I’m playing with an idea of using 0.5 granularity for SPs, for lower powered games where pretty large differences between characters can be completely lost with base rules.
For example, I want John to have MIG 3.5 SP, showing he’s somewhat better than average but not really an athlete, and James to have MIG 2.5 SP, showing he’s weaker than average, but not half as weak (paying 35 and 25 CP respectively, and having 1 SP difference between each other, even if both are still close to average).
It would also help with small annoyances such as one day being 14 SP of Time except not really (it becomes 14.5 SP), or dead simple metric conversion (0.5 SP difference, inexact but good enough), or more correct weight (MBT being 12.5 SP of Weight, not 12), as well as remove the bump on odd power levels (where max power level is half power limit, now it can be increased by 0.5 SP and it would still be meaningful), and same for when power levels have to be halved for range.
To me it seems that just adding more rows to CHART, SP and Health/damage tables, using middle values (x1.5 instead of x1.4142 for simplicity and neater numbers), as well as halved variable cost in CPs to buy 0.5 SP of power should work well enough.
But I’m new to the Ascendant system, and it’s quite complex with lots of math under the hood (including the rounding in different places), so I have a nagging feeling I might be missing something that will bite me in the charsheets later.
I’m also sure I’m not the first to think about it. So…Any advice ? Pitfalls to watch out for ? Other ideas for greater granularity ?
PS: Incidentally, what’s the point of always rounding 0.5 to even ? It would make John and James have 2 SP of difference (rounding 3.5 to 4, and 2.5 to 2) instead of 1 SP (their actual difference, or if always rounding to lowest or highest) or 0 SP (with no extra granularity).
I’d be very wary about messing with the CHART and SPs like that until you have a very thorough understanding of them mechanically. For example, it’s x1.4142 because 1.4142 is the square root of 2, which ensures everything continues to scale nicely in a log2 system. In addition, the numbers of the CHART are done such that a guy with 11 MIG & 11 VAL will deal, on average, twice as much damage as someone with 10 MIG & 10 VAL, which you will need to account for in any re-worked tables.
That said, on the Autarch Discord, the user Malex did make a version of the CHART that does much of what you want, and if you give him a poke he may be able to provide it for you.
If you’re not planning to go up beyond what peak real-world humans can do, I suggest it may be less work if you halve the effectiveness of the SP scales as they currently exist. Currently, a generic NPC human has 3 SPs in all 6 primary stats. If they had 6 in each primary stat instead, but the effect was the same (eg Carrying Capacity, Running Speed, Weight…) then you’ve effectively introduced half SPs to the game without having to redo as much.
You’ll have to adjust the DVs of many tasks (eg investigating crime scenes will be much easier if everyone has 2x INS to what is expected in the default game), but it’s probably less likely to result in breaking anything.
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On the topic of rounding to even, it’s explained on Wikipedia here (“Rounding half to even”): Rounding - Wikipedia
It does lead to (to my mind) odd outcomes whereby rounding goes something like “20, 20, 20, 21, 22, 22, 22…” but it works, so hey.
That’s exactly why I asked, and why I mentioned it, yes. It’s quite intricate under the hood, and thus requires more care when tinkering with it.
For x1.5 vs x1.4142, I don’t see the difference as being that big when we already go for x2 for everything, and full SPs serve as an anchor. I mean, 2.5 is still twice as big as 1.5, no matter what linear multuplier we use (5.557 and 2.828, vs 6 and 3), so that small difference is applied exactly once in any calculation, instead of adding up, yet easier to eyeball.
And we already use middle values when figuring out the SP value out of linear value. Let’s take an example from the rules:
“How fast is 12mph? 4 SPs; 12mph is halfway between 8mph (3 SPs) and 16mph (4 SPs) and 4 is even.”
Except that halfway between 3 SP and 4 SP (i.e. 3.5 SP) is 11.3mph, if we calculate it properly. 12 still rounds to 4 SP, except not because it’s in the middle, but because it’s more than 3.5 SP.
By the rules, we’d round 24mph to 4 SP as well (despite it being twice as fast as 12mph, pretty huge difference, both going to the same value), although it’s more than halfway between 4 SP and 5 SP (which is 22.6), but we, as human beings, can’t eyeball square roots, for some inexplicable reason (I mean, couldn’t there have been some use for it 38.5 SPs of Time ago in the African savanna ?).
It’s also used in Variable Attributes table (which is basically what I’m trying to do for the main attributes). 2 SP of Health is 20, 4 SP is 40, but 3 SP is 30, not 28. And 5 SP of Health is 60, which is exactly twice of 3 SP of Health.
So that small (and consistent) difference is already there, and thus the system is already a bit wobbly, just so we don’t have to do everything with a spreadsheet. Increasing the granularity doesn’t increase the wobbliness, it reduces it, and picking the middle value on linear scale is just easier for human brains (…although I wouldn’t presume about Alex’s).
But of course it’s not that difficult to put the proper values into the SP tables either. It has to be done once, along with proper middle values. For example, making ranges from x.25 to x.75, rounding to closest full SP:
5.0 SP Height is 160ft (from 134ft to 190ft) (instead of from 140ft to 200ft)
5.5 SP Height is 226ft (from 191ft to 269ft) (instead of 240ft, from 201 to 279)
6.0 SP Height is 320ft (from 270ft to 380ft) (instead of from 280 to 400ft)
Basically removing the need for finding the middle during the game, giving specific precalculated ranges which are correct. Would make tables even larger, but easier to eyeball during the game, I think. But even then it’s still simpler with middle values (numbers not as messy, more zeroes everywhere, easier to guess). Note that 140ft is still half of 280ft, because even with 0.25 granularity +1 SP is still x2, but looks much better.
As for the CHART, larger ranges can be split properly for the chances to be exact, if we go for the proper value (either both for CHART and SP/Variable tables, or neither, to reduce wobbliness). Smaller ranges (such as, say, 01 to 09 rolls), where difference between x1.5 and x1.4142 is rounded out, will always distort the chances even if larger ranges are fixed, but then again, that distortion is in the CHART already (because you can’t make a range of 02 to 11.5 for a dice roll, plus distortion to have at least 1% chance of failure even at RV 4, even though statistically it’s much less, plus distortion of no RED result at RVs -1 and less). As I said, it’s already somewhat wobbly, but it has to be, otherwise it would be unplayable, or at least unenjoyable (…for most people, again, I wouldn’t presume about Alex)
So what I’m thinking about is not a problem of “how”, but “how far to go” (without making it unplayable, and/or requiring too much conversion effort) and “what else might break”.
As in examples above the magnitude of errors is always relatively small and the same at all levels (in percentage terms), and those I consider fine, but I’m not sure what other mistakes might be introduced, which will rise with SPs, instead of staying fixed.
But that’s exactly the kind of discussion I wanted, to see if I’m missing something else, other than the obvious. Maybe my calculations above are wrong too, and I’m missing something ?
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As for the halved SP effectiveness, it’s an interesting idea, and again not unlike Variable Attributes table which does the same, but I think it would require much more work, going through pretty much all the rules and thinking on what would change (every fixed number, for one), with more chances of messing up somewhere. That would be a much more thorough conversion.
It also loses the benefit of nice middle values (as you basically have to do it as log1.4142, instead of log2 (middle values would require log1.5, and that WILL lead to a propagating error, higher with more SP difference, and lose the +1 SP = x2 rule, breaking all formulae) (works for Variable Attributes because it’s not log1.5, but middle values from log2)
(Although IIRC some games use log1.5, and even original DCH log1000 modified to 0.05 per step, basically a log1.4125, which is pretty close, but they don’t tie the scale to the dice roll or other game mechanics other than the simplest ones, making it effectively pointless)
If it’s the fractions that are a problem, for example aesthetically, then it could be done with a + (so John would have MIG 3+, and James would have MIG 2+, which is the same as 3.5 and 2.5), without having to comb through all the rules for fixed numbers, but it would probably make the rules more unclear (especially when it comes to later formulae).
…and still doesn’t solve the question of “what else might break”. Sigh.
The way I see it, nothing should break as long as we don’t change the log base (and thus 1SP = x2 rule). But if it does, I hope someone points me to that.
Also that’s, uh, actually incorrect. It would be correct for 11 MIG & 10 VAL vs 10 MIG & 10 VAL, but if VAL is also +1, then the theoretical average damage would be x2.8 (or x1.4, if we only increase VAL, but not MIG).
Except that’s theoretically, of course, and not practically, as EV 1 average damage on DV 0 is 1.02, at DV 1 is 1.34, and at DV 2 is 2.00.
As I said, wobbly, and not even x1.4 between rows. But it doubles for each 2 DV (or 1 DV for non-attack rolls), so that log2 is still there.
And honestly, that particular kind of wobbliness isn’t even that important, I think, for it doesn’t propagate (not increasing with increasing SPs), it evens out statistically with time (it would work both for PCs and against them), and most importantly it’s there to better manage player expectations while retaining that small chance of a great result even when DV is not very good, or that small chance of failure even when odds are overwhelming.
Take 10 MIG (base damage 64) & assume an RV of +0. The average damage will be 65.28. 12 MIG (base damage 128) with an RV of +0 yields 130.56, and 11 MIG (base damage 96) with an RV of +1 yields 128.64. That’s about as close to perfect as you can get given you’re only rolling a d100 .
Oh ! Yeah, you’re right, sorry for mixing it up ! I forgot that damage is a variable number that doubles with +2 SP too ! And when it applies to AV which scales the same way (for attacks), they’re interchangable.
The fact that in some places it doubles on 1 SP and others on 2 SP occasionally throws me off, especially when real-world value doubles (like weight) but damage doesn’t. I understand the reasoning (not all force applies), and agree with it, but it’s easy to forget sometimes.
Nice catch, and thanks !
PS: I should probably start thinking of Ascendant not as of a log2(n) system, but as of a mixed log2(n) and log1.4142(n) system (which happens during interaction of the former, but not vs fixed numbers).
But also confirms that halving SP efficiency would be quite annoying to properly convert, as then it would be a mixed system of log1.4142(n) and log1.1892(n), haha.
PPS: Although now that I think about it, and strictly separating the log base for specific situations…maybe not that annoying ?..
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