carmen510
Deity
Well, I just don't find spreadsheets that useful, though they might be to some. That might be biased by the fact I have almost never used them though. 
WORKSHOP: Universal Simulationist Military System
- Thread starter Symphony D.
- Start date
I think that spreadsheets are an age-related affliciton.
WRONG! WRONG! WRONG!
I'm only 14 and love spreadsheets, especially yours Birdy.
....
....
....
But now I'm a tiny bit scared that Symphony is going to scold me for wondering of topic.
carmen510
Deity
Grammar Nazi Mode: Its actually wandering off-topic, not 'wondering of topic'.
Anyways, I'll stop with the spreadsheet talk.
I've read the entire formula, and its still a bit fuzzy for me. (Hence the original reason why I actually didn't want to use it) Is there any way to simplify the math, or do I just suck?
Anyways, I'll stop with the spreadsheet talk.
I've read the entire formula, and its still a bit fuzzy for me. (Hence the original reason why I actually didn't want to use it) Is there any way to simplify the math, or do I just suck?
To keep this thread on Sym's system, I will post my combat resolution model in my "Black Box" thread.
How about Hastings?
http://forums.civfanatics.com/showpost.php?p=7473732&postcount=52
Fair enough. But finding enough details on that many battles will be a challenge.
2nd Punic War: Zama, Cannae, Trebbia, Lake Trasimeno
Greek Wars: Plataea, Marathon, Mantinea, Delium, Leuctra
Alexander: Granicus, Issus, Gaugamela
Early Roman: Pynda, Raphia, Cynoscephalae, Magnesia
Ok there is a nice collection of battles. What is next?
Fair enough. But finding enough details on that many battles will be a challenge.
2nd Punic War: Zama, Cannae, Trebbia, Lake Trasimeno
Greek Wars: Plataea, Marathon, Mantinea, Delium, Leuctra
Alexander: Granicus, Issus, Gaugamela
Early Roman: Pynda, Raphia, Cynoscephalae, Magnesia
Ok there is a nice collection of battles. What is next?
Symphony D.
Deity
Retroactively deleted.
So, problems with this list, or at least qualifications. Due to a tactic employed by the Romani commander on the field, the elephants at Zama must be discounted. Plataia's figures are if anything less exact than those of Gaugamela. Mantineia - I assume you mean the 418 BC(E) battle, not the 362 BC(E) one - is possible, but I'm not sure how you're supposed to represent the willingness of the Argive Thousand to let their fellow-countrymen die out of oligarchic spite. Delion works. Leuktra...is there any mechanism for demonstrating the device of the deep column of attack, plus the echeloned formation? I do not know. (And I would suggest that the training factor would be rather difficult to describe there, comparing Epaminondas' new model Theban army to the usual Spartan homoioi of Kleombrotos.) Pydna is bad because it relies on the disorder of the Makedonian phalangitai as they went over rough terrain; how is that meant to be represented? Raphia is okay I suppose, but it's not well documented. With Kynoskephalai, one must be sure to account for the aforementioned phalangial disorder that can be seen at Pydna. And Magnesia turned on the sudden absence of the Seleukid cavalry under Antiochos, which decided, in rather Ipsos-like fashion, to pursue their enemy off the field. QJM(A)'s ability to account for something like that...?
Symphony D.
Deity
Retroactively deleted.
No it is not a lost cause. You have to take the next step and show by example what you want people to do. this is new and different. Youhave to lead people to the water. You need to show your methodology in a concrete way.
Choose a simple battle like Cannae
List the relevant comparatives for each army
Post an intelligible, excel useable formula for each factor you will use
Post your results for each of the various success factors
Draw conclusions
By seeing exactly how you think it should be done, you will get better consistency of results.
Yes, you have to walk everyone though it at least once. If you don't, then everyone will do their own way (if they do it at all) and you will reprimand them for not following non existent directions. If you want this project to make any progress, you have to lead it.
Dach: Of course there are problems. War is messy and rarely fits into an organized pattern. Battles are won and lost on things that cannot be planned or programmed (Marengo). In the Ancient world, data is a tough issue and all you can do is state your assumptions.
Birdjag, I'm mostly worried about coming up with the 'correct' outcome.
So to represent the departure of the cavalry from the battlefield, they'd just be killed off? Hurm.
Symphony D.
Deity
Retroactively deleted.
You have missed the point. The book you posted is not suitable as a model for what you propose. It needs to be spelled out in NESer English step by step, or people will not participate.Yes, because I did not give an entire chapter of a book with multiple examples laid out about as clearly as they can be, with a step-by-step methodology to boot.What you are saying is that somehow an example becomes suddenly comprehensible if I make it, which is nonsense, as is the mandate of building an Excel model now when that is precisely the end-goal of the program. Calculators are not advanced and mystical technology beyond the pale of mortal comprehension, particularly as virtually every person on this forum by now probably has at least a TI-83 grade calculator, and I would assume access to pens and paper.
The ancient world does not need most of the variables used, so as leader of this project it is your job to distill it down to what is needed. This should not be a test to see who can and cannot untangle the book. If that is your goal, then say so and we can all go on to something else. If you want this to move forward and have other people contribute to it, then you have to prepare the way.
An example is paramount to understanding. Not only how the process works, but as to what you want and expect. If you are unwilling to provide one, what does that say about your committment to the work? Show me that you have thought through the process enough to demonstrate your command of the material and the ability to translate it into the age of ancient warfare.
I only mentioned Excel, because that is my calculator, I don't use anything else if I cannot do it in my head.
I missed your edit.
It is not an excuse, it is the way things get done in the real world if you want to work with and through other people. With all of your talents, Symphony, you lack an understanding of how work with others. It is worth learning.
Perfectionist
Angel of Verdun
You're probably not going to be able to find sufficiently reliable information on anything between 500 and 1450. Agincourt is about the best documented and researched battle in that period, and estimates of force strength still range from 12,000 v. 9,000 to 36,000 v. 6,000. Earlier, things are worse, and you get crazy stuff like there being more Vikings at the siege of Paris than likely existed in the entire Viking Age.
Anyway, for the second half of the fifteenth century, Fornovo, Grandson, and Bosworth Field come to mind. For the first half of the sixteenth century, Marignano, Pavia and Ceresole, and perhaps Nordlingen, Naseby and Rocroi for the seventeenth century. The century in between is problematic, because set piece battles were practically irrelevant and didn't happen much between developed states. How would you handle the Eighty Years War, with its constant actions and sieges, using QJM? Deciding a war based on attrition rates seems undesirable.
Anyway, for the second half of the fifteenth century, Fornovo, Grandson, and Bosworth Field come to mind. For the first half of the sixteenth century, Marignano, Pavia and Ceresole, and perhaps Nordlingen, Naseby and Rocroi for the seventeenth century. The century in between is problematic, because set piece battles were practically irrelevant and didn't happen much between developed states. How would you handle the Eighty Years War, with its constant actions and sieges, using QJM? Deciding a war based on attrition rates seems undesirable.
Less than ideal because the Bastard got really, really lucky. By rights, his army should have broken once the Bretons on his left routed, and even though it didn't it almost certainly would have if Harold had been able to order the housecarls to charge in support of the fyrdmen.
Symphony D.
Deity
Retroactively deleted.
flyingchicken
Deity
- Joined
- Feb 3, 2007
- Messages
- 3,783
Frig this unproductive nonsense, here's Cannae (stats from Wikipedia):
Hannibal
27,000 heavy infantry
6,000 light infantry
8,000 cavalry
41,000 TOTAL
Roman dudes
40,000 Roman infantry
40,000 Allied infantry
2,400 Roman cavalry
4,000 Allied cavalry
86,400 TOTAL
Variables
Terrain: Flat - bare, hard
Weather: Dry - Sunshine - Temperate
Season: Summer - Temperate
Posture: Both were on the Attack (i.e. will not be factored)
Morale: Both at Excellent
Tactical Surprise: Substantial by Hannibal
Operational Lethality Index
Since I didn't find any nice infos on weaponry form Wikipedia, I'll go on ahead and pull stuff from the depths of my bottom: The Carthaginian's 27,000infantry were using hand-to-hand weapons (Wcarthaginian heavy infantry = 23.5 * 27,000 * 1.0 [this be the terrain factor]), while his skirmishers used slings (Wcarthaginian light infantry = 23.7 * 6,000 * 1.0)[1], and his cavalry used hand-to-hand weapons (Wcarthaginian other cavalry = 23.5 * 8,000 * 1.0 * 1.0 [this be the weather factor]). I'm not counting javelins because they suck and can't be sustained for more than an hour I'm guessing aka pulling out of the crack of my buttocks.
--> Shannibal = 634,500 + 142,200 + 188,000 = 964,700
The Romans had swords and javelins, all of them, but I'm not counting the javelins like I said. Wikipedia didn't say anything else so I'm going with 80,000 doods with swords (Wroman infantry = 80,000 * 23.5 * 1.0). Same with cavalry (Wroman cavalry = 6,400 * 23.5 * 1.0 * 1.0).
--> Sroman pigs = 1,880,000 + 150,400 = 2,030,400
Relative mobility of the Carthaginian to the Romans was something like:
Mhannibal the cannibal = sqrt( [(41,000 + 8000 + 8000 * 23)/41,000] / [(86,400 + 6,400 + 6,400 * 23)/86,400] ) --> [5.68292682926829268292682926829268]/[2.77777777777777777777777777777778] --> 2.04585365853658536585365853658569 ~ 2.046.
mhannibal the cannibal = Mhannibal the cannibal - (terrain mobility factor - weather mobility factor) * (Mhannibal the cannibal - 1)
---> mhannibal the cannibal = 2.046 - (1.05 - 1.0) * (2.056 - 1) = 1.9932. Compare Napoleon's mobility advantage in Austerlitz of 1.0997. Implication? Hannibal's forces were very mobile and they took advantage of it!
Now the big question: Who won? Here's the stuffs before we let intangibles like leadership and training cloud our judgment:
Phannibal = 964,700 * 1.9932 = 1,922,840.04
Proman piggies = 2,030,400
That gives us a hannibal to roman piggies ratio of 1,922,840.04/2,030,400 or 0.947025236406619385342789598108747. According to the QJM, ratios between 0.9 and 1.1 are INDETERMINATE OUTCOMES.
Oh yeah, surprise, almost forgot (actually, the stuffs say that this should be done after the preliminary calculations for QJMA):
Mhannibal the cannibal with surprise = ~Mhannibal the cannibal * sqrt(3) = 3.54377595228592294255715521472101 ~ 3.544
--> mhannibal the cannibal with surprise = 3.544 - (1.05 - 1.0) * (3.544 - 1) = 3.4168.
--> Phannibal surprise = 964,700 * 3.4168 = 3,296,186.96
Proman piggies = 2,030,400
--> hannibal to piggie ratio of ~1.623. CLEAR VICTORY TO HANNIBAL (casualties: 9,020 for hannibal, 32,832 for piggies [2]), even without his vaunted leadership (which I won't bother to calculate with anymore) [3]!
Notes
Dupuy's model sneers at your tactical specifics! I say if you decide that a tactical system is "super effective" against another, then give them an arbitrary (or less so, if you have the knowledge) percentile bonus along with the other intangibles like leadership and training.
Surprise, since it is calculated after the fact, can be done in a NES-QJM by means of a randomizatorifier, maybe dependent on the captain (if its a genius versus Nitwit then the chances should be high INDEED). As far as I know, a randomifitizificationer is all sound in this deterministic model if we're going to use it games. DISCUSS PLEASE.
There is no factoring in of armor and shields; either this can be entered as ******** enemy weapon values (lower accuracy or reliability or range or anything), or a big multiplicative value like an intangible, is open for discussion.
Footnotes
[1] Since the charts don't have anything on slings, and I'm too lazy to thoroughly search the Net for stats, I made the sling have a rate of fire of 60 strikes per hour (compare to ordinary bow's 55), 1 potential target (same as bow), 0.3 effectiveness (bow and hand-to-hand weapons have 0.4), 540 effective range (compare to bow's 80 and longbow's 200; based on Wikipedia's assertion that its theoretical range is 600 meters)--giving a range factor of ~1.735 (bow has 1.28)--accuracy of 0.8 (same as bow, compare to javelin's 0.75), and a reliability of1.0 (always reliable; compare to hand-to-hand's 1.0, bow's 0.95, and AK-47's 0.8) whoops I changed it to 0.95 (same as bow).
[2] The actual casualties were 6,000 for Carthage (bah, close enough -- besides, this is a 1960s model we're talking about here: there are much more modern ones that cost shatloads) and a total slaughterfest for the Romans--of course, if the tactic applied was total envelopment (like, if the player said that his generals would attempt to do so every time, or something), the mod will have to decide whether the casualty rates would apply. Maybe another randomizificationizer?
[3] Well, actually, you can say the surprise was from his leadership if we follow the randomizerifyization system I propose about it.
Final Words
Got a nitpick since you know better (than Wikipedia + my reading comprehension)? THEN YOU SHOULD HAVE DONE IT YOURSELF, MORE KNOWLEDGEABLE PERSON.
Also I didn't do a QJMA because I AM LAZY (OR AM I...??? hint: I am)... but maybe I will later or one of you guys can start picking up off where I left and do it yourself.
Hannibal
27,000 heavy infantry
6,000 light infantry
8,000 cavalry
41,000 TOTAL
Roman dudes
40,000 Roman infantry
40,000 Allied infantry
2,400 Roman cavalry
4,000 Allied cavalry
86,400 TOTAL
Variables
Terrain: Flat - bare, hard
Weather: Dry - Sunshine - Temperate
Season: Summer - Temperate
Posture: Both were on the Attack (i.e. will not be factored)
Morale: Both at Excellent
Tactical Surprise: Substantial by Hannibal
Operational Lethality Index
Since I didn't find any nice infos on weaponry form Wikipedia, I'll go on ahead and pull stuff from the depths of my bottom: The Carthaginian's 27,000infantry were using hand-to-hand weapons (Wcarthaginian heavy infantry = 23.5 * 27,000 * 1.0 [this be the terrain factor]), while his skirmishers used slings (Wcarthaginian light infantry = 23.7 * 6,000 * 1.0)[1], and his cavalry used hand-to-hand weapons (Wcarthaginian other cavalry = 23.5 * 8,000 * 1.0 * 1.0 [this be the weather factor]). I'm not counting javelins because they suck and can't be sustained for more than an hour I'm guessing aka pulling out of the crack of my buttocks.
--> Shannibal = 634,500 + 142,200 + 188,000 = 964,700
The Romans had swords and javelins, all of them, but I'm not counting the javelins like I said. Wikipedia didn't say anything else so I'm going with 80,000 doods with swords (Wroman infantry = 80,000 * 23.5 * 1.0). Same with cavalry (Wroman cavalry = 6,400 * 23.5 * 1.0 * 1.0).
--> Sroman pigs = 1,880,000 + 150,400 = 2,030,400
Relative mobility of the Carthaginian to the Romans was something like:
Mhannibal the cannibal = sqrt( [(41,000 + 8000 + 8000 * 23)/41,000] / [(86,400 + 6,400 + 6,400 * 23)/86,400] ) --> [5.68292682926829268292682926829268]/[2.77777777777777777777777777777778] --> 2.04585365853658536585365853658569 ~ 2.046.
mhannibal the cannibal = Mhannibal the cannibal - (terrain mobility factor - weather mobility factor) * (Mhannibal the cannibal - 1)
---> mhannibal the cannibal = 2.046 - (1.05 - 1.0) * (2.056 - 1) = 1.9932. Compare Napoleon's mobility advantage in Austerlitz of 1.0997. Implication? Hannibal's forces were very mobile and they took advantage of it!
Now the big question: Who won? Here's the stuffs before we let intangibles like leadership and training cloud our judgment:
Phannibal = 964,700 * 1.9932 = 1,922,840.04
Proman piggies = 2,030,400
That gives us a hannibal to roman piggies ratio of 1,922,840.04/2,030,400 or 0.947025236406619385342789598108747. According to the QJM, ratios between 0.9 and 1.1 are INDETERMINATE OUTCOMES.
Oh yeah, surprise, almost forgot (actually, the stuffs say that this should be done after the preliminary calculations for QJMA):
Mhannibal the cannibal with surprise = ~Mhannibal the cannibal * sqrt(3) = 3.54377595228592294255715521472101 ~ 3.544
--> mhannibal the cannibal with surprise = 3.544 - (1.05 - 1.0) * (3.544 - 1) = 3.4168.
--> Phannibal surprise = 964,700 * 3.4168 = 3,296,186.96
Proman piggies = 2,030,400
--> hannibal to piggie ratio of ~1.623. CLEAR VICTORY TO HANNIBAL (casualties: 9,020 for hannibal, 32,832 for piggies [2]), even without his vaunted leadership (which I won't bother to calculate with anymore) [3]!
Notes
Dupuy's model sneers at your tactical specifics! I say if you decide that a tactical system is "super effective" against another, then give them an arbitrary (or less so, if you have the knowledge) percentile bonus along with the other intangibles like leadership and training.
Surprise, since it is calculated after the fact, can be done in a NES-QJM by means of a randomizatorifier, maybe dependent on the captain (if its a genius versus Nitwit then the chances should be high INDEED). As far as I know, a randomifitizificationer is all sound in this deterministic model if we're going to use it games. DISCUSS PLEASE.
There is no factoring in of armor and shields; either this can be entered as ******** enemy weapon values (lower accuracy or reliability or range or anything), or a big multiplicative value like an intangible, is open for discussion.
Footnotes
[1] Since the charts don't have anything on slings, and I'm too lazy to thoroughly search the Net for stats, I made the sling have a rate of fire of 60 strikes per hour (compare to ordinary bow's 55), 1 potential target (same as bow), 0.3 effectiveness (bow and hand-to-hand weapons have 0.4), 540 effective range (compare to bow's 80 and longbow's 200; based on Wikipedia's assertion that its theoretical range is 600 meters)--giving a range factor of ~1.735 (bow has 1.28)--accuracy of 0.8 (same as bow, compare to javelin's 0.75), and a reliability of
[2] The actual casualties were 6,000 for Carthage (bah, close enough
-- besides, this is a 1960s model we're talking about here: there are much more modern ones that cost shatloads) and a total slaughterfest for the Romans--of course, if the tactic applied was total envelopment (like, if the player said that his generals would attempt to do so every time, or something), the mod will have to decide whether the casualty rates would apply. Maybe another randomizificationizer?[3] Well, actually, you can say the surprise was from his leadership if we follow the randomizerifyization system I propose about it.
Final Words
Got a nitpick since you know better (than Wikipedia + my reading comprehension)? THEN YOU SHOULD HAVE DONE IT YOURSELF, MORE KNOWLEDGEABLE PERSON.
Also I didn't do a QJMA because I AM LAZY (OR AM I...??? hint: I am)... but maybe I will later or one of you guys can start picking up off where I left and do it yourself.
flyingchicken
Deity
- Joined
- Feb 3, 2007
- Messages
- 3,783
I don't have stats on how far the Hannibal army went, so I can't do a QJMA of that battle. However, I can do another half-assed QJM, this time for "less than ideal" Hastings (from Wikipedia and Google again; if you know better, do better!).
William
2,200 cavalry
1,700 archers
4,500 men-at-arms
8,400 total
Harold
2,000 housecarls
5,500 fyrd
7,500 total
Variables
Terrain: Rolling - Mixed
Weather: Between Dry - Sunshine - Temperate and Wet - Light - Temperate
Season: Fall - Temperate
Posture: William on the Attack, Harold on the Defense (hasty as in Hastings hyuk hyuk hyuk but seriously it was)
Morale: Both at Excellent
Tactical Surprise: Substantial for William for killing Harold at some point OR for Harold when William's troops thought he died OR irrelevant
OLIs
William
William's horsies = 2,200 * 23 * 0.8 * 0.85
William's archers = 1,700 * 19 * 0.9
William's men-at-arms = 4,500 * 23 * 0.9
Silliam = 156,628
Harold
Whousecarl = 2,000 * 23 * 0.9
Wfyrd = 5,500 * 23 * 0.9
Sharold = 172,500
Mobility
Milliam = sqrt(((8,400 + 2,200 + 2,200 * 23)/8,400)/((7,500 + 0 + 0 * 0)/7500)) = 2.69920623
milliam = 2.69920623 - (1 - 0.8 * 0.9) * (2.69920623 - 1) = 2.22342849
milliam surprise = (2.69920623 * sqrt(3)) - (1 - 0.8 * 0.9) * ((2.69920623 * sqrt(3)) - 1) = 3.64611688
Mharold = sqrt(((7,500 + 0 + 0 * 0)/7500)/((8,400 + 2,200 + 2,200 * 23)/8,400)) = 0.370479287
mharold = 0.370479287 - (1 - 0.8 * 0.9) * (0.370479287 - 1) = 0.546745087
mharold surprise = (0.370479287 * sqrt(3)) - (1 - 0.8 * 0.9) * ((0.370479287 * sqrt(3)) - 1) = 0.742016043
This shows that surprise on Harold's side helped slightly in offsetting his severe mobility disadvantage.
Theoretical Outcome
Pilliam = 156,628 * 2.69920623 * 0.95 * 1.1 = 441,795.981
Pharold = 172,500 * 1.3 = 224,250
Pilliam/Pharold = 1.97010471
VICTORY TO WILLIAM
Casualties:
William: 8,400 * 0.2 * 1.8 = 3,024
Harold: 7,500 * 0.4 * 1.8 = 5,400
Pilliam surprise = 156,628 * 3.64611688 * 0.95 * 1.1 = 596 782.774
Pharold = 172,500 * 1.3 = 224,250
Pilliam surprise/Pharold = 2.66123868
VICTORY TO WILLIAM
Casualties:
William: 8,400 * 0.2 * 1.8 = 3,024
Harold: 7,500 * 0.4 * 1.8 = 5,400
Pilliam = 156,628 * 0.95 * 1.1 = 163 676.26
Pharold surprise = 172,500 * 0.742016043 * 1.3 = 166 397.098 [1]
Pilliam/Pharold surprise = 0.983648525
INDETERMINATE [2]
Casualties: [3][4]
William: 8,400 * 0.3 * 1.8 = 4,536
Harold: 7,500 * 0.3 * 1.8 = 4,050
Footnotes
[1] I believe there is a difference between defending and having a Defensive posture.
[2] This would be under the assumption that surprise worked only on the English side. Clearly this was not the case, and either we completely take out surprise (leading to the first case of Norman victory) because both sides had their fair share of big surprises, or we only take into account Norman-side surprise (because breaking through the English shield wall and killing their King had a bigger effect than mistaken and quickly-rectified death).
[3] The percentage I used here is between winner and loser.
[4] The actual speculated (heh) casualties by whoever the guys at Wikipedia were referring to were 5,000 for the English and 3,000 for the Normans. Yes, the closeness of these QJM-born estimates and that of the ones estimated by the doods make us think: were those speculations based on QJM, or is QJM, by virtue of being based on several real-world battles, quite accurate at predicting casualties for non-spectacular battles (unlike that of Cannae), or did I edit Wikipedia to match my results?
Final Words
I say, the horrid comparative lack of mobility by the Englishmen cost them the battle, and not even the fumbling of the Norman King could have saved them. I did not factor in training and leadership and stuff because I think they were roughly equal (i.e. both sides sucked).
Also, QJM rocks so far, though I cannot do QJMAs because I don't have big fancy books or scholarly websites detailing exactly how far winners went and held land.
Oh and using Google as a calculator is a lot easier than Windows' calc.
William
2,200 cavalry
1,700 archers
4,500 men-at-arms
8,400 total
Harold
2,000 housecarls
5,500 fyrd
7,500 total
Variables
Terrain: Rolling - Mixed
Weather: Between Dry - Sunshine - Temperate and Wet - Light - Temperate
Season: Fall - Temperate
Posture: William on the Attack, Harold on the Defense (hasty as in Hastings hyuk hyuk hyuk but seriously it was)
Morale: Both at Excellent
Tactical Surprise: Substantial for William for killing Harold at some point OR for Harold when William's troops thought he died OR irrelevant
OLIs
William
William's horsies = 2,200 * 23 * 0.8 * 0.85
William's archers = 1,700 * 19 * 0.9
William's men-at-arms = 4,500 * 23 * 0.9
Silliam = 156,628
Harold
Whousecarl = 2,000 * 23 * 0.9
Wfyrd = 5,500 * 23 * 0.9
Sharold = 172,500
Mobility
Milliam = sqrt(((8,400 + 2,200 + 2,200 * 23)/8,400)/((7,500 + 0 + 0 * 0)/7500)) = 2.69920623
milliam = 2.69920623 - (1 - 0.8 * 0.9) * (2.69920623 - 1) = 2.22342849
milliam surprise = (2.69920623 * sqrt(3)) - (1 - 0.8 * 0.9) * ((2.69920623 * sqrt(3)) - 1) = 3.64611688
Mharold = sqrt(((7,500 + 0 + 0 * 0)/7500)/((8,400 + 2,200 + 2,200 * 23)/8,400)) = 0.370479287
mharold = 0.370479287 - (1 - 0.8 * 0.9) * (0.370479287 - 1) = 0.546745087
mharold surprise = (0.370479287 * sqrt(3)) - (1 - 0.8 * 0.9) * ((0.370479287 * sqrt(3)) - 1) = 0.742016043
This shows that surprise on Harold's side helped slightly in offsetting his severe mobility disadvantage.
Theoretical Outcome
Pilliam = 156,628 * 2.69920623 * 0.95 * 1.1 = 441,795.981
Pharold = 172,500 * 1.3 = 224,250
Pilliam/Pharold = 1.97010471
VICTORY TO WILLIAM
Casualties:
William: 8,400 * 0.2 * 1.8 = 3,024
Harold: 7,500 * 0.4 * 1.8 = 5,400
Pilliam surprise = 156,628 * 3.64611688 * 0.95 * 1.1 = 596 782.774
Pharold = 172,500 * 1.3 = 224,250
Pilliam surprise/Pharold = 2.66123868
VICTORY TO WILLIAM
Casualties:
William: 8,400 * 0.2 * 1.8 = 3,024
Harold: 7,500 * 0.4 * 1.8 = 5,400
Pilliam = 156,628 * 0.95 * 1.1 = 163 676.26
Pharold surprise = 172,500 * 0.742016043 * 1.3 = 166 397.098 [1]
Pilliam/Pharold surprise = 0.983648525
INDETERMINATE [2]
Casualties: [3][4]
William: 8,400 * 0.3 * 1.8 = 4,536
Harold: 7,500 * 0.3 * 1.8 = 4,050
Footnotes
[1] I believe there is a difference between defending and having a Defensive posture.
[2] This would be under the assumption that surprise worked only on the English side. Clearly this was not the case, and either we completely take out surprise (leading to the first case of Norman victory) because both sides had their fair share of big surprises, or we only take into account Norman-side surprise (because breaking through the English shield wall and killing their King had a bigger effect than mistaken and quickly-rectified death).
[3] The percentage I used here is between winner and loser.
[4] The actual speculated (heh) casualties by whoever the guys at Wikipedia were referring to were 5,000 for the English and 3,000 for the Normans. Yes, the closeness of these QJM-born estimates and that of the ones estimated by the doods make us think: were those speculations based on QJM, or is QJM, by virtue of being based on several real-world battles, quite accurate at predicting casualties for non-spectacular battles (unlike that of Cannae), or did I edit Wikipedia to match my results?
Final Words
I say, the horrid comparative lack of mobility by the Englishmen cost them the battle, and not even the fumbling of the Norman King could have saved them. I did not factor in training and leadership and stuff because I think they were roughly equal (i.e. both sides sucked).
Also, QJM rocks so far, though I cannot do QJMAs because I don't have big fancy books or scholarly websites detailing exactly how far winners went and held land.
Oh and using Google as a calculator is a lot easier than Windows' calc.
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