The Source of the U.S. Army Three-to-One Rule

Oddly enough, 1991 was when this rule was first published, that we are aware of. It was published in the CGSC (Command and General Staff College) Student Text 100-9: Techniques and Procedures for Tactical Decision Making dated July 1991. There may have been work or materials prepared before then that we are not aware of.

The actual statement in that publication is that “Historical experience has shown that a defender has approximately a 50-50 probability of successfully defeating an attacking force approximately three times his equivalent strength.” The publication then goes on to recommend that for planning purposes that they “Therefore, as our start part, we will attempt to defend on each avenue of approach with, roughly, a 1-to-3 force rations expressed as a US unit defending against the next higher level enemy unit. For example, a US battalion would defend against an enemy regiment. There are only tools for the plan. Table 3-2 shows the preferred minimum planning ratios used to initially array forces.” The key here is the words “initially” and “to start with.” When deploying out a force, seeing up a blocking force that may be initially outnumbered three-to-one in an planned deployment does not mean that it will be outmatched in combat power by three-to-one as the battle develops. It is possible to reinforce the unit, provide it with artillery or air support, or withdraw to a more favorable position. So, the guidance that forces should be arrayed one level lower than the expected opposition is not bad guidance, even though one of the arguments made in that 1991 document supporting this is clearly wrong. The problem is that this rule is now repeated in other army documents without fully clarifying that this is just a planning factor for initial dispositions. It is also serving as the basis for charts in manuals and informal casualty estimation and modeling procedures. The army now commonly publishes the following table (from the proposed ATP 5-0.2, 31 July 2019):

Historical minimum planning ratios

Friendly Mission                     Friendly: Enemy

Hasty defend                          1:2.5

Deliberate defend                   1:3

Hasty attack                            2.5:1

Deliberate attack                     3:1

Delay                                       1:6

Counterattack                         1:1

Penetration (lead element)      18:1


This table, as shown by the data leave the impression that you need to have three-to-one odds to attack and that one-to-three odds is sufficient for defense. This would be the wrong impression to give. To claim that it is “historical” gives it more authority than it deserves, as the historical data in fact does not support this table. They are “minimum planning” factors, and that needs to properly stressed.

The bigger problem is that you fight as your train. So, if the officer corps is trained that you need at least a three-to-one force ratio to have a 50% chance of winning, then what kind of war planning and offensive action is now being envisioned? In World War II, the most common attack in our database are those at odds 1.00- to 1.49-to-one and they win 63% of the time. In the post-World War II engagements, the most common attack is done at 0.54- to 0.97-to-1 and the attacker wins 75% of the time (20 cases). So to what reality are we training our officers? Are we training the next generation of George B. McCellans?

Share this:
Christopher A. Lawrence
Christopher A. Lawrence

Christopher A. Lawrence is a professional historian and military analyst. He is the Executive Director and President of The Dupuy Institute, an organization dedicated to scholarly research and objective analysis of historical data related to armed conflict and the resolution of armed conflict. The Dupuy Institute provides independent, historically-based analyses of lessons learned from modern military experience.
Mr. Lawrence was the program manager for the Ardennes Campaign Simulation Data Base, the Kursk Data Base, the Modern Insurgency Spread Sheets and for a number of other smaller combat data bases. He has participated in casualty estimation studies (including estimates for Bosnia and Iraq) and studies of air campaign modeling, enemy prisoner of war capture rates, medium weight armor, urban warfare, situational awareness, counterinsurgency and other subjects for the U.S. Army, the Defense Department, the Joint Staff and the U.S. Air Force. He has also directed a number of studies related to the military impact of banning antipersonnel mines for the Joint Staff, Los Alamos National Laboratories and the Vietnam Veterans of American Foundation.
His published works include papers and monographs for the Congressional Office of Technology Assessment and the Vietnam Veterans of American Foundation, in addition to over 40 articles written for limited-distribution newsletters and over 60 analytical reports prepared for the Defense Department. He is the author of Kursk: The Battle of Prokhorovka (Aberdeen Books, Sheridan, CO., 2015), America’s Modern Wars: Understanding Iraq, Afghanistan and Vietnam (Casemate Publishers, Philadelphia & Oxford, 2015), War by Numbers: Understanding Conventional Combat (Potomac Books, Lincoln, NE., 2017) , The Battle of Prokhorovka (Stackpole Books, Guilford, CT., 2019), The Battle for Kyiv (Frontline Books, Yorkshire, UK, 2023), Aces at Kursk (Air World, Yorkshire, UK, 2024), Hunting Falcon: The Story of WWI German Ace Hans-Joachim Buddecke (Air World, Yorkshire, UK, 2024) and The Siege of Mariupol (Frontline Books, Yorkshire, UK, 2024).
Mr. Lawrence lives in northern Virginia, near Washington, D.C., with his wife and son.

Articles: 1516


  1. Hi Chris,

    I obviously just read your column, and I have a couple comments:

    First, FM 71-2, 30 June 1977 on page 1-11 states “The battalion task force comander must be able to shift company teams rapidly from one area to another. If the enemy attacks with a regiment, US Army forces must concentrate tank killing systems of three or four company teams to stop him – one company team will not do the job. Concentration of force and superiority are essential to do this.”

    A regiment can be considered to have 9 motorized rifle companies (either BTR, BMP, or Tank), 3 tank companies, 1 recon company, and an anti-tank company for a total of 12 – 14.

    A US battalion at the time consisted of 3 maneuver companies + a CSC company for than in infantry battalions had 1 or 3 AT Platoons, for an equivalent of 4 companies. (but in the lifetime of this manual) went to 4 tank companies or four infantry companies and an anti-tank company in the the eighties.

    3:14 = a ratio of 1:4.6 (tank battalion TF with three companies)
    4:14 = a ratio of 1:3.5 (Early infantry battalion TF with 4 companies or a late tank battalion TF with 4)
    5:14 = a ratio of 1:2.8 (late infantry battalion TF with 4 manuever companies an an AT Company).

    When I went to CAS3 in 1983, we had ST which talked about the 3:1 ratio but also used a planning sheet that divided the battle area into 2 – 4 columns and 3 rows for the Covering Force, Main Battle, and Reserve areas of a division. For our planning, we used (as I recall) a ratio of 1:6 in the Covering Force, 1:3 in the MBA, and 1:6 for the Reserve. This also included use of attack helicopters.

    We did not inventory systems to determine the ratio so this ratio is probably not quite the same as you would use in your calculations.

    Finally, in the early 90’s after Desert Storm, the 1st ID had a gunnery exercise for at least its tank battalions called PKB – Platoon Kills Battalion. This was with M1A1s. I don’t remember the results of the engagements or what the standard was. Perhaps someone else does.

    While evaluating companies of the 2nd Brigade, we used a simple technique to estimate if we thought a company could kill a battalion or more. I shall simplify it even more for this by just using a tank company (and feel free to substitute different numbers, I’m making this up this morning so the numbers might be way off):

    Determine the number of tank killing systems you have (14 M1A1s)
    Ph = .75
    Pk = .75
    Rounds per minute: 4/tank

    Kills/MInute = 14*.75*.75*4 = 31

    Enemy systems presented in the killing zone: 31 BMP + 14 Tanks = 45.
    Size of the kill zone: 1000m x 2500 meters
    Enemy advance rate: 400m/minute (15 mph)
    Time for the enemy to move through the kill zone = 2500/300 = 8.3
    Time that you have to observe the enemy (derived by driving vehicles through the kill zone (if you have time and the situation permits) and timing how much time you see them give the rate of advance. It will be less than 8.3 minutes of course, so lets say 4.

    Given no friendly casualties, we can theoretically destroy the enemy array in about two minutes of exposure. Of course this was get extended when you factor in losses.

    For an illustrative training story, my tank company (originally composed of 10 tanks and 4 M113s) as part of a battalion, was to defend a battle position after conducting a 100km night road march, I was reduced to 4 tanks and 1 M113, due to accidents, people getting lost, and throwing track. Just as I moved into position, an OPFOR regiment (-) consisting of the other two battalions in the brigade, began its attack. I estimated I had a battalion aimed at my battle position. Using MILES, we destroyed the battalion in about 8 – 10 minutes without any losses. The enemy probably consisted of 3 infantry companies, a tank company, and an AT Platoon (28 tanks, 36+ TOW, and 84 M113, so at the beginning only the tanks were a factor and the AT Company did not become visible in the attack till the end. They never closed to Dragon range (of which I had none on the position by the way).

    Obviously, the other companies of the battalion contributed to the fight, but the OC singled out my companies performance as the key factor and was dumbfounded to learn that it was not my whole company. He remarked at the end, “I admit I had no idea of the power of a company team and to watch my battalion reduced to nothing in less than 10 minutes was very sobering, and you only had 4 tanks?”

    These are only anecdotes and probably poorly remembered memories (except for the FM 71-2 quote) but do provide some context to the quote.

    Kind regards


  2. The “3:1” mantra fits with the emphasis that one hears about needing/wanting/requiring “overwhelming force” when attacking. Who doesn’t want overwhelming force (unless that would reduce forces needed for other purposes)? So, someone hears something about a “3:1 rule” and that seems to fit with a desire for overwhelming force; thus, 3:1 it is!

    Reminds me of the line from Gettysburg (both the movie and the battle) that parlays the desirability for defending on higher ground into a quip about progressivbely higher ground being available as one moves further west from Gettysburg!

Leave a Reply

Your email address will not be published. Required fields are marked *