Has anyone figured out the relationship between Starship Tier and BP? I'm trying to homebrew some rules for starships but every time I try to do any major rules revision it all comes back to that relationship.
I've been trying to extrapolate the algorithm/relationship between Starship tiers and the amount of BP granted at each level but so far I haven't been able to tease it apart. I was wondering if anyone else had figured it out.
I know I'm not the only one who thinks this, but Starfinder's Shipbuilding Rules are a total mess. I'm trying to bring some order to the chaos.
Every component BP cost feels completely arbitrary, like there's is no mathematical foundation behind the numbers. Here's a perfect example:"The heavy nuke launcher is too good of a deal for 10BP? Meh, just bump the BP cost by 25 points; that should git'er'dun." This seems to be an entirely arbitrary increase without any numeric basis. For weapons, there should must be a formula which returns a BP value based on damage X range X effect but as I pointed out above, it seems to be entirely arbitrary values based on what "seems" to be "fair", rather than any mathematical basis.
Other examples include starship base frames; there should be a relationship to the frame BP cost and what it offers (weapon mounts, expansion bays, number of crew, base HP and increment) but there literally seems to be no logic whatsoever behind the design, especially when it comes to designing your own frames: pick a size, pick a number of weapon mounts, pick a number of expansion bays, pick a number of crew, then assign a BP number based on.....what, exactly?
Compare the Pioneer frame to the Shuttle frame: both Small, but one has 3 Expansion Bays, 1 weapon mount, and 4 crew for 6BP, the other has 1 Expansion Bay, 3 weapon mounts, and 3 crew, for 2BP. The BP cost doesn't add up unless there are additional numbers used in the calculation, which there probably is should be but for some reason Paizo considers this to be a State Secret, else the calculations would be more obvious or else simply made available.
I also think the CRB errata for weapon BP costs is far too much of an over-correction (nothing new for Paizo; anyone remember the Quickrunner's Shirt nerf? Jingasa of the Fortunate Soldier? Arcane Deed magus arcana? They could have just raised their prices or created PFS-specific rules but noooooo, utter destruction instead); I'm trying to reduce them to a more reasonable and appropriate level (10BP-35BP for a heavy nuke launcher? Are you kidding me?!).
Contrary to what the printed rules would have us believe, there is a mathematical foundation behind the numbers, but it all rests on the BP/Tier relationship. Without knowing that relationship, every attempt to balance Starship building is essentially just throwing a bucket of peas at a wall to see which pea sticks.
That's no way to build a game.
So. Anyone know how Tier and BP relate to each other, mathematically speaking? And no, I don't mean "How many BP do I get at each Tier?" I can read tables. :)
I really hope that Paizo gets serious about incorporating Starships with the upcoming book because they really dropped the ball with Starships 1e.
Anyone know how Tier and BP relate to each other, mathematically speaking? And no, I don't mean "How many BP do I get at each Tier?" I can read tables.
Not sure exactly what you mean by this, since the mathematical relationship between tier and BP is, literally, a table.
My graphing calculator estimates the curve to be BP = (2.77256 * tier^2) – (11.8741 * tier) + 103.066, but I don't know how helpful that is.
Anyone know how Tier and BP relate to each other, mathematically speaking? And no, I don't mean "How many BP do I get at each Tier?" I can read tables.Not sure exactly what you mean by this, since the mathematical relationship between tier and BP is, literally, a table.
My graphing calculator estimates the curve to be BP = (2.77256 * tier^2) – (11.8741 * tier) + 103.066, but I don't know how helpful that is.
You're not wrong that it's a table, but that table doesn't explain the relationship between the Tier and BP progression.
The reason is I'm trying to extrapolate beyond Tier 20, and as I mentioned in my OP, the BP costs for everything seem to be entirely arbitrary and nonsensical (see my examples of Shuttle vs. Pioneer frames, and weapon BP cost increases).
In fact, Starfinder's devs have essentially admitted that they half-assed Starships because they "knew players would freak out" if it was absent and that they "actively encourage players to homebrew"; they basically included it to forestall any outcry from us. Those a direct quote from a dev, BTW (I've been trying to find the relevant Reddit post stating this but no luck). Starships was lifted almost entirely from FFG's X-Wing but overall poorly incorporated into SF. I absolutely know I'm not alone in this sentiment, as both Paizo's Starfinder boards and subReddit are positively littered with complaints and clarifying questions on this topic.
I'm trying to sort it out to some degree to the best of my (admittedly limited) abilities.
Thank you for doing the math! I'm not much of a mathematician so your help is very much appreciated. Your answer is extremely helpful and I think I can definitely use that in my efforts.
Well, I guess be aware that the equation is just an estimation, and gets less and less accurate as you plug in higher tiers, probably because the curve isn't really a proper parabola, it just sort of resembles one. I think by the time you get to tier 20 it's off by about 25 BP.
Another way to look at it is that the table starts at 55 BP and then goes up by 20 for the first six tiers, then up by 25 for a few tiers, then up by 40, then up by 50, and then there's a big jump where the last five tiers go up by 100 each. It's not consistent, and it obviously was designed by feel rather than by any mathematical progression.
If you were going to extrapolate past tier 20 you could probably do worse than having the next few tiers go up by 150 each, or maybe 200. I think if you dig down you're going to discover that lots of the numbers are, in fact, quite arbitrary, and imposing a system onto it means you're going to have to make some arbitrary decisions of your own.
Well, I guess be aware that the equation is just an estimation, and gets less and less accurate as you plug in higher tiers, probably because the curve isn't really a proper parabola, it just sort of resembles one. I think by the time you get to tier 20 it's off by about 25 BP.
Another way to look at it is that the table starts at 55 BP and then goes up by 20 for the first six tiers, then up by 25 for a few tiers, then up by 40, then up by 50, and then there's a big jump where the last five tiers go up by 100 each. It's not consistent, and it obviously was designed by feel rather than by any mathematical progression.
If you were going to extrapolate past tier 20 you could probably do worse than having the next few tiers go up by 150 each, or maybe 200. I think if you dig down you're going to discover that lots of the numbers are, in fact, quite arbitrary, and imposing a system onto it means you're going to have to make some arbitrary decisions of your own.
I mean, obviously ALL starting points for systems like this are going to have an arbitrarily-chosen starting point (after all, how DO you calculate the fictional value of a fictional Starship?), but once that arbitrary base is set, then everything else should follow from a mathematical standpoint. If it weren't then there wouldn't be an entire branch of study dedicated to the mathematics of gaming. But yes, it definitely seems as though the Tier/BP relationship was determined by Dartboard rather than math.
I'm having some trouble using that formula you gave me though. I get some really crazy numbers that don't come anywhere close to what the table shows. I may not be a mathematician but I do know how to use BEDMAS, however it's obvious I'm doing something wrong.
Taking Tier 1 as an example and for simplicity's sake: BP = (2.77256 * tier^2) – (11.8741 * tier) + 103.066
BP= (2.77256 * 1^2) - (11.8741 * 1) + 103.066
BP= (2.77256) - (11.8741) + 103.066
BP= 93.96
You can see I get the wrong answer but I don't know why. What am I missing here?
I don't think you're missing anything -- looks like the fit isn't very accurate at either end. Full disclosure, I didn't really test it, I just let the computer take its best guess. It doesn't surprise me that there's not a clean fit, because as I said, the designers just put up some numbers in a roughly quadraticish-looking curve.
If it were a real quadratic equation you'd see the rate of increase in y going up in a nice, smooth, curve, but that's not what the BP/tier table is. Someone at Paizo said, "Let's start at 50 and go up by 20s until we hit tier 6, then go up by 30s, then 40s, then 50s, then for the really big, tier 15-20 ships let's just go up by 100." Then they went back and said, "Hmm, those tier 7-9 numbers look a bit too big, let's nudge those down a little," and then they called it a day. There's no way to capture that in a simple math equation because that's not math.
I'll lead off with my most pressing question before it gets buried in the text: What do you think of the Mech building rules from Tech Revolution? Is that more of what you're looking for with starships, with the tier-scaling damage tables and costs being tier-based, or is that the wrong direction?
With that out of the way:
For weapons, there should must be a formula which returns a BP value based on damage X range X effect but as I pointed out above, it seems to be entirely arbitrary values based on what "seems" to be "fair", rather than any mathematical basis.
The BP cost doesn't add up unless there are additional numbers used in the calculation, which there probably is should be but for some reason Paizo considers this to be a State Secret, else the calculations would be more obvious or else simply made available.
Contrary to what the printed rules would have us believe, there is a mathematical foundation behind the numbers, but it all rests on the BP/Tier relationship. Without knowing that relationship, every attempt to balance Starship building is essentially just throwing a bucket of peas at a wall to see which pea sticks.
The "secret" is that there isn't one. There is no consistent mathematical formula for any part of starship combat, hidden or otherwise. There are guidelines, but no formal calculations. A great example is the BP budget per tier; it goes up as tiers go up, but not consistently. It's as much an art as it is a science.
As for weapons costing X BP for Y damage and Z features: If you're old enough to remember the Jingasa of the Fortunate Soldier from PF1e's Jade Regent and Ultimate Equipment, then you might be old enough to remember the custom weapon creation rules from PF1e's Weapon Masters Handbook. Remember how that turned out? (For those who don't know, it was functional but not balanced very well.)
A game system that is perfectly balanced with precise numbers is a good design goal, but a practical impossibility. I can't think of a single system in PF1e, PF2e, or Starfinder that has accomplished that, though several have come close. In my experience, a perfectly balanced game is a boring game; the variance makes for a more interesting experience, and a good GM can compensate or houserule if any major flaws are found.
Also...
In fact, Starfinder's devs have essentially admitted that they half-assed Starships because they "knew players would freak out" if it was absent and that they "actively encourage players to homebrew"; they basically included it to forestall any outcry from us. Those a direct quote from a dev, BTW (I've been trying to find the relevant Reddit post stating this but no luck).
I'd appreciate if you could find that, because I've never seen that comment, and this is the first time I'm hearing of anything like that.