he makes the claim that the charge was entirely Lee's idea.

As Shaara'a argument he refers to a study/paper written by Longstreet prior to the war. In it Longstreet had argued that due to the increased range of the rifled musket it would be necessary for an attacker to have a 3 to 1 advantage over a defender in future engagements.

Shaara states that Longstreet's contention was that the defender would get off two shots while the attackers were closing and that the probability was that one would be would be killed and one wounded leaving one man to complete the attack.

Presuming Shaara was not fabricating evidence to exonerate Longstreet, this could seem to be a possible source.

badger2219 Jan 2012 1:54 p.m. PST

100% hits would be devistatiing, no matter what the ratio. And if an attacker took 66% casualties I dont really they are going to press on.

Another thing to consider is that no pitched battle has a 3 to 1 ratio, or it would not be pitched. Unless of course there is a great combat power discrepency.

And really I think that is what is needed, not so much absolute numbers, but how much power can you bring to bear on the point of penetration. So things like artillery and engineers can really change the equation, rather than just the number of infantry commited.

As for Longstreet, I have always felt he had a pretty good idea what it was going to take to push the attack through to victory. And he knew he didnt have what he needed.


PS I didnt know about the paper, and am glad to learn something new.

Grizzlymc19 Jan 2012 3:17 p.m. PST

I get the impression that 3:1 is generally considered to be what it takes to secure success, not to avoid failure – there is a big grey area there.

Also the 3:1 thing needs only be local, switching the access of your attack can give you that local with a much smaller overall margin.

MajorB19 Jan 2012 3:21 p.m. PST

What Grizzlymc said, although I think he meant "axis of attack" rather than "access of attack".

Mako1119 Jan 2012 3:28 p.m. PST

Yes, the 3:1 ratio is to pretty much ensure success.

Actually, that occurs a lot, as mentioned above, by using various tactics, and concentrating your efforts on a small frontage. When successful, you hope the rest of the defending unit will collapse, due to a morale failure, or attacks from the side or rear of it, giving the attacker the element of surprise.

VonBurge19 Jan 2012 3:55 p.m. PST

"Battlefield Calculus."

Back in the Cold War we (US Army) planned and trained based off the 3:1 ratio for an attack. Since then, it's been shown that a large technology mismatch can bring it back down to 1:1 or even invert the force ratio needed.

The 3:1 ratio that we were trained on was what was required to have an "even" chance of sucesss against defenders in prepared positions (deliberate defense). Nobody ever said it would be an automatic win at 3:1. Just that victory was reasonably achieveable at that point.

Grizzlymc19 Jan 2012 5:34 p.m. PST

U hve teh rite of it, homonymious distress is all over my face along with egg.

Hornswoggler19 Jan 2012 7:41 p.m. PST

Launch all of your attacks at 3:1 in "The Russian Campaign" boardgame and you will get your rear end severely kicked !! :oP

BlackWidowPilot Fezian19 Jan 2012 7:42 p.m. PST

"Since then, it's been shown that a large technology mismatch can bring it back down to 1:1 or even invert the force ratio needed."

Ain't technology grand? Mwahahahahaahaaaaa!!!evil grin

Leland R. Erickson

Personal logo gamertom Supporting Member of TMP19 Jan 2012 8:43 p.m. PST

Charles S. Roberts based the combat results table he used in Tactics II and most of the classic early Avalon Hill games on this 3-1 principle. I'll have to dig around in some of my board wargame books to see if I can find what he based this on. I'm tempted to say it came from the RAND Corporation, but I'm pretty sure he got the idea for using hexes from RAND rather than the 3-1 ratio.

Personal logo gamertom Supporting Member of TMP19 Jan 2012 10:00 p.m. PST

Here's what Peter Perla had to say about it in his book, The Art of Wargaming, Naval Institute Press, 1990, ISBN 0-87021-050-5:

"In the early 1950s Rand had contacted Roberts and in a circumspect manner inquired about the source of the CRT used in Tactics (and virtually all of the early Avalon Hill games). Roberts's CRT bore an uncanny resemblance "to the more complex one that Rand was using to wargame World War III and other horrors." This fact was probably somewhat embarrassing to Rand when they discovered that Roberts had devised his own table in about fifteen minutes, basing it on the popular military notion that an attacker required a three-to-one superiority in order to be reasonably assured of success. After this encounter with the think-tank wargamers, Roberts became more interested in Rand. Later, he saw a photograph of one of the Rand gaming facilities and noted that they were using an hexagonal grid. This grid allowed movement between adjacent hexagons (or hexes, as they are more frequently called) to be equidistant, whereas movement along the diagonals in a square grid covered more distance than movement across the sides of the squares. Roberts immediately saw the usefulness of this technique and adapted it to his subsequent games."

Unfortunately this still doesn't answer where the three-to-one notion came from.

vojvoda20 Jan 2012 12:02 a.m. PST

While 3 to 1 might be doctrine, SOF is a force multiplier training and grit go all the way.
James Mattes

Early morning writer20 Jan 2012 12:05 a.m. PST

Sun Tzu.

UshCha20 Jan 2012 12:09 a.m. PST

It a while since I did the reading but certaiy in the open versions of the US manuals it referes to the evaluation of relative combat strenght. This, at least in theory, accounts for troop quality, defences and available resources of the enemy. I think it still covers the need for about 3 to 1 in combat power to ensure a reasonable success in an attack.

Of more interest in some ways for tank battles is the basic ratio that assuming thet the tanks are the same side. The combat force is proportional to the square of the number of tanks present. Thus 2 tanks vs 2 tanks is an even fight, 2 vs 3 is a combat power of 4 vs 9, and 2 tanks vs 4 is 3 vs 8. This gives weight to the fact that tanks should be deployed in large numbers and not piecemeal.

hope thi helps.

Richard Baber20 Jan 2012 3:21 a.m. PST

I seem to recall a comment by a Russian observer in Normandy watching an allied attack (or the preparations), he asked what the ratio for the attackers was Vs expected German defence. He was told 3:1 and expressed shock and disbelief, explaining the Soviets wouldn`t consider attacking dug-in Germans without at least a 5:1 advantage!

Memory fades as to where I read this though – sorry :-(

Gwydion20 Jan 2012 3:22 a.m. PST

2 tanks vs 4 is 3 vs 8

4 v 16

This is Lanchester's Square Law, and it isn't that simple- it ignores sneaky things like tactics and getting the first shot in. But basically its right – Nicht Kleckern, klotzen!

Which also messes up the 'proportionality of response' arguments in the UN.

As for 3:1 I always thought this dictum was way after the ACW – but I could be wrong.

Martin Rapier20 Jan 2012 5:03 a.m. PST

"Unfortunately this still doesn't answer where the three-to-one notion came from."

As per my comments on the other thread, Dupuy discusses the source in some detail. I shall have to dig it out.

One of the big issues is of course, what are you actually measuring numbers or modified combat power. Against an opponent with equal levels of training and equipment, numbers are a reasonable proxy for combat power, against opponents with widly differing equipment, training, doctrine etc, they aren't.

As a planning rule of thumb, it is a perfectly reasonable approximation. Battalion vs company, regiment vs battalion etc.

" what was required to have an "even" chance of sucesss against defenders in prepared positions (deliberate defense)."

Which again, seems entirely reasonable. 'Deliberate defence' has a very specific meaning in terms of unit posture.

"This is Lanchester's Square Law, and it isn't that simple"

Indeed. It is also but one of numerous combat models and takes no account of the effect of target density on weapon effectiveness. Put 30 tanks vs 10 and you do not have a combat power 900 vs 100 as the inferior numbers have more firing oportunities (at 3-1 weapon effectiveness of the inferior side roughly doubles).

Assume a basic kill probability of 0.1, then 30 vs 10 means 3 kills vs 1, then 2.9 kills vs 0.9 etc etc in a sequence until the weaker is wiped out in roughly four rounds of combat for an attacker loss of roughly 3 (so the loss ratio is indeed 1:3 in the basic Lanchester model, but the linear version, not the square one).

Taking account of target density the weaker sides kill prob is 0.2, so the sequence goes 3 k vs 2 k, 2.8 k vs 1.6 k etc etc. A much more expensive proposition for the attacker although they will still 'win'.

An alternate approach to 'winning' is to increase your troops relative combat effectiveness (so side As kill prob is e.g. 0.3), in which case you can make their numbers work against you as well and produce e.g. the 6:1 kill ratio managed by Heer tank crews in Russia in 1942.

In extreme cases the target density issue can make it advantageous to attack vastly larger numbers with very small ones just as the RAF did during the Battle of Britain against large LW bomber formations. Lancesters 'Law' becomes inverted in that case.

Sorry, bit of a ramble, but I find this stuff really, really interesting. If I'm writing rules I want them to reflect real outcomes. Some of these effects are quite hard to model in a simple way.

BullDog6920 Jan 2012 5:34 a.m. PST


I have nothing to back this up, but I would agree that the 3:1 'concept' would have surfaced some little time after the ACW the latter part of the 19th Century largely saw relatively tiny Imperial forces taking on and beating 'native' forces of many times their number and must have completely skewed / dominated military planning for a time? I imagine there were still accepted 'odds' worked into planning for European warfare (what did Kriegspiel use?), and equally, one would imagine that there would be a similar rule-of-thumb for Colonial warfare? There must have been some set of standards used to decide how large a force to despatch to a trouble-zone? The size of the Gordon Relief force, for example, must have been decided upon in some way?
I have read that British intelligence reports prior to the Boer War reported a 200,000 strong Imperial force would be needed to defeat the two Boer Republics which were reckoned to be able to put 60,000 / 70,000 men into the field… obviously, there is a lot of difference between a strategic calculation and a tactical one, but could this number have been calculated using the 3:1 rule?

Skarper20 Jan 2012 6:19 a.m. PST

I remember the quote from the Russian observer too – but can't remember where either!

There was a follow as far as I can remember which was that the Germans defences in Normandy were so densely manned (compared to the situation in Russia at least) that to achieve a 5:1 ratio or indeed the 10:1 ratio the Soviets usually employed where a rapid breakthrough was required – that it would have been nearly impossible to fit all the tanks and infantry [let alone guns and supply units] into the bridgehead.

This is a very interesting thread.

In my home grown rules I was looking at the probable result of a tank on tank meeting engagement given even quality of vehicles and crews.

The side that moves into combat obviously needs more tanks to 'win'.

The formula is y = 2x + 1, where x = he number of enemy tanks and y = the number of attacking tanks.

This reflects the lack of abilty of moving tanks to acquire and hit the enemy tanks when they first move into LOS.

So – if you have 4 Shermans then 9 PzIVs are needed to have one left after all the Shermans are KO'd.

You might get away with 7 or 8 PzIVs because they have a small advantage in quality over the basic Sherman. If your are advancing with Shermans you'd have more chance with 10 or 11 to 4.

I think some of the 'simplistic' sets that are popular today really fall down on this. Quite often the attacker has enormous advantageous because they can concentrate one or two powerful units in a very small area and destroy everything – then move on and repeat. This is possible in real life too but it can be very easy in some games. So many seem to lack any kind of 'opportunity fire' rule.

I remember playing WH40K over 20 years ago in an attempt to bridge the gap between us 'serious' gamers and the kids whose subscriptions we needed to pay for our hall. It was going Ok until the first kid ran his space womble around a corner into LOS of our 3 borrowed 'squats' who had to wait patietly until the space womble shot at them! Our cries of – 'but we should be able to fire first' were met with 'but you can only fire in your turn'. It seems that some of the same 'attacker bias' is built into Flames of War.

Griefbringer20 Jan 2012 7:14 a.m. PST

I remember playing WH40K over 20 years ago in an attempt to bridge the gap between us 'serious' gamers and the kids whose subscriptions we needed to pay for our hall. It was going Ok until the first kid ran his space womble around a corner into LOS of our 3 borrowed 'squats' who had to wait patietly until the space womble shot at them! Our cries of 'but we should be able to fire first' were met with 'but you can only fire in your turn'.

I presume this was prior to the introduction of the overwatch rules in WD129?

Eclaireur20 Jan 2012 7:35 a.m. PST

I can recall from the dim and distant memory of the Cold War, and short spell at officer school, being instructed that 3:1 was the MINIMUM for a 'deliberate attack' on a prepared position. That was our doctrine, as we were taught it. I remember being told that 6 or 9 to 1 might be required too, depending on the circs.
As others have pointed out, during the latter war Red Army offensives, the Soviets became almost obsessive about concentrating more and more guns per km of front, higher and higher ratios of men or tanks, in order to overwhlem their enemy.
It might seem like overkill – but then think of those two guys with a Spandau MG on Omaha beach who killed hundreds of attacking US soldiers…

Skarper20 Jan 2012 8:01 a.m. PST

Yep Griefbringer – I guess so…. 20+ years ago.

(Phil Dutre)20 Jan 2012 9:10 a.m. PST

Wrt Lanchester:

The square rule only holds when ALL participants in the combat have an equal chance of hitting something with the same probability. The underlying mathematical notion is that my losses at any given point in time are linearly proportional to my enemy's strength at that same moment in time, and vice versa.
Thus, the strength off both forces is decreasing over time, always in proportion to the strength of the enemy (which is also decreasing). It's a coupled system of differential equations.

Working through the math (some integration and differentials involved; and integrating away time) produces the square law.

I wrote a longish post about it some time ago:
TMP link

VonBurge20 Jan 2012 11:24 a.m. PST

Like I said…"Battlefield Calculus!" ;)

Last Hussar20 Jan 2012 2:05 p.m. PST

3:1 is good.
5:1 is better
7:1 if you can get it…

badger2220 Jan 2012 2:39 p.m. PST

I suspect the Gordan relief force was a matter of what could be shipped there, rather than what was needed.

Real military operations just dont have enough data available to make things like 3 to 1 happen all the time. Sure, you try to get there, but often dont have the intel to make an absolute decision. Go with what you got and try to overcome.


just visiting20 Jan 2012 4:19 p.m. PST

Medieval example of the "three to one" working because the enemy gave it away: the French at Agincourt lined up in column of divisions with an army that at least outnumbered the English by 50%, and possibly more: then they attacked over 5,000 archers and c. 1,500 men at arms, with less than 8,000 SLOW men at arms, across a field 300 yards deep. Figure it out: each archer got off somewhere in the number of six arrows per minute during the five minutes it took for the French to finally arrive within weapon stroke. The ones who arrived fit to fight were outnumbered a lot more than three to one….

WarpSpeed20 Jan 2012 6:17 p.m. PST

I was under the impression that during the cold war, 6/1 odds were deemed necessary to guarentee success.Mathematical models such as these however dont take into account varying levels of training,efficiency,force modifiers and they are often associated with saturation tables to be used by artillery.Literally fire "x" amount of high explosive ordinance into such and such terrain area to guarentee the neutralization of op forces.

Skarper20 Jan 2012 8:27 p.m. PST

BTW – Nugget 238 with the 'tank surptise' article is available to non-members now. Interesting stuff.

Issues raised seem to further cast doubt on the FOW tank park effect – such formations should suffer extra losses without much increase in the damage they can cause.

I enjoyed the post Phil Dutre linked to – thanks.

It seems – more tanks helps, but the first shot helps more. The defender should usually get the first shot – but might not always. This helps the nearly invulnerable 'Tiger' types who can soak up the first and indeed first few hits with impunity. [though enough hits that don't kill can still degrade your tanks' effectiveness]

Martin Rapier21 Jan 2012 9:52 a.m. PST

I had a look through various books last night but still couldn't find the source of the original 3:1 contention. Like others, I think it originated from the ACW.

I ended up getting distracted reading Dupuy again. One of the first things he does is disprove the 3:1 rule by analysing 42 battles over a period of 200 years and in which some 45% were won by an attacker with inferior numbers. He does go on to say that this is trivial as numbers aren't a good proxy for combat power (which fits with Bulldog69s comments re ambush doctrine in the earliet thread). His own combat model gives troops in mixed terrain in a posture of prepared defence a force multiplier of around 2.5, so an atacker would indeed need a combat power advantage pf 3:1 to have a reasonable chance of dislodging the defence. Combat power and numbers aren't the same thing of course, a small force with superior training and morale, terrain favourable to their weapon systems and surprise can easily generate a 3:1 force superiority even though they are numerically weaker.

He did show later on that Lanchesters linear and square laws do apply to combat results, but only if the force ratios are calculated using combat power modified for environmental factors (training, terrain, weather etc).

goragrad21 Jan 2012 2:08 p.m. PST

Well Martin, the first instance I have seen of it being mentioned is the attribution in passing to Longstreet by Shaara. And the actual paper was from just prior to the war.

Additional 'support' for that argument would be the interest in the various wars of the mid/later 19th century by other nations' militaries. Quite a few foreign observers tagging along with both the Union and Confederates in the field (and US observers with European armies later in the century).

Also, as I recall, there was a lot of respect/admiration for the accomplishments of Lee and the ANV. Longstreet was a major figure in the ANV and anything he wrote before or after the war would be read with interest.

Wish I could have tracked down some other reference to that study though.

UshCha21 Jan 2012 2:14 p.m. PST

Sorry for the typo on what is Lanchesters Law. It is proably not that far off say ting Shermans vs PZ IV's as they are not that different and tanks gain somthing from defence but not as much as infantry. Inevitably simple laws like this are over implifications but they usefull if treated as simplifications. One of my experiences is that Wargamers generally are not good at modelling prepared defences well. Admittedly modelling a real anti tank minefield,literally in somecses a 1000m or more deep is a tall order. However very few wargamers (even me) do defences well. Almost every platoon has 6 or so Claymore type devices for defence but we rarely ever use them. Similarly barbd wire is much more common in defence than is seen on a wargames table. This proably skwes wargames to need less than the real thing as ther prepared defence is proably not as well prepared as the real thing. Defining combat power is hard, getting 3 to 1is easy if you know what the "1" represents.

donlowry21 Jan 2012 3:00 p.m. PST

I don't believe Longstreet makes any mention of such a paper in his book, From Manassas to Appomattox.

Theron21 Jan 2012 5:48 p.m. PST

So far I think the 3:1 rule has held up in this discussion! How's this for a suitably colorful definition?

"All things being equal, an attacker, desiring victory, should strive for a 3:1 numerical advantage before challenging a prepared defender."
~ ancient proverb

Martin Rapier22 Jan 2012 9:33 a.m. PST

Although the moral is to the physical as three is to one. N. Bonaparte:)

Last Hussar22 Jan 2012 6:01 p.m. PST

Martin's right – there is a difference between an army and an armed rabble.

goragrad22 Jan 2012 9:00 p.m. PST

Don, Shaara's note was that it was written/published(?) before the war.

BullDog6922 Jan 2012 11:31 p.m. PST


I admit there would be an aspect of that, but do not believe that there was NO decision making process whatsoever. In any such case, the powers-that-be would have had to decide whether to mobilise reserves / militia / yeomanry, juggle garrison forces from Gibraltar / Malta etc or in the case of Napier's expedition a few years earlier mobilise troops from India etc.

Someone at the War Ministry must have decided that the troops they were mobilising in the UK / raising in Egypt would be sufficient to do the job. There must have been a process where someone decided that 100 men would not be enough and 100,000 would not be needed. I don't think this happened randomly, which suggests there was some sort of 'rule of thumb' at work.

Grizzlymc23 Jan 2012 2:44 a.m. PST

That was the Duke of York's job.

Martin Rapier23 Jan 2012 3:21 a.m. PST

" I don't think this happened randomly, which suggests there was some sort of 'rule of thumb' at work."

I'm sure there was, although I suspect it was more to do with what could be transported and supplied. There would have been previous experience of the number of battalions/brigades needed to subdue X number of 'natives' in Y square miles of territory though.

BullDog6923 Jan 2012 3:36 a.m. PST

'There would have been previous experience of the number of battalions/brigades needed to subdue X number of 'natives' in Y square miles of territory though'


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