We have not made much use of our Campaign Data Base. (See: The History of the DuWar Data Bases | Mystics & Statistics (dupuyinstitute.org)). We used it as part of the Enemy Prisoner of War (EPW) studies back in 2000-2001 and have not made use it in the last two decades. But, for a presentation I did last year on force ratios, I blew the dust off of it because I wanted to see if force ratios were different for army-level operations than for division-level engagements. I mean, in the ETO data we have (116 cases), in the force ratios ranging between 1.15-to-1 to 1.88-to1 the attacker won 79% of the time (so much for needing 3-to-1). See: The 3-to-1 rule and the War in Ukraine | Mystics & Statistics (dupuyinstitute.org). So the question became, is the pattern we see at army-level different than division-level?
The Campaign Data Base consists of 196 campaigns from 1905 to 1991. They from two days in length to 155 days in length. Only three were over 60 days in length. The problem is that the database is not complete. We assembled it, used it once and have not used it again. There are some holes. For example, we only had the starting strength ratios calculated for 163 cases, we only had the total casualty ratios calculated for 162 and only had the winner calculated for 156 cases. In most cases the missing data is available but has not been assembled. The database just needs a little tender loving care.
The average attacker strength (99 cases) was 188,909. The average defender strength (96 cases) was 95,497. This comes out to a 1.98-to-1 ratio.
The average attacker losses (176 cases) was 36,076. The average defender losses (172 case) was 47,004. This comes out to a 1-to-1.30 ratio.
The average attacker percent losses per day (163 cases) was 0.69%. The average defender percent losses per day (162 cases) was 1.85%. This comes out to a 1-to-2.68 ratio.
The starting strength ratio (163 cases) was 2.24 (2.24-to-1). The total casualty ratio was (164 cases) 1.35-to-1.
Now, the holes in the database become an issue. This are holes that can be filled given time (read: budget). We have 97 cases where the attacker is coded as the winner, and 38 cases where the defender wins. We have draws in 21 other cases. The rest (40 cases) are currently not coded.
Anyhow, this all produces the following table:
Attacker Defender Draw
Av. Attacker Strength 208,835 156,821 171,312
Av. Defender Strength 91,486 100,729 96,582
Ratio 2.28 1.56 1.77
Av. Attacker Losses 34,630 69,098 15,232
Av. Defender Losses 52,466 64,271 12,632
Ratio 0.66 1.08 1.21
Av. Attacker % per day 0.73 0.98 0.32
Av. Defender % per day 2.59 0.98 0.39
Ratio 0.28 1.00 0.82
Starting Strength Ratio 2.42 2.24 1.79
Casualty Ratio 1.04 2.51 1.22
Contemplate for a moment what this data is telling you. A few observations:
There is a difference in force ratios between winning and losing engagements (2.28-to-1 vice 1.56-to-1).
There is a difference in casualties between winning and losing engagements (0.66-to-1 vice 1.08-to-1).
The data for these army-level operations does not look significant different than for a division-level operation. This is significant.
I will stop here for a moment. This is from slides 12 – 18 for my force ratios briefing. There is more to come (because my briefings, like some of my books, are never short).
Trevor Dupuy’s argument was always that it took a combat power advantage to advance (attack successfully). This combat power calculations considers weapons, terrain, posture, air support, human factors, etc. Because of the current artillery shell shortages for the Ukrainian Army, logistics may also be a factor.
This combat power advantage often happens at 1.5-to-1 or 2-to-1. Usually is happens by around 2-to-1 (my conclusions – see War by Numbers). For example, here is my chart of force ratios for division-level combat in the European Theater of Operation (ETO) in 1944 from page 10 of War by Numbers:
FORCE RATIO…………………..RESULT……………..PERCENTAGE OF 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….ATTACK ADVANCES……………………..0…………………………………..42
A rigidly defined 3-to-1 rule tends to create an officer corps of McLellan’s. This rule-of-thumb is doing more damage than good as constructed.
What got my attention is that some people are trying to apply some 3-to-1 rule in Ukraine, and then come to the conclusion that one or the other side cannot advance because they don’t have a 3-to-1 force ratio. Yet, people have been advancing. In fall of 2022 Ukraine re-took Kherson and surrounding areas (see: 2022 Kherson counteroffensive – Wikipedia) and achieved a breakthrough at Balakliya that took back a significant portion of Donetsk province (see: Battle of Balakliia – Wikipedia) and conducted a successful offensive around Kharkiv (see: 2022 Kharkiv counteroffensive – Wikipedia). In 2023 Russia did advance on Bakhmut and took it (see: Battle of Bakhmut – Wikipedia) and in 2023/2024 Russia did advance on Avdiivka and took it (see: Battle of Avdiivka (2023–2024) – Wikipedia). I think in three for those five cases the attacker did not have anything approaching a 3-to-1 advantage. Of course, I have no reliable manpower statistics for either side in any of these five battles, so this is sort of a guess, as is most of the analysis and expert opinions on this war.
I do not know how many troops Ukraine currently has. I am guessing at least 300,000 deployed. Some people throw out figures in the 600-700,000 range. I have no idea if that are total mobilized estimates or total deployed estimates. The same with Russia, where figures of 600-700,000 are also thrown out, but not sure that is what is actually deployed in Ukraine. I am guessing some number closer to 300,000. Don’t really know, and don’t know who does for certain (see the “Force Involved’ section of this post: The Russo-Ukrainian War – Day 699 | Mystics & Statistics (dupuyinstitute.org)).
Anyhow, I gather the two sides are somewhere near parity in force size. They can certainly concentrate forces to get a local advantage. With current modern intelligence gathering capabilities, concentrating forces is often seen while it is happening and opposing side can respond promptly. So not sure where anyone can get their 3-to-1 advantage.
I did do a test recently, comparing the force ratios in a database over 700 division-level combat engagements to the force-ratios in over 100 Army-level operations. The question was whether force ratios and the success from those force ratios was different at division-level vice army-level. My tentative conclusions were that force ratios for army level campaigns had the “Same patterns as for division-level combat.”
Happy New Year to all. 2023 is over. Not the best year for many in the world. Wanted to take a moment to list out our top ten blog posts for 2023 (based upon number of hits). They are:
18. The Russo-Ukrainian War – Day 560 | Mystics & Statistics (dupuyinstitute.org) – for a while we did post daily (then two-three times a week) about the war in Ukraine. This was our most popular one of those posts. We will probably restart these again sometime this winter, like when there is a danger of the front lines again moving.
Anyhow, the blog has been quieter for the last three months. This was in part because I was on travel and in part because I needed to finish up a book (The Siege of Mariupol). To date, I have not learned how to multi-task and complete a book, so the book has had the priority. Sorry to anyone I have not responded to as a result.
The Battle for Kyiv book will be available in the U.S. on Amazon.com come 18 January 2024.
Two conferences in Norway from 31 October to 2 November that might be of interest to people. They are both in Oslo in the same week, but at different hotels:
Was searching around on YouTube yesterday on “Dupuy Institute” and ran across this video: People Always Get This Wrong – YouTube. This was posted three weeks ago. Preston Stewart is not known to me.
I am called out by name on 5:14 in the video. It is clear he pulled up one of our old reports, the charts at 6:00 and 6:14 are ours. The chart at 6:36 is ours and was later republished in War by Numbers. It appears to be abbreviated. The complete chart is on page 10 of War by Numbers. The chart at 6:44 has also been republished in War by Numbers. The chart at 7:30 is from our reports. The one high odds attack that failed on that chart was an Iraqi attack against the coalition. See: TDI – The Dupuy Institute Publications.
Anyhow, would recommend that Mr. Stewart look at Trevor Dupuy’s Understanding War, Chapter 4: The Three-to-One Theory of Combat, and at my book War by Numbers, Chapter 2: Force Ratios.
Also, he might might the following blog posts are useful:
We do have a YouTube site: The Dupuy Institute – YouTube. So far the only video posted is a test video. The husky is named Max. We may be posting some more videos there in the next couple of months. There are three subscribers to our site. I gather we can get some funding if we get a 100,000 or more subscribers. So only 99,997 to go. Please subscribe.
A friend just pointed me to a recent 2019 paper done out at C&GSC at Leavenworth. It is called “An Examination of Force Ratios” and is by Major Joshua T. Christian. It is 37 pages. It is here: AD1083211.pdf (dtic.mil)
A few notes
“The nature of the inputs required for models such as the QJM or COFM mean that they are backwards looking, require numerous inputs, effort, and time to develop which limited their effectiveness to operational planners.”
3. Page 13: Hate to nit pick, but peak strength in Vietnam was higher and earlier than what he states. There are a number of other such statements in this paper I could argue with, but will avoid doing that. See Vietnam War chart drawn from page 274 of America’s Modern Wars: Insurgency & Counterinsurgency | Mystics & Statistics | Page 4 (dupuyinstitute.org).
5. Page 14: “This section highlights the work of operations research analysts, particularly those produced by the Historical Evaluation and Research Program (HERO), ad how it contributed to the Army’s transformation of the 1960s and 1970s.”
This is an odd statement. HERO was mostly historians. There were no OR people on staff, although people like Dr. Janice Fain, Robert McQuie and Dr. James Taylor were friends of Trevor Dupuy and provided independent inputs as friends and consultants. I was the first employee with some background in quantitative analysis of historical data (primarily from econometrics). It is part of the reason I was hired in 1987.
The idea that HERO “contributed to the Army’s transformation of the 1960s and 1970s” is jolting to me. All my experience is that in general, we tended to be ignored, downplayed or just dismissed. The Army’s support for what we do is clearly demonstrated by the low levels of funding that have been provided over the decades.
6. Page 15: “…establishing Dupuy as a prominent figure in the operational research field by the 1970s.”
7. Page 26: Now he gets to discussing me. I will try to withhold commenting too much.
8. Page 27: “Lawrence utilized the Tactical Numerical Deterministic Model (TNDM), which succeeded the QJM, to conduct his analysis, and more specifically to determine the winner and loser of an engagement, assess personnel and equipment losses, and determine the rate of advance.
No, I did not. I did not use the TNDM or any combat model for any of my analysis in the book. I did due a few simple statistical comparisons but did no combat modeling. He is not the first person to have made such mistake, which can only have come about by skimming my book (vice reading the whole thing) and then making false assumptions. I do have a chapter towards the end of the book that discuss some of the validation tests we ran using the TNDM, which is what seems to confuse people, but the TNDM was not used for any of the analysis in the book. He does correctly describe the validation tests of the model.
9. “As a result, the TNDM is more frequently used by companies to develop requirements that drive the development of hypothetical weapons more so than operation planners.”
10. Pages 31-32: In his discussion of insurgencies, it is clear has not seen my book America’s Modern Wars, or Dr. Andrew Hossack’s work or the work done by CAA on this using our databases (see pages 70-77 in America’s Modern Wars). He probably needs to.
There are 34 references to Dupuy in the paper, 11 references to The Dupuy Institute, 8 references to me (I know, very vain of me), 8 references to Dr. Janice Fain, 15 references to HERO, 17 references to the QJM and 15 references to the TNDM.
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.
What catches my attention about this article is the discussion of whether “troop-to-task” ratios, also known as tie-down ratios, sometimes also known as force ratios; should be measured based upon population or based upon insurgent strength.
To quote from his article: “Throughout the Iraq and Afghanistan campaigns, American analysts and military officials referred to a 20:1,000 (2%) troop-to-population ratio for successful counterinsurgency.”
He also notes: “These troop-to-population security ratios are notoriously unreliable and have weak empirical basis for planning.”
That is more polite than how I refer to them in private. I did discuss this subject on pages 70-71 of my book America’s Modern Wars.
He then states: “Another popular way to analyze troop requirements in through troop–to-insurgent ratios.”
Popular? I have not seen anyone do this in recent times. I do have a book published on the subject (America’s Modern Wars). Perhaps I am missing out on something that is going on in the basement of the Pentagon.
He does note that “This approach falls apart at step one: Counting insurgents.”
I have a chapter on the subject (Chapter 11: Estimating Insurgent Force Size, pages 115-120). It is possible. It is not perfect or easy; but doing something vague and difficult is better than doing something that is conceptually flawed. To date, I have not seen anyone else do anything further on estimating insurgents. My work was a tentative first cut on the subject. My customers were completely uninterested in this analysis, and nothing further was done. Clearly something further needs to be done. I think that is better than doing something that is conceptually flawed.
I have discussed this before on this blog and in my book: America’s Modern Wars. My discussion of the previous RAND work on the subject is on pages 70-71. It includes the following table from our work:
If anyone can tell me from that table where a 2% figure could come from, have at it.
Listed below are a collection of four relevant blog posts on the subject (there are some 1,288 posts on this blog). We do have categories like “Insurgency and Counterinsurgency,” “Force Ratios” and “Estimating Insurgent Force Size” this blog. We have done a few posts on the subject.
Needless to say, I think that basing the “troop-to-task” ratios on population is at best marginally relevant. For example, the troop-to-task ratio for Vietnam was 88.4. We did not win that one. On the other hand, when the Symbionese Liberation Army (SLA) with its two dozen members, raised hell in San Francisco and Los Angeles in the early 1970s, doing a political assassination, kidnapping Patty Hearst, and robbing banks, we took care of it using the LA police. We did not need to deploy 2% of the population of the United States (estimated at 213 million in 1974) to deal with the SLA. We did not need to raise over 4 million troops to suppress this insurgency.
I do think the size of the insurgency is relevant.
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:
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).
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
