Firepower Part 1

V1.01 - updates 17/2/18

Headlines

After reading David Rowland's excellent The Stress of Battle: quantifying human performance in combat, I decided to try an quantify the relative casualty producing performance on the battlefield of different classes of weapons. After a great deal of research and  data manipulation I came up with the following figures:

 

Rifles

MG

Mortars

Artillery

Ratio

1.0

14.9

54.5

42.3

Casualties per "day"

 0.5

7.45

27.25

21.15

This shows that the average MG is about fifteen times more effective than a rifle and a mortar is over fifty times as effective. As Rowland demonstrated that on average a rifleman does half a casualty a day we can work out other weapons casualty producing potential

Main Essay

As a Christmas present to myself I brought a second hand copy of The Stress of Battle: quantifying human performance in combat by David Rowland (I paid considerably less than the 198 currently showing on Amazon). A useful synopsis of the findings from the book can be found here: http://www.themself.org/2013/12/book-review-the-stress-of-battle-by-david-rowlands-part-1/

I was particularly taken with the following equation, quoted from the link above: MG equivalents for casualty causing are: 9 rifles = 1 MG; 1 medium mortar (81mm) = 3 MG. Or normalised to a rifle;

1 rifle = 1 rifle , 1 MG = 9 rifles and 1 81mm Mortar = 27 rifles

Furthermore there was a a note in the book that artillery fire could be related to the effectiveness of of the 81mm Mortar by comparing the product of the sustained Rate of Fire (ROF) and the Mean Area of Effectiveness (MAE) . As luck would have it I'd compiled a fairly extensive set of ROF and MAE figures for another project so computing relative artillery firepower would be a few minutes with a spreadsheet.

When writing the BBWW2B rules I had picked the firepower factors based on experience of widely reading around the subject and having played an awful lot of wargames. None the less the factors could best be characterised as being select by "gut feeling". Obviously it would be useful to come up with better factors based on research and it looked like Rowland's formula would be just the trick. A quick look in a few books with TO&Es gave me a selection of battalion organisations to work with, so I calculated the battalion fire-power using Rowland's formula.

The good news is that battalions have pretty much the same firepower figures. On average a battalion inflicts 751 casualties a day, the highest in my chart was a 1944 German Panzer Grenadier Bataillon at 895 (those extra LMGs make a difference) and the lowest was the 1944 German Volks Grenadier Bataillon at 637 (the light manning of the battalion makes a difference despite all the heavy weapons). Note these are the final figures, rather than those I started with but the pattern was the same. This was pleasing because I could reasonably get away with using "generic" figures for battalion in BBWW2B and would not have to rate each one individually.

The bad news is that Rowland's figures seem off for mortars and  artillery. Table 1 shows the relative performances of weapons in inflicting casualties.

  Weighting Rifles MG Mortars Artillery
Dupuy TLI (basic)   1.0 10.0 78.1 780.9
Dupuy TLI (no range)   1.0 10.0 50.0 331.8
Korean War Turks 1301 1.0 12.7    
Korean War US 50894 1.0 14.3 65.3 69.1
Korea 7th Cav (intense period) 185.5 1.0 14.3 91.6 10.2
Manoeuvre Control   1.0 5.0 13.5 37.0
Rowland (adjusted) 47 1.0 6.5 69.1 45.2
Rowland (basic)   1.0 9.0 27.0  
Vietnam 9207 1.0 11.2 37.4 41.8
Vietnam 2 500 1.0 6.7 14.4  
WW2 Bourgainville 1788 1.0 7.2 38.7 49.4
WW2 Burma 369 1.0 34.1 18.4 32.3
Average   1.0 13.4 47.9 41.3
Weighted Average   1.0 13.7 58.7 62.3
Average Coloured   1.0 14.9 54.5 42.3
           
Supression   1.0 7.5 36.2 43.3

Table 1: Infantry Firepower Normalised to a Rifle

If you look at the "Rowland (basic)" line you can see Rowland's ratios expressed. As you can see the mortar rating is almost the lowest in the table. When I calculated the artillery values for my typical battalions the artillery rate was lower still, much lower than any other rating in the table.

Even a cursory look for "causative agent" for casualties on the internet indicates that "fragments" (i.e. mortars and artillery) cause 60-70% of battlefield casualties. If you apply Rowland's figures to my "average" battalion, rifles kill 56% of the casualties, MGs 37%, mortars 22% and artillery 8%. The artillery portion is from a slice of the regimental guns and (usually) a battery of divisional guns. My first thought was that by limiting the supporting artillery to a battalion slice I did not have enough guns represented. However a sensitivity analysis showed I needed to add over 100 guns to each battalion to get 60% or so casualties.

The next step was to get some detailed causative agent information. Luckily the US was a keen researcher in this area and has given us some detailed databases, one for the Bougainville campaign, one for US troops in Burma, a database of the whole Korean War, database of the 7th Cavalry's engagements in Korea and two separate studies of Vietnam casualties. Handily these are available on line

The  Bougainville and Burma data bases are the detailed and break out casualties for enemy rifles, MG, mortars and artillery. They also have data for fratricide casualties (a shocking 18% in Burma), which I subtracted form the overall casualty tables. Japanese forces on Bougainville had considerable artillery support, similar to what would be available in NWE. The forces in Burma had much less mortar and artillery support, plus much of the combat was in think jungle where it is difficult to see targets to call artillery upon. This gives a much reduced ratio of artillery and mortar casualties to rifle casualties. To compensate the proportion of MG casualties is much increased. The Burma data is quite far removed from figures in more open terrain and certainly different from the NWE battlefields studied by Rowland.

Causative agent Total casualties Dead Living
Number Percent Number Percent Number Percent
Rifle 445 24.9 143 32.1 302 67.9
Machinegun 151 8.4 87 57.6 64 42.4
Artillery 194 10.9 44 22.7 150 77.3
Mortar 693 38.8 82 11.8 611 88.2
Grenade 224 12.5 14 6.2 210 98.3
Mines 34 1.9 13 38.2 21 61.8
Miscellaneous 47 2.6 12 25.5 35 74.5
Total 1,788 100 395 22.1 1,393 77.9

Table 2: Casualties in the Bougainville Campaign

Causative agent Total casualties Dead Living
Number Percent Number Percent Number Percent
Machinegun 119 32.3 53 44.5 66 55.5
Rifle 94 25.5 24 25.5 70 74.5
Mortar 62 16.8 10 16.1 52 83.9
Grenade 52 14.1 6 11.5 46 88.5
Artillery 33 8.9 6 18.2 27 81.8
Miscellaneous 9 2.4 2 22.2 7 77.8
Total 369 100 101 27.4 268 72.6

Table 3: Casualties in the Burma Campaign

Korea has two interesting datasets. it has casualties by causative agent for al US forces in the war and it has a table for the Turkish battalion which indicates the casualties they believed they inflicted on the NKPA. The latter only deals with small arms. In the tables below the yellow rows are the summation of the next (orange) rows

Causative agent All operations1 Offensive operations Pursuit operations Maintain defensive lines Limited operations from MBP Defensive operations Withdrawal operations
  Number Percent Number Percent Number Percent Number Percent Number Percent Number Percent Number Percent
Aviation 5 0.03 0 -- 4 0.57 1 0.03 0 -- 0 -- 0 --
Land transport 27 0.15 6 0.15 3 0.43 4 0.11 4 0.13 8 0.12 2 0.65
Tank 9 0.05 2 0.05 0 -- 0 -- 4 0.13 1 0.01 2 0.65
Other 18 0.1 4 0.1 3 0.43 4 0.11 0 -- 7 0.1 0 --
Bullets, small arms 2,584 13.97 986 25.01 118 16.81 633 17.44 348 11.47 471 6.84 28 9.03
Fragments or explosives 4,883 26.39 1,222 30.98 54 7.7 1,753 48.3 1,341 44.22 508 7.38 5 1.61
Explosive projectile shells 3,859 20.86 958 24.29 47 6.7 1,317 36.28 1,130 37.26 402 5.84 5 1.61
Rockets or aerial bombs 6 0.03 0 -- 0 -- 5 0.14 0 -- 1 0.01 0 --
Land mines 305 1.65 95 2.41 0 -- 175 4.82 29 0.96 6 0.09 0 --
Boobytraps 9 0.05 4 0.1 0 -- 5 0.14 0 -- 0 -- 0 --
Grenades 97 0.52 21 0.53 0 -- 55 1.52 7 0.23 14 0.2 0 --
Other and unqualified 607 3.28 144 3.65 7 1 196 5.4 175 5.77 85 1.24 0 --
Chemical warfare agents 14 0.08 3 0.08 0 -- 5 0.14 4 0.13 2 0.03 0 --
White phosphorus 9 0.05 1 0.03 0 -- 5 0.14 1 0.03 2 0.03 0 --
Other 5 0.03 2 0.05 0 -- 0 -- 3 0.1 0 -- 0 --
Accidents in use of own weapons 112 0.61 11 0.28 2 0.28 70 1.93 9 0.3 19 0.28 1 0.32
Other and unknown instruments of war2 10,643 57.53 1,704 43.22 512 72.93 1,146 31.58 1,323 43.62 5,692 82.72 266 85.81
All other causative agents3 230 1.24 11 0.28 9 1.28 17 0.47 4 0.13 181 2.63 8 2.58
Total 18,498 100 3,943 100 702 100 3,629 100 3,033 100 6,881 100 310 100

Table 3: Percent distribution of US KIA by causative agents in Korea

 

Causative agent All operations1 Offensive operations Pursuit operations Maintain defensive lines Limited operations from MBP Defensive operations Withdrawal operations
  Number Percent Number Percent Number Percent Number Percent Number Percent Number Percent Number Percent
Aviation 96 0.13 55 0.28 33 0.02 3 0.02 0 -- 5 0.03 0 --
Land transport 454 0.63 69 0.35 64 2.43 28 0.16 19 0.15 218 1.18 56 4.38
Tank 123 0.17 20 0.1 22 0.83 16 0.19 11 0.09 38 0.21 16 1.25
Other 331 0.46 49 0.25 42 1.6 12 0.07 8 0.06 180 0.97 40 3.13
Bullets, small arms 19,833 27.42 6,764 34.66 1,139 43.32 2,658 15.15 2,018 15.65 6,670 36.1 584 45.62
Fragments or explosives 46,781 64.66 11,337 58.1 1,089 41.42 13,610 77.55 10,211 79.19 10,086 54.6 448 35.01
Explosive projectile shells 36,379 50.29 8,852 45.36 781 29.71 9,902 56.42 8,080 62.66 8,446 45.72 318 24.84
Rockets or aerial bombs 45 0.06 5 0.03 5 0.19 23 0.13 1 0.01 10 0.05 1 0.08
Land mines 2,401 3.32 599 3.07 74 2.81 1,312 7.48 272 2.11 134 0.73 10 0.78
Boobytraps 261 0.36 37 0.19 2 0.08 173 0.99 36 0.28 11 0.06 2 0.16
Grenades 6,557 9.06 1,548 7.93 161 6.12 1,961 11.17 1,655 12.83 1,144 6.19 88 6.88
Other and unqualified 1,138 1.57 296 1.52 66 2.51 239 1.36 167 1.3 341 1.85 29 2.27
Chemical warfare agents 344 0.48 90 0.47 11 0.42 95 0.54 66 0.51 77 0.41 5 0.39
White phosphorus 303 0.42 85 0.44 10 0.38 79 0.45 60 0.46 65 0.35 4 0.31
Other 41 0.06 5 0.03 1 0.04 16 0.09 6 0.05 12 0.06 1 0.08
Accidents in use of own weapons 1,377 1.9 313 1.6 90 3.42 502 2.86 119 0.92 286 1.55 67 5.23
Other and unknown instruments of war2 1,262 1.74 297 1.52 58 2.21 280 1.6 209 1.62 388 2.1 30 2.34
All other causative agents3 2,196 3.04 590 3.02 145 5.52 373 2.12 253 1.96 745 4.03 90 7.03
Total 72,343 100 19,515 100 2,629 100 17,549 100 12,895 100 18,475 100 1,280 100

Table 4: Percent distribution of US WIA by causative agents in Korea

Weapon Enemy killed or wounded Turkish soldiers involved
M1 rifle 268 65
Carbine 5 2
Pistol 4 2
Machinegun 838 16
Submachinegun 45 6
Browning automatic rifle 6 1
Hand grenade 100 17
Bazooka 6 3
Bayonet 22 9
Knife 1 1
Strangled 3 1
Burned 3 1
Total 1,301 124

Table 5: NKPA casualties inflicted by Turkish Soldiers in Korea

Table 6: US casualties in Vietnam (Vietnam 1 in Table 1)

Table 7: US casualties in Vietnam (Vietnam 2 in Table 1)

To find the relative effectiveness of weapons in these cases I needed to get an enemy TO&E. For the Bougainville campaign the intelligence summaries of the 3rd Marine Division are available on line: www.dtic.mil/dtic/tr/fulltext/u2/a639068.pdf which gives an accurate enemy OB. For the Burma campaign I assumed the opposition had the same mix of weapons as a supported Japanese Infantry Battalion, the organisation of which came from Leland Ness's excellent Rikugun Vol 1. The 7th Cavalry report has a very detailed account of the North Korean opposition. I used the proportions from that study to apply to the overall Korean data as it was clear using the full official NKPA TO&E gave highly suspect results. The Vietnam data assumes the opposition is an NVA regiment.

To generate the numbers in table 1, I divided the total casualties per weapon type by the numbers of such weapons in a battalion or division as appropriate. I then normalised the data so a rifle was shown as a factor of 1, and all other weapons were shown in proportion to a rifle.

The coloured cells indicate the places where the data was originally presented broken down into rifles, MGs, mortars and artillery. The non-coloured cells have been calculated by making assumptions that the data is similar to another data set.

For the overall Korean data I took only the offensive and defensive engagements, as in gaming these are the scenarios most likely to be fought out. For the 7th Cavalry data I took the data from what the author of the report calls the "intense period". Static warfare gives much higher proportional artillery and mortar casualties and would distort the figures for a "typical" wargames scenario.

Despite taking the intense period for the 7th Cavalry data the artillery still looks low compared to other data sets, even the Burma figures. Thus I examined the war diaries contained in the report and calculated that the artillery only fired 76% of the time compared to the mortars. I adjusted the artillery firepower score to reflect this. Even so the artillery factor is by far the lowest of any data set, for which I conclude the North Korean Artillery was not well handled in this battle. This is backed up by other ORO reports on the Korean War. The statistics for the overall war are much more in line with  other data sets, though this will have figures for many static periods which will inflate the artillery casualty rate compared to sets that only deal with battle data.

The astute reader will note that the Korean War data only has a line for "bullets, small arms", and we need it broken down into Rifles and MGs. I assumed that the ratio of casualties would be the same as for the 7th Cavalry data set. As both sets use the same TO&E data for the opposition the relative values are the same in table 1.

Both sets of Vietnam data have a similar problem, so we need to unpick the rifle and MG casualties. We have four data points:

The average figure is 59.5%, so this was used for the Vietnam calculations.

I also looked at a couple of other measures, Trevour Dupuy's famous TLI measure http://www.dupuyinstitute.org/blog/2016/11/12/what-is-the-relationship-between-rate-of-fire-and-military-effectiveness/ & https://calhoun.nps.edu/bitstream/handle/10945/26997/dimensionalanaly00clar.pdf  and the figures used in the US Army's Manoeuvre Control manual FM105-5: https://www.scribd.com/document/312035037/Maneuver-Contol-1973

The TLI is an attempt to classify the lethality of weapons based on their physical characteristics, such as rate of fire. It is interesting that when normalised to a factor of 1 for a rifle it gives 10 for an MG which is in close accordance with Rowland's figure (see table 1). The mortar and artillery scores are very high compared to others. The TLI has a range factor. I reasoned that if a weapon was causing casualties it must already be in range. So I re-ran the figures neglecting the range factor. This brought the mortar into line but the artillery factor it was still considerably higher than any other data. My conclusion is the TLI model will probably produce disproportionately high artillery casualties.

FM105-5 is a manual for running field manoeuvres. It has a section that has guidelines for umpires so they can resolve combats. This gives the numbers shown in table 1. It seems to overstate the power of the rifle thus understate the power of other weapons, though all figures are in the same ballpark as other data.

Lastly I looked for a way to make Rowland's figures fit actual casualty data more closely. The mortar data for Rowland is based on the product of the Mean Area of Effectiveness (MAE) of the weapon and its sustained Rate of Fire (ROF). Luckily I had a database of MAEs from a previous project. One issue is that MAE is hugely dependant on type of target, the ground the target is on and the arrival angle of the shell. Rowland is coy about saying which criteria he used but I suspect that its for troops standing in the open in open ground. Those criteria emphasise the effectiveness of mortar bombs over artillery. As one of the issues with Rowland's data is that artillery produces insufficient casualties compare to mortars I changed the MAEs to those for men lying prone. This reduced the artillery MAE by 40% but the mortars by 60%. This marginally improved the artillery numbers but not enough. Next I removed the ROF factor. Mortars generally have a higher ROF than artillery, so be removing the ROF this again boosted the artillery compared to the mortars. Removing the ROF factor is valid as its the number of missions that can be fired in a given time not how fast the shells for those missions arrive that is key. This finally put mortar and artillery fire on a par effectiveness wise. However the casualty ratios were still off compared to other data sets. I realised that Rowland's data was only for defences. Data from Korea shows that the effect of different types of weapons changes depending whether they are used in attack or defence. Artillery and mortars cause more casualties, proportionally, in defence that rifles and MGs. By finding these ratios and applying to the modified Rowland data, we get the "Rowland (adjusted)" entry in table 1. These factors are more in line with historical totals though the MG figure is fairly low.

So far we have only looked at the physical effects of weapons on soldiers. However much of weapons' effect is psychological. A great deal of research has been done on the suppressive effect of weapons, for example: http://handle.dtic.mil/100.2/ADA081134. In the same way as we can normalise the destructive effect of a weapon to the destructive effect of a rifle we can do the same with the suppressive effect. This is reported on the suppression line of table 1. Its interesting that the suppressive effects of weapons are very much in line with the destructive effects. Form a game designer's point of view it means an integrated results table, like that in BBB, that includes both suppression and destruction is a reasonable way to model both effects. As an aside I am starting to believe that most peace time studies grossly under-rate the suppressive effect of fire, but that's a subject for another essay.

Averages

We have multiple data points which we need to distil down to a representative average. In Table 1 there are three averages. None of them use the data on the grey lines. The line that says average is an average of al the non-grey cells. The weighted average gives more weight to the larger databases and the average (coloured) only uses only the coloured data and is not weighted.

The weighted average is not particularly useful as its dominated by the Korea data. The Korea data has long periods of static warfare which tends to show a much higher proportion of artillery casualties, so it's not representative of high intensity conflict. It also seem spurious to emphasise the Korean experience over, for example, the WW2 data.

The average (coloured) I consider the "best" average as its not affected by manipulation of data to break down small arms and fragmentation data. However its not very far from the overall average which seems to confirm my data manipulation as reasonably valid.

The 7th Cavalry artillery figure is so low and such an outlier that I removed it from the coloured average. For reading other ORO reports on the conflict its clear that North Korean artillery was poorly handled and fired infrequently, thus is not representative of the normal destructive effect of shells. However, it is a clear indication of the effect of doctrine on effectiveness.

Firepower

The following table shows the relative effects of weapons in causing infantry casualties.

 

Rifles

MG

Mortars

Artillery

Ratio

1.0

14.9

54.5

42.3

Casualties per "day"

 0.5

7.45

27.25

21.15

This is saying that the average MG is nearly 15 times as effective as a rifle, and that a mortar is fifty times as effective. If we accept Rowland's original thesis that rifles cause half a casualty a day we can derive proportional figures for other arms. Of course most units are not in combat continuously for 24hrs so just dividing the daily rate by 24 will not give a realistic hourly rate.

Further Questions

Are all rifles created equal? Rowland's data was derived from battles with bolt action rifles. He had no problem comparing his results with those from exercises using semi-automatic rifles. However the Vietnam data is for US forces facing enemies armed with the fully automatic AK-47. Does it make a difference?

Update 17/2/18: The author has done some research on this and the short answer is that it doesn't make any difference. See the Rules of Infantry Combat

What is a realistic hourly rate? Which is another way of saying how long on average are soldier engaged in intense combat for? This is vital if ewe are to use the figures in games development.

All MGs are most certainly not created equal. Can we work out factors for automatic rifles, LMGs and MMGs? The same for mortars and artillery?

What about other weapons, bayonets, RPGs and Grenades?

What about tanks and armour casualties?

Do the ratios hold for the horse and musket period?

Update 17/2/18: The author has done some research on this. It seems an artillery piece is worth at most 75 muskets, though this is sensitive to the level of artillery casualties. 75 casualties only holds if you believe that 20% of casualties are caused by artillery fire. Many observers hold the percentage is 10%, so that would make a an artillery piece worth 36 muskets. See The Tactics and Experience of Battle in the Age of Napoleon by Rory Muir for a discussion of this.