I'm updating my excel character sheet and was wondering if anyone had figured out a formulaic method for calculating a current attribute score?
In other words, is there an equation that can solve for the current attribute score (x), given the score before aging (y) and the number of aging points accumulated into the characteristic (z). [Note I mean the total amount z - the rules say to 'erase' the aging points back to 0 once a characteristic point moves].
I'm doing the calculation right now with a big lookup table I created, but it seems to me that there must be a formulaic way of doing it.
My maths skills are not what they used to be, but this result from Wolfram Alpha seems to indicate that a formula is plausible: wolframalpha.com/input/?i=5+ ... 75+105+140, might be a good starting place.
Since you are considering the total number of aging points, I would say no, since the same number of aging points could result in different reductions in scores, depending on how they were accumulated. In math terms, aging points are not associative, the order in which they are accumulated matters as to the effect on the characteristic.
Suppose Beatrice has a Quickness of +2 and rolls 14 seven years in a row.
Year 1 score is Quickness +2 (1)
Year 2 score is Quickness +2 (2)
Year 3 score is Quickness +1
Year 4 score is Quickness +1 (1)
Year 5 score is Quickness +0
Year 6 score is Quickness -1
Year 7 score is Quickness -1 (1)
In contrast, suppose John has a Quickness of +2, has a decrepitude score of 1 (3) and rolls a 13. He would need to put 7 Aging points into a Characteristic, but if he puts them all into Quickness, he would only drop it to +1.
So attribute X has a cost of (X+1)(X+2)/2, and it drops when you accumulate X+1 decrepitude or more.
So attribute {4} has a cost of {(4+1)(4+2)/2 = 15}, and it drops when you accumulate {4+1 = 5} decrepitude or more.
=CEILING((SQRT(1+(initial-decrepit+lost)8)-1)/2,1)-1
where
initial = (X+1)(X+2)/2
decrepit = decrepitude in that attribute
lost = decrepitude lost every time you use up too many point from an Aging Crisis {yeah, you have to keep track of that}
And the formula would be different if you go below -1 when [decrepit - lost > initial] or something close to that.
Callen, I plugged your formula into my table to see if it recreated it accurately and it worked great.
For those wondering why I'm doing this (although maybe its obvious and doesn't need stating), the reason this is desirable to do is that the rules as written create a bookkeeping problem. You need to keep track of aging points as you get them in perpetuity for purposes of calculating decrepitude. OTH you need to 'erase' the points accumulated as you put them in a characteristic and that characteristic gets decreased. It occurred to me that there ought to be way where you don't have to 'erase' the points. It's better if I just ask a player to indicate the total points added into each characteristic because then I can use the number for the double duty of calculating decrepitude (by adding all the points together) and also calculating what the 'current' attribute score is (as opposed to its starting value).
Because I couldn't figure out a formula for this, I just ended up doing it by using the above table and an vlookup function.
Dwight's point is interesting and its the first I've heard this interpretation of RAW. By his interpretation, accumulating aging points is a 'transaction' rather than a 'function' and he interprets that 'excess' aging points (points accumulated in a single transaction above and beyond what are needed to decrease the attribute) are lost in the transaction. I'm not sure what the interpretation is for those lost points for calculating decrepitude. I assume he thinks they are 'lost' for decrepitude purposes as well.
If Dwight's interpretation is true, then there is a problem with applying the total points gained with a formula because the total points might not actually be the total points you gain (some might be excess). I can simulate this phenomenon by having players add points one at a time until they see the characteristic change and then stop. (Note that this only really works if 'excess' points are to be 'lost' for purposes of tracking decrepitude as well, otherwise I'll need to keep track of two numbers that don't necessarily relate to each other - points accumulated for characteristics and points accumulated for decrepitude.)
Any thoughts one way or another from others on Dwight's interpretation?
So for example, someone with 5 aging points total (and a current decrepitude of 1) gets a 13 result on an aging roll:
Ok, so the first sentence says they are going to get 10 aging points. Say they choose their Stamina (+2).
Do they gain only 3 points (enough to drop +2 to +1) and then stop?
Do they gain 3 points for purposes of stamina but 10 points for purposes of decrepitude?
Do they gain 3 and then have to apply the other 7 toward more characteristics?
Do they apply all 10 points into stamina? (3 to get to +1, 2 more to get to 0, 1 more to get to -1, 2 more to get to -2, and 2 more for 10 total)
I always assumed it was the last one - which means the whole process really is formulaic rather than transactional, in which case Callen's last sentence isn't necessary to even mention because 'excess' aging points don't really exist.
You don't want to record "Decrepitude" and "lost" for "z" for Characteristics. Each Characteristic is handle separately, and Decrepitude would require another calculation. Stick with Aging Points in each Characteristic. But just don't count the lost points at all. If you want a running total so you can calculate Decrepitude from the sum of nine values (eight sets of Aging Points applied to each Characteristic plus one set of Aging Points that got "lost"), record a single number for the lost points elsewhere. Using the example of rolling a 13 and applying it to Stamina +2, record 3 for Stamina's Aging Points and place the remaining among the "lost" ones. Those lost ones don't need to ever go into the Stamina calculation, though.
You can track your decrepitude score as the sum of the points that affected characteristics and points that did not affect characteristic. Still, since the goal was to be simpler and not have to track two values when one would do, this does not do that. For each aging roll, you could track the change to characteristic aging points and points that were above the threshold. Or you can just track changes to aging points and changes to total decrepitude points.