By the Numbers

[Shepard]

I've been thinking lately about whether or not the RCC can actually win the Battle for GK by numbers alone. Here's the setup as I see it:

We have 2 exact accounts of the numbers on both sides (albeit they are snapshots at certain points of time) as well as assessments by Wanda and Ansom as to the relative strength of the forces.

Here we see that the Coalition's forces consist of 9751 units as of this comic. Things have obviously changed since then. Charlescomm has backed out (-15 very strong units), and Vinny, Jillian, and some Gwiffons, bats, orlies, Unipegtaurs, etc, left to head off Stanley (- ~20-25, estimated between panel 2 here and panel 5 here). But most significantly, Parson's rout of the enemy attack in the tunnels has decreased the Coalition's forces by over 1000 (most of which are Jetstone forces in particular). Instead of that 9751, that number's more like 8710 now, if not lower.


From Parson's Klog #7 we see that the forces left in GK at that point of the comic number at about 754. Since then there have been some minor losses in the tunnels (assumed), but more importantly there's been a great swelling in the ranks by a little over 1000 uncroaked thanks to Wanda. This puts GK's number of troops up around 1754.


Now for the odds. Wanda says here that they are outnumbered 25-1 (though that's since mitigated by actual numbers we're shown and is probably therefore a bit of an exaggeration). Ansom claims here that the Coalition has 4 times the forces needed to take GK. Bearing in mind that these figures need to be taken with a grain of salt, lets do some calculations:

If the original size of the Coalition's forces (9751 + the 40% of their seige which they lost; for the sake of argument let's say it was around 16250 - 9751/0.6) was 4x stronger than actually necessary to take GK. That means that ~4063 units were needed to counter the threat posed by GK's 754. This essentially means that in order to take the city the ratio of their troops to GK's troops would need to be ~ 5.4.

Now take the new numbers. The Coalition's units attacking GK now number ~8710 and GK's number ~1754. If we take 8710/1754 we get a ratio of 4.97 - a number which is less than the ratio devised above which they seem to need in order to be able to take the city. Based on this analysis, it doesn't seem possible for the Coalition to conventionally take GK.

I realize that a lot of this hinges on supposition, as well as the relative strength of the units now making up both sides. As a result there's a a lot of room for interpretation as to how things could still go. I'm interested in what other people think of this break down of the numbers and their meaning.


Horray for my first post :)

[SteveMB]

Hello. You have some good points, but there's one big problem with your caluclation:

If the original size of the Coalition's forces (9751 + the 40% of their seige which they lost; for the sake of argument let's say it was around 16250 - 9751/0.6)

The RCC lost 40% of their seige units -- that calculation "rolls back" a 40% loss to all units. So, their actual pre-airstrike numbers would be considerably lower, depending on just how many of their original units were seige units (probably not all that many, since seige units are presumably a lot more expensive and thus less common than ordinary infantry).

[DevilDan]

Welcome. That's a real humdinger of a first post, too.

Yeah, I'd had that "four times" ratio in the back of my head for a while.

On the one side the RCC lost 40% of siege units. On the other side, those siege units would have only been used to breach the outer wall, or so I believe; perhaps they could be used to assault the garrison, but far fewer ones would be needed given that Ansom originally brought enough siege units to surround GK. So, that loss is important when it comes to breaching the walls; once that is accomplished, those losses won't come into play.

Uncroaked units are not as good as the original (uncroaked bonuses aside); we would need to know a rough ratio of strengths for the lowest-quality uncroaked infantry versus living infantry to better estimate what the relative strengths are.

Plus, we also have to think in terms of the strategic changes. Ansom's calculations were also based on using a relatively small force in the tunnels in order to draw some of Stanley's troops away from the walls. In theory, now Parson can put many more troops on the wall now that the tunnels are sealed off and because Ansom probably lost most of his units that were best suited to tunnel warfare.

I have to assume that it is still doable, though, since at least two other warlords consider it possible; we don't know why precisely Duke Nozzle reacted as he did, but I would guess that it was because he was tired of Ansom's blunders rather than because it then became apparent that taking GK was impossible.

[Shepard]

Hello. You have some good points, but there's one big problem with your caluclation:



The RCC lost 40% of their seige units -- that calculation "rolls back" a 40% loss to all units. So, their actual pre-airstrike numbers would be considerably lower, depending on just how many of their original units were seige units (probably not all that many, since seige units are presumably a lot more expensive and thus less common than ordinary infantry).

Point well taken. I thought about that when I was doing my calculations and estimations, but since there was no way to know exactly how much of the seige there was/is left I went for the most conservative estimate I could. Since the actual original number would be lower, that should shift the numbers back to the Coalition having a slight advantage as of the latest comic.

[SmallFurryMamml]

I have to assume that it is still doable, though, since at least two other warlords consider it possible; we don't know why precisely Duke Nozzle reacted as he did, but I would guess that it was because he was tired of Ansom's blunders rather than because it then became apparent that taking GK was impossible.

Duke Nozzle seems to be the least competent warlord among the RCC. We've seen he's the most easily scared, and least willing to take casualties. Rather than considering the odds, he's just looking at the surface - to the casual observer, GK's military just doubled. He doesn't seem to be one to take the risk that there's anything else as damaging in GK's arsenal.

Basically, Duke Nozzle is up the styx without a sword of ruthlessness.

[Maxymiuk]

I'm afraid there's a few things you forgot to factor in.

1) The troop ratios and "4 times the troops" estimates were made back when Stanley still had 48 dwagons on his side. That number has changed significantly since, even assuming that Stanley gets back to Gobwin Knob before it falls.

2) On the other hand, Ansom was operating on the assumption that he'd be able to get all his pieces into place and then crush Gobwin Knob in one, swift attack. Things didn't work out that well for him - not all of his forces are at the city walls for example.

So on one hand, Gobwin Knob lost it's single strongest force. On the other, Ansom's been goaded into an attack under conditions that are far from ideal. I think at this point any estimates based on the info we were given across the last 100 pages are long since defunct.

[Godskook]

Ratios are not always accurate in combat math. For instance, arithmetically, we could calculate the new troops that the RCC needed as:

Old GK forces: 754
Needed RCC force: 4063

New GK forces: 754 + 1000 = 1754
Needed RCC force: 4063 + 1000 = 5063

This new number is well below the RCC's current forces. Problem is, whatever math we use, except mathamancy, we can't fully represent the situation at hand. Here's why:

1.Tactics
2.Unkown force multipliers
3.As mentioned by others, disparity in unit power
4.Charlie

1)This comic has shown time and again that poor tactics can not be made up for with numbers. That Ansom isn't using any at the moment is far more damning than not outnumbering Parson by 'enough'.
2)They're all over the place, and we only know a handful. The tunnel battle illustrated just how crucial they are.
3)Parson has added 1k low-level zombies. He's lost dozens of dwagons, possibly all of them, as far as he is concerned. Those dwagons were probably more useful to him than those zombies, yet numerically, there were less of them.
4)Charlie is a big unknown, and can change the tide of this battle completely on his own.

All that said, I enjoyed reading your analysis because it was well researched in regards to the factual numbers concerning each side. In the future, approach your math from multiple venues to see how different maths affect your predictions. Statistics is impossible to apply from a reader's standpoint(we lack a sample size adequate for it), but I'm sure there are one or two others that could work.

[DevilDan]

Duke Nozzle seems to be the least competent warlord among the RCC. We've seen he's the most easily scared, and least willing to take casualties. Rather than considering the odds, he's just looking at the surface - to the casual observer, GK's military just doubled. He doesn't seem to be one to take the risk that there's anything else as damaging in GK's arsenal.

Basically, Duke Nozzle is up the styx without a sword of ruthlessness.

Is he the least competent simply because he's angry at the pathetic leadership shown? Sure, it would be good for him to control his emotions and to make decisions less impulsively, but I'd love to know how you can ascertain his overall competence, experience, skills, and his strategic and tactical chops from three lines of dialog.

I think he may very well be at least as experienced as the other two RCC warlords shown or at least of an equivalent level, given that Sofa King is the second largest contingent within the RCC and a sufficiently experienced warlord would be sent at the head of these troops. And because of the number of Sofa King forces, it's likely that they've also lost the most troops in previous battles save for Jetstone and will lose a proportionately high number of troops in the continued siege of GK. Why shouldn't he be concerned?

Why shouldn't he react with anger at Ansom's multiple blunders, especially given that the last one, the Jetstone assault of the tunnels under Webinar's command, was the result of injured pride, recklessness (because better leadership was available), and possibly greed or desire for glory (because he wanted Jetstone to be the principal victors, the ones taking the garrison).

As I've speculated, different sides of the RCC may have had different motivations for joining up; as such, they will be willing to weather different levels of casualties. And don't forget that the landscape has changed since the start of the war: Stanley has flown the coop, has lost many dwagons and other units, has a nearly nonexistent leadership corps, and has only GK left out of his original 11 cities. He is not the threat he once was.

[K2]

You and your silly logic/math. It is flawed, though you are right in a sense. The Tool will win. He will win ecause it is the Titans will. So say it the Titans, And so it will be. For TOOL!