Three books to be published this year

I have been quiet about the books that I am working on and publishing because some of them have been slower to release than expected.

I have three books coming out this year. The UK hardcover release dates are:

Aces at Kursk: 30 July 2023
The Battle of Kyiv: 30 August 2023
The Hunting Falcon: 30 September 2023

The U.S. hardcover release dates according to Amazon.com are:

Aces at Kursk: 30 September 2023
The Battle of Kyiv: 30 October 2023
The Hunting Falcon: 31 October 2023

So for a brief moment in time I will be pumping out a book a month. I am currently working on two other books (they might be released in 2023) and I have one other listed on Amazon.com (UK) called “The Other Battle of Kursk” with a release date of 16 July 2024. This is the book “The Battle of Tolstoye Woods.” This has been discussed with the publisher and I may get it published in 2024.

Of course, the only way one gets a book done is to ignore everything else. If some people feel I should be responding in a timely manner to their emails or requests, there is a reason I have not been. Sorry. Three books coming out in one year is evidence that there is some validity to that.

Some relevant links related to Aces at Kursk:

Aces at Kursk – Chapter Listing | Mystics & Statistics (dupuyinstitute.org)

Aces at Kursk | Mystics & Statistics (dupuyinstitute.org)

Is this my last Kursk book? | Mystics & Statistics (dupuyinstitute.org): The answer is no. I will be working on (and maybe completing) The Battle of Tolstoye Woods in 2024.

145 or 10? | Mystics & Statistics (dupuyinstitute.org)

So did Kozhedub shoot down 62, 64 or 66 planes? | Mystics & Statistics (dupuyinstitute.org)

5th Guards Fighter Regiment, 7 July 1943 | Mystics & Statistics (dupuyinstitute.org)

The 728th Fighter Regiment on 16 July 1943 | Mystics & Statistics (dupuyinstitute.org)

Soviet versus German kill claims at Kursk | Mystics & Statistics (dupuyinstitute.org)

So What Was Driving the Soviet Kill Claims? | Mystics & Statistics (dupuyinstitute.org)

Aces at Kursk – Chapters | Mystics & Statistics (dupuyinstitute.org)

And related to The Battle for Kyiv: most of this blog from December 2021 through April 2022:

December | 2021 | Mystics & Statistics (dupuyinstitute.org)

January | 2022 | Mystics & Statistics (dupuyinstitute.org)

February | 2022 | Mystics & Statistics (dupuyinstitute.org)

March | 2022 | Mystics & Statistics (dupuyinstitute.org)

April | 2022 | Mystics & Statistics (dupuyinstitute.org)

And related to Hunting Falcon:

Award Dates for the Blue Max (1916) | Mystics & Statistics (dupuyinstitute.org)

 

Advance Rates in Combat

M4A3E2

Advance Rates in Combat:

                Units maneuver before and during a battle to achieve a more favorable position. This maneuver is often unopposed and is not the subject of this discussion. Unopposed movement before combat is often quite fast, although often not as fast as people would like to assume. Once engaged with an opposing force, the front line between them also moves, usually moving forwards if the attacker is winning and moving backwards for the defender if he is losing or choosing to withdraw. These are opposed advance rates. This section is focused on discussing opposed advance rates or “advance rates in combat.”

            The operations research and combat modeling community have often taken a short-hand step of predicting advance rates in combat based upon force ratios, so that a force with a three-to-one force ratio advances faster than a force with a two-to-one force ratio. But, there is not a direct relationship between force ratios and advance rates. There is an indirect relationship between them, in that higher forces ratios increased the chances of winning, and winning the combat and the degree of victory helps increase advance rates. There is little analytical work that has been done on this subject.[1]

            Opposed advance rates are very much influenced by 1) terrain, 2) weather and 3) the degree of mechanization and mobilization, in addition to 4) the degree of enemy opposition. These four factors all influence what the rates will be.

            In a study The Dupuy Institute did on enemy prisoner of war capture rates, we ended up coding a series of engagements by outcome. This has proven to a useful coding for the examination of advance rates. Engagements codes as outcomes I and II (limited action and limited attack) are not of concern for this discussion. The engagement coded as attack fails (outcome III) is significant, as these are cases where the attacker is determined to have failed. As such they often do not advance at all, sometimes have a very limited advance and sometimes are even pushed back (have a negative advance). For example, in our work on the subject, of our 271 division-level engagements from Western Europe 1943-45 the average advance rate was 1.81 kilometers per day. For Eastern Europe in 1943 the average advance rate was 4.54 kilometers per day based upon 173 division-level engagements.[2] These advance rates are irrespective of what the force ratios are for an engagement.

            In contrast, in those engagements where the attacker is determined to have won and is coded as attacker advances (outcome IV) the attacker advances an average of 2.00 kilometers in the 142 engagements from Western Europe 1943-45. The average force ratio of these engagements was 2.17. In the case of Eastern Europe in 1943, the average advance rate was 5.80 kilometers based upon 73 engagements. The average force ratio of these engagements was 1.62.

            We also coded engagements where the defender was penetrated (outcome V). These are those cases where the attacker penetrated the main defensive line of the defending unit, forcing them to either withdraw, reposition or counterattack. This penetration is achieved by either overwhelming combat power, the end result of an extended operation that finally pushes through the defenses, or a gap in the defensive line usually as a result of a mistake. Superior mechanization or mobility for the attacker can also make a difference. In those engagements where the defender was determined to have been penetrated the attacker advanced an average of 4.12 kilometers in 34 engagements from Western Europe 1943-45. The average force ratio of these engagements was 2.31. In the case of Eastern Europe in 1943, the average advance rates was 11.28 kilometers based upon 19 engagements. The average force ratio of these engagements was 1.99.

            This clearly shows the difference in advance rate based upon outcome. It is only related to force ratios to the extant the force ratios are related to producing these different outcomes.

 

            Also of significance is terrain and weather. Needless to say, significant blocking obstacles like bodies of water, can halt an advance and various rivers and creeks often considerably slow them, even with engineering and bridging support. Rugged terrain is more difficult to advance through and easier to defend and delay then smoother terrain. Closed or wooded terrain is more difficult to advance through and easier to defend and delay then open terrain. Urban terrain tends to also slow down advance rates, being effectively “closed terrain.” If it is raining then advance rates are slower than in clear weather. Sometimes considerably slower in heavy rain. The season it is, which does influence the amount of daylight, also affects the advance rate. Units move faster in daylight than in darkness. This is all heavily influenced by the road network and the number of roads in the area of advance.

            No systematic study of advance rates has been done by the operations research community. Probably the most developed discussion of the subject was the material assembled for the combat models developed by Trevor Dupuy. This included addressing the effects of terrain and weather and road network on the advance rates. A combat model is an imperfect theory of combat.

            Even though this combat modeling effort is far from perfect and fundamentally based upon quantifying factors derived by professional judgment, tables derived from this modeling effort have become standard presentations in a couple of U.S. Army and USMC planning and reference manuals. This includes U.S. Army Staff Reference Guide and the Marine Corps’ MAGTF Planner’s Reference Manual.[3]

The original table, from Numbers, Predictions and War, is here:[4]

 

STANDARD (UNMODIFIED) ADVANCE RATES

 

                                                                                    Rates in km/day

                                                Armored          Mechzd.          Infantry           Horse Cavalry

                                                Division           Division           Division           Division or

                                                                                                or Force           Force

Against Intense Resistance

    (P/P: 1.0-1.1O)

Hasty defense/delay                4.0                   4.0                   4.0                   3.0

Prepared defense                    2.0                   2.0                   2.0                   1.6

Fortified defense                     1.0                   1.0                   1.0                   0.6

 

 Against Strong/Intense Resistance

    (P/P: 1-11-125)

Hasty defense/delay                5.0                   4.5                   4.5                   3.5

Prepared defense                    2.25                 2.25                 2.25                 1.5

Fortified defense                     1.25                 1.25                 1.25                 0.7

 

Against Strong Defense

    (P/P: 1.26-1.45)

Hasty defense/delay                6.0                   5.0                   5.0                   4.0

Prepared defense                    2.5                   2.5                   2.5                   2.0

Fortified defense                     1.5                   1.5                   1.5                   0.8

 

Against Moderate/Strong Resistance

    (P/P: 1.46-1.75)

Hasty defense                         9.0                   7.5                   6.5                   6.0

Prepared defense                    4.0                   3.5                   3.0                   2.5

Fortified defense                     2.0                   2.0                   1.75                 0.9

 

Against Moderate Resistance

    (P/P: 1.76-225)

Hasty defense/delay                12.0                 10.0                 8.0                   8.0

Prepared defense                    6.0                   5.0                   4.0                   3.0

Fortified defense                     3.0                   2.5                   2.0                   1.0

 

Against Slight/Moderate Resistance

    (P/P:2.26-3.0)

Hasty defense/delay                16.0                 13.0                 10.0                 12.0

Prepared defense                    8.0                   7.0                   5.0                   6.0

Fortified defense                     4.0                   3.0                   2.5                   2.0

 

Against Slight Resistance

    (P/P: 3.01-4.25)

Hasty defense/delay                20.0                 16.0                 12.0                 15.0

Prepared defense                    10.0                 8.0                   6.0                   7.0

Fortified defense                     5.0                   4.0                   3.0                   4.0

 

Against Negligible/Slight Resistance

    (P/P:4.26-6.00)

Hasty defense/delay                40.0                 30.0                 18.0                 28.0

Prepared defense                    20.0                 16.0                 10.0                 14.0

Fortified defense                     10.0                 8.0                   6.0                   7.0

 

Against Negligible Resistance

    (P/P: 6.00 plus)

Hasty defense /delay               60.0                 48.0                 24.0                 40.0

Prepared/fortified defense      30.0                 24.0                 12.0                 12.0

 

*Based on HERO studies: ORALFORE, Barrier Effectiveness, and Combat Data Subscription Service.

** For armored and mechanized infantry divisions, these rates can be sustained for 10 days only; for the next 20 days standard rates for armored and mechanized infantry forces cannot exceed half these rates.

 

                This is a modeling construct built from historical data. These are “unmodified” rates. The modifications include: 1) General Terrain Factors (ranging from 0.4 to 1.05 for Infantry (combined arms) Force and from 0.2 to 1.0 for Cavalry or Armored Force, 2) Road Quality Factors (addressing Road Quality from 0.6 to 1.0 and Road Density from 0.6 to 1.0), 3) Obstacles Factors (ranging from 0.5 to 0.9 for both a River or steam and for Minefields), 4) Day/Night with night advance rate one-half of daytime advance rate and 5) Main Effort Factor (ranging from 1.0 to 1.2). These last five sets of tables are not shown here, but can be found in his writings.[5]

 

 

[1] The most significant works we are aware of is Trevor Dupuy’s ORALFORE study in 1972: Opposed Rates of Advance in Large Forces in Europe (ORALFORE), (TNDA, for DCSOPS, 1972); Trevor Dupuy’s 1979 book Numbers, Predictions and War; and a series of three papers by Robert Helmbold (Center for Army Analysis): “Rates of Advance in Land Combat Operations, June 1990,” “Survey of Past Work on Rates of Advance, and “A Compilation of Data on Rates of Advance.”

[2] See paper on the subject by Christopher A. Lawrence, “Advance Rates in Combat based upon Outcome,” posted on the blog Mystics & Statistic, April 2023. In the databases, there were 282 Western Europe engagements from September 1943 to January 1945. There were 256 Eastern Front engagements from February, March, July and August of 1943.

[3] See U.S. Army Staff Reference Guide, Volume I: Unclassified Resources, December 2020, ATP 5-0.2-1, pages xi and 220; and MAGTF Planner’s Reference Manual, MSTF pamphlet 5-0.3, October 2010, page 79. Both manuals include a table for division-level advances which is derived from Trevor Dupuy’s work, and both manuals contain a table for brigade-level and below advances which are calculated per hour that appear to also be derived from Trevor Dupuy’s division-level table. The U.S. Army manual gives the “brigade and below” advance rates in km/hr while the USMC manual, which appears to be the same table, gives the “brigade and below” advance rates in km/day. This appears to be a typo.

[4] Numbers, Predictions and War, pages 213-214. The sixth line of numbers, three numbers were changes from 1.85 to 1.25 as this was obviously a typo in the original.

[5] See Numbers, Predictions and War, pages 214-216.

 

 

The actual paper this was drawn from is here: Advance Rates in Combat

Average Losses per Day in Division-level Engagements on the Eastern Front in 1943

Trevor N. Dupuy, among his 56 verities of combat, states that “Average World War II division engagement casualty rates were 1-3% a day.”[1]

This was based primarily on his research on the Western Front during World War II. For example, just to draw from data from real world experience, the average losses per U.S. division in 82 selected engagements was 1.2% per day in 1943-44. The average strength of these divisions was 14,000. The average loss per German division in 82 selected engagements was 1.8% per day. The average strength of these divisions was 12,000. These engagements were all from the Italian Campaign and the European Theater of Operations (primarily France).[2]

Now for Germany versus the Soviet Union, the loss rates in 1943 were higher for both sides. We do have daily unit records and have assembled them into a series of 192 division-level engagements for the southern part of Battle of Kursk in July 1943 and 64 division-level engagements for the battles around Kharkov in February, March and August of 1943. They show the following statistics:[3]

Battle of Kursk:

                                                            Average Losses:            Average           Average

                                             Cases     Mean     Median             Strength          Force Ratio

Germans attacking               124         0.99        0.78                21,487               1.44

Germans defending                68         0.68        0.52               16,945                0.91

Soviets attacking                    68         3.25        1.67               18,631                1.10

Soviets defending                 124         4.31        3.82               14,930                0.69

 

Battles for Kharkov:

Germans attacking                 35         0.58        0.48                17,326                2.77

Germans defending                29         0.64        0.50                14,834                0.87

Soviets attacking                    29         2.18        1.56                 17,001               1.15

Soviets defending                   35         5.21        3.05                  6,837                0.36

 

Slightly different figures will be created using differing selection criteria, but out of the 124 cases of the Germans attacking at Kursk, in only two cases were German losses greater than 3% [4]. They were both cross-river attacks done on 5 July 1943 by the 106th and 320th Infantry Divisions. German losses at Kursk while defending never exceeded 3%. German losses in the Kharkov engagements never exceeded 2% a day.

Soviet losses exceeded 3% per day in 24 cases while attacking at Kursk and exceeded 6% in ten of those cases. Soviet losses exceeded 3% per day in 67 cases while defending at Kursk (in over half the cases) and exceeded 6% in 39 of those cases. Soviet losses exceeded 3% a day in only two cases while attacking at Kharkov and in 16 cases while defending, of which in seven of those cases Soviet losses exceeded 6% per day.

 

 

[1] See Colonel Trevor N. Dupuy, Understanding War: History and Theory of Combat (Paragon House Publishers, New York, 1987), page 179.

[2] See Dupuy, Understanding War, page 169. Note that all these WWII engagements were tagged with the note that the data was approximate, more research required. The Dupuy Institute has 282 division-level engagements from the Italian Campaign and ETO that are created from the unit records of both sides. We have not done this comparison using our further developed and more extensive data collection, but suspect the results would be similar.

[3] The data used for this calculation is presented for the Battle of Kursk in a series of 192 engagement sheets in the book by Lawrence, Kursk: The Battle of Prokhorova. This work can be cross-checked by others. The data used for the battles around Kharkov have not been published yet. It might be at some point in the future. The data is currently company proprietary of The Dupuy Institute.

[4] More precise would be to remove all the engagements coded as limited action and limited attack, leaving only those coded as failed attack, attack advances, defender penetrated, defender enveloped and other. In the 124 Kursk cases of the German attacking this would remove 15 cases of limited action, 14 cases of limited attack, and 26 cases where the outcome has not been coded yet. The force ratio is now up to 1.56-to-1 and the average German percent losses are 1.25% while the average Soviet percent losses are 5.83%. Conversely, in the 68 cases where the Soviet are attacking, there are 7 cases are limited action, 9 cases are limited attack and 33 cases where the outcome has not been coded yet. The force ratio for these remaining 19 cases is 1.27 and average Soviet percent losses are 4.05 while the average German percent losses are 0.86.

 In all cases, the mean is calculated as a weighted mean, meaning that it is based upon total strengths compared to total losses. The median is calculated, naturally, by finding the midpoint of all 124 or 68 engagements.

 

The actual paper this was drawn from is here: Average Losses per Day

Presentations from HAAC – Fitting Lanchester Equations

The third presentation of the first day was given by Dr. Tom Lucas of the Naval Post-Graduate School (49 slides):  Fitting Lanchester equations to time-phased battle data

The two of the databases used for this work were the Ardennes Campaign Simulation Data Base (ACSDB) and the Kursk Data Base (KDB). I was the program manager for both of these efforts.

———-

We had a total of 30 presentations given at the first Historical Analysis Annual Conference (HAAC). We have the briefing slides from most of these presentations. Over the next few weeks, we are going to present the briefing slides on this blog, maybe twice a week (Tuesdays and Thursday). In all cases, this is done with the permission of the briefer. We may later also post the videos of the presentations, but these are clearly going to have to go to another medium (Youtube.com). We will announce when and if these are posted.

The briefings will be posted in the order given at the conference. The conference schedule is here: Schedule for the Historical Analysis Annual Conference (HAAC), 27-29 September 2022 – update 16 | Mystics & Statistics (dupuyinstitute.org)

The conference opened with a brief set of introductory remarks by me. The seven supporting slides are here: Opening Presentation

It was then followed by a briefing by Dr. Shawn Woodford on Studying Combat; The “Base of Sand” Problem: 20220927 HAAC-Studying Combat

The second presentation of the first day was given by me. It is here (45 slides): Data for Wargames (Summary) – 2

Vincent B. Hawkins has passed away

I just heard that Vincent Hawkins, former HERO and DMSI employee, passed away yesterday. Born in August 1955 he was 66 years old.

He came to work for Trevor Dupuy’s HERO/DMSI around 1986 and was there when I arrived. Always outgoing and welcoming, he had a master’s degree in history, was fluent in German and led the German research team for the Ardennes Campaign Simulation Data Base (ACSDB). He was the co-author of one chapter in Trevor Dupuy’s Understanding Defeat.

He continued at DMSI until around 1991, when it closed down. He was the editor for weekly defense newsletter they were doing, which I thought was a worthwhile effort. He then did some historical research for George Kuhn’s casualty estimation efforts at LMI.

Always outgoing and humorous, Vince was a good friend at DMSI. His office was always one of my stops when I took a break for coffee.

The Key to Victory: Machine Learning the Lessons of History

Robert L. Helmbold has published a new book (his first book) called The Key to Victory: Machine Learning the Lessons of History. Bob Helmbold was one of the senior analysts at CAA (Center of Army Analysis). It was published by MORS (Military Operations Research Society) with the help of Dean Hartley, formerly of Oakridge. This is Bob Helmbold’s first book, and at 91 years old, I hope to see a dozen more from him.

Bob Helmbold will be doing a virtual presentation on this on the second day (Wednesday the 28th of September) of the Historical Analysis Annual Conference (HAAC).

The book is only available through Barnes and Noble, not through Amazon. A link to it is here: The Key to Victory: Machine Learning the Lessons of History: by Robert Helmbold, Paperback | Barnes & Noble® (barnesandnoble.com)

 

Some Background on TDI Data Bases

The Dupuy Institute (TDI) are sitting on a number of large combat databases that are unique to us and are company proprietary. For obvious reasons they will stay that way for the foreseeable future.

The original database of battles came to be called the Land Warfare Data Base (LWDB). It was also called the CHASE database by CAA. It consisted of 601 or 605 engagements from 1600-1973. It covered a lot of periods and lot of different engagement sizes, ranging from very large battles of hundreds of thousand a side to small company-sized actions. The length of battles range from a day to several months (some of the World War I battles like the Somme).

From that database, which is publicly available, we created a whole series of databases totaling some 1200 engagements. There are discussed in some depth in past posts.

Our largest and most developed data is our division-level database covering combat from 1904-1991 of 752 cases: It is discussed here: The Division Level Engagement Data Base (DLEDB) | Mystics & Statistics (dupuyinstitute.org)

There are a number of other databases we have. They are discussed here: Other TDI Data Bases | Mystics & Statistics (dupuyinstitute.org)

The cost of independently developing such a database is given here: Cost of Creating a Data Base | Mystics & Statistics (dupuyinstitute.org)

Part of the reason for this post is that I am in a discussion with someone who is doing analysis based upon the much older 601 case database. Considering the degree of expansion and improvement, including corrections to some of the engagements, this does not seem a good use of their time., especially as we have so greatly expanded the number engagements from 1943 and on.

Now, I did use some of these databases for my book War by Numbers. I am also using them for my follow-up book, currently titled More War by Numbers. So the analysis I have done based upon them is available. I have also posted parts of the 192 Kursk engagements in my first Kursk book and 76 of them in my Prokhorovka book. None of these engagements were in the original LWDB. 

If people want to use the TDI databases for their own independent analysis, they will need to find the proper funding so as to purchase or get access to these databases. 

More Force Ratio Posts

The last two posts I made on force ratios was drawn from my book War by Numbers. There are additional posts I did early last year on the subject based upon my in-process follow-on book More War by Numbers. They are summarized here:

Summation of Human Factors and Force Ratio posts | Mystics & Statistics (dupuyinstitute.org)

I have been fairly diligent about making sure the “categories” that are listed on the right hand column of the blog are maintained. Therefore, clicking on Force Ratio will lead you to all 29 Force Ratio related posts on this blog. There are 1,129 posts on this blog (as of this post).

 

 

More Combat Results Tables from War by Numbers

Now, the purpose of War by Numbers was not to create Combat Results Tables (CRT) for wargames. Its real purpose was to test the theoretical ideas of Clausewitz, and more particularly, Trevor N. Dupuy to actual real-world data. Not as case studies, but as statistical compilations that would show what the norms are. Unfortunately, military history is often the study of exceptions, or exceptional events, and what is often lost to the casual reader it what the norms are. Properly developed statistical database will clearly show what the norms are and how frequent or infrequent these exceptions are. People tend to remember the exceptional cases, they tend to forget the norms, if they even knew what they were to start with.

Chapters 3, 4 and 5 of War by Numbers is primarily focused on measuring human factors (which some people in the U.S. DOD analytical community seem to think are unmeasurable, even though we are measuring them). As part of that effort I ended up assemble a set of force ratios tables based upon theater and nationality. The first of these, on page 10, was in my previous blog post. Here are a few others, from page 11 of War by Numbers.

Germans attacking Soviets (Battles of Kharkov and Kursk), 1943

 

Force Ratio                          Result                                    Percent Failure   Number of cases

0.63 to 1.06-to-1.00             Attack usually succeeds      20%                        5

1.18 to 1.87-to-1.00             Attack usually succeeds        6%                      17

1.91-to-1.00 and higher      Attacker Advances                 0%                       21

 

Soviets attacking Germans (Battles of Kharkov and Kursk), 1943

 

Force Ratio                          Result                                    Percent Failure   Number of cases

0.40 to 1.05-to-1                  Attack usually fails                70%                      10

1.20 to 1.65-to-1.00             Attack often fails                    50%                      11

1.91 to 2.89-to-1.00             Attack sometimes fails          44%                       9

 

 

 

Pacific Theater of Operations (PTO) Data, U.S. attacking Japanese, 1945

 

Force Ratio                          Result                                    Percent Failure   Number of cases

1.40 to 2.89-to-1.00             Attack succeeds                        0%                     20

2.92 to 3.89-to-1.00             Attack usually succeeds        21%                      14

4.35-to-1.00 and higher       Attack usually succeeds          4%                     26

 

Force Ratios and CRTs

Page 10 for War by Numbers includes the following table:

European Theater of Operations (ETO) Data, 1944

 

Force Ratio                          Result                        Percent Failure  Number of cases

0.55 to 1.01-to-1.00             Attack Fails                         100%                       5

1.15 to 1.88-to-1.00             Attack usually succeeds      21%                       48

1.95 to 2.56-to-1.00             Attack usually succeeds      10%                       21

2.71-to-1.00 and higher       Attacker Advances                 0%                       42

 

Many commercial wargames have something called a CRT or Combat Results Table. It is based upon force ratios. For example, this was one of the earliest CRTs used on Avalon Hill Games in the 1960s.

As can been seen from this Combat Results Table, at 1-to-1 the chances of an attack winning is one-in-three. At 2-to-1 odds the chances of the attacker winning is either the same as the defender winning or is a two-thirds chance of winning. At 3-to-1 odds, the attacker will always win.

Now the variable factor is the exchange result, which is defined that the defender removed everyone and the attacker removes as much as the defender. This usually results in an attacker win, if the attack has the right “spare change.” If the attacker was attacking with a single 7 strength unit against a 3 strength defender and they roll and exchange, then both units are eliminated.  

Compare that to the table from my book based upon 116 division-level engagements from the European Theater of Operations (1944-145).

Needless to say, some elements of my book War by Numbers are of interest to the commercial wargaming community.