You get one extra artifact dot per rank per player past the first. So if you have four players with a pool of 12 dots between them that's (4-1)x12=36, plus 20 from the background (5 x 4), or 56.
It's... not really complex at all. Add up the total number of players in the pool and subtract one. Multiple that by the pool of dots. Add in the base artifact dots granted by the background for each.
Let me show you:
I have five players, with Arsenal 1, 3, 0, 2 and 1 between them. That's four players adding to the pool and a total pool of 7. 7 x3 = 21. Add in the background granted dots (2, 5, 0, 3 and 2) and you get 33 dots of Artifacts (none higher than 3). Or 8 resources worth of mundane gear per dot (33x8= 264).
I am personally of the opinion that if your background requires you to calculate (p-1)*t=x (where p = the number of people with the Background and t = equals the total number number of dots between all players and x= the final pool) then your Background is to complex. Not because its hard, but because holy shit why are you even bothering with that level of complexity. I also note that since you laid it out like this it looks simple. This is the text:
Arsenal Background said:
Characters may choose to pool their Arsenal ratings, representing the combined treasury of a House military unit, legion payroll and arsenal, the assets of a trading company or other organizational unit. Those who do so gain additional benefits, in the form of an additional dot of assets per level per character pooling their resources past the first. So, for example, four characters' pooling three levels of Arsenal creates an asset pool totaling 56 dots of assets, with a maximum rating of 3. If this option is taken, each asset dot converts to eight dots of Resources.
Not quite as easy to parse, to put it mildly.
Also: blargle, missed the asset dot conversion. I'll note for some god forsaken reason they did not apply that to the main Background breakdown. Because apparently the writer thought complexity and exceptions were a good thing in a single Background.
But that is exactly the kind of campaign basically every Alchemical game is going to be. You're not really going to have an Assembly from four different Nations wandering around together. Heck, the only reason you might not be contributing to the pool (seriously, its one background dot to contribute for so much reward) is if you had an exceptional reason not to... like being an Adamant Caste that isn't actually part of the City you're stationed in but only has really good forged IDs...
No, you don't understand. Players tend to specialize into different niches, mostly to avoid toe stepping. So people like the socialite or the crafter tend not to buy this. Further, the instant the words 'thing can be removed if the ST feels like it' enters play, they tend to get squirrelly. Add into the fact this is basically intrinsically a military logistics based background, which many players decide doesn't fit their concept. Oh, andArsenal is kinda a pain in the ass to engage with (when you have multiple threads, both on RPGnet and the old Exalted forums, asking 'how the hell does this actually work', this is actually an issue), so many don't bother. Net effect, you tend to get one or two players taking it, because the rest have better things to spend their Background points, BP, and XP on.
Also, of course every Alchemical game is not going to be an all soldiers group, what the actual hell. Their setting isn't even setup to support that, outside of Estasia. Seriously, I have never seen a group that is all soldiers. People seem to innately resist it when making characters in Exalted. My own game, which is fairly combat focused and advertised as such... two, maybe three players might have taken it, and I practically was raining Background points on their heads.
56 dots (four players, three dots each) = 448 dots worth of mundane equipment. An exceptional Spear is two dots, an exceptional Reinforced Buff Jacket is three. Five dots per soldier. That's 89 Exceptionally Equipped Soldiers. Command 1 is 25 soldiers, so three Alchemicals with Command 1 is 75 soldiers (elite troops), giving those players a bunch of really damn crack units with 73 resources dots/9 artifact dots left to spare. Best of all, you can have this level of martial might around only when you need it and instead spend those purchases on say... 89 bottles of Celestial Wine (who says Exalted doesn't have cheap healing...).
You know, the funny thing about this example? You deliberately set the number of troops low. You didn't mention the fact that if one Alchemical takes Command 2, they get 125 soldiers. Command 3, 250. That's assuming you get the level of Arsenal you postulated, which is higher then my experiences. So in other words, the number of troops vastly outstrips your ability to equip them if anyone makes the slightest effort to invest.
So while I did underestimate the ability to of the background (and made a further mistake in my original post because I was working with false information), I wasn't exactly wrong either, I just misjudged the size of the gap. And further, I'm not sure why you are trying to characterize my position as wrong, given a simple glance at Command would reveal the numbers not matching what you present.
(Further hilarity: Celestial Wine is unavailable in Autochthonia, due to it coming from Yu-Shan. Example work better when they actually apply.)
In short, you have no idea what you are talking about.
Aaron: kindly go fuck yourself. You want to say I am wrong, that is fine. I did indeed make a mistake, and its more then fair to call me out on that. Arguing with bad information is not good on my part. But you know what? I've played using this, as a player. And it was not fun. Nobody else really wanted to buy into the background (note: this was PbP with
20+ players). The backgrounds mechanics are not obvious at a glance, which made it a pain when I needed to recalculate the pool. I had to look up how the hell the thing actually worked, and I was far from the first to do so (and those threads had a few wrong calcs for getting the pool to).
I know what I am talking about, because I am drawing from my own experiences. Are you telling me I did not experience what I did? Further you are deliberately cherry picking your evidence to hide flaws, or it at least it damn well seems like it. I'm not sure how you could look up Command for the number of troops and fail to notice the next tier was larger then your combined example, but anything is possible. Have you actually used Arsenal in play? Looked at games where it is available and see how often players take it?
In short: get off your high horse. I know what I'm talking about well enough to know when your trying to sell bullshit to win an argument.