Morien
10-13-2013, 01:56 PM
So I was doing a stat roller thingy for my Knight Generator, and that got me thinking about the aging in Pendragon. Since I have been on a bit of a Pendragon coding spree lately, I decided to see how does Pendragon aging actually look like.
Taking 10000 knights, I aged them according to the rulebook rules first 10, then further 10 and then final 10 years for a total of 30 years (aged 65), recording their stat losses along the way. Then I took a look at the (mathematical) statistics of the stat loss.
Points lost in: years median mean std min max
Points lost in: 10 9.0 9.26 3.49 0 23
Points lost in: 20 18.0 18.56 4.92 4 43
Points lost in: 30 28.0 27.78 6.04 7 51
10 years, 0 loss: 14
Percentage of people with minimal stat loss:
Total of 2 or less points lost in 10 years: 1.63%
Total of 4 or less points lost in 20 years: 0.03%
So we see that about on average, the characters should lose about 9-10 points per decade of aging, total. We shouldn't see much difference from one decade to another, since Pendragon doesn't accelerate aging (nor does it need to). But we can also see that there is significant variation (std) in stat loss. For instance, the first 10 years gives an average (mean) of 9.26 points lost, with standard deviation of 3.49. What this means is that about two-thirds of the knights lost between 5.8 and 12.8 points (call it 6-13) during that decade. But there are still outliers, as can be seen by min and max; some knights would not lose any points while some unlucky sods might lose 23. 23 is probably a single occurence as it is many std steps away from mean; however, 0 is closer to the mean, and we can see that there were 14 lucky knights out of 10000, so 0.14%, who didn't lose any points during their first decade. Had I been rolling only 1000 knights, I would have been likely to see just one such a lucky knight.
Anyway, how does this translate to individual stat-loss?
Point-loss by stat: stat years median mean std min max
Point-loss by stat: SIZ 10 2.0 1.87 1.4 0 9
Point-loss by stat: DEX 10 2.0 1.86 1.41 0 10
Point-loss by stat: STR 10 2.0 1.85 1.39 0 10
Point-loss by stat: CON 10 2.0 1.82 1.38 0 11
Point-loss by stat: APP 10 2.0 1.86 1.4 0 9
Point-loss by stat: SIZ 20 4.0 3.71 1.97 0 16
Point-loss by stat: DEX 20 4.0 3.73 2.0 0 13
Point-loss by stat: STR 20 4.0 3.72 1.97 0 15
Point-loss by stat: CON 20 3.0 3.67 1.98 0 12
Point-loss by stat: APP 20 4.0 3.72 1.99 0 15
Again, since all stats have equal probability to get rolled up in the aging and thus reduced, they should be statistically the same (as evidenced by the mean and the std). But since it is possible that you just happen to miss rolling one particular stat, you get more 'clumpiness': some guys don't lose any from one or more stats, but then get hit several times into another stat. This is shown by the min/max, and also the huge proportional standard deviation (std) in the 10 year mean: 1.9+-1.4. Which is trying to say that while on average the knights lose around 2 points per stat, the actual odds are more like losing between 0 - 4 stat points.
I was curious to see just how clumpy this distribution would be, so I printed out another couple of statistics
Percentage of people with
2 or less points lost in each stat in 10 years: 21.61%
4 or less points lost in each stat in 20 years: 17.54%
That was quite sobering. It says that even if you take the averages, you are still only sampling about 20% of the population (and not even them, since you are overestimating the stat loss of those who lost less than 2 or 4 points in their stat). Thus, 80% of the knights do lose more in at least one stat.
Since death by aging in Pendragon comes when your stats collapse to 0, losing predominately from one stat can actually doom you while you might otherwise stay healthy. I put the threshold of 'death' in this case to 'bedridden', which is when your stat is 3 or less. So take death in this case to mean: not able to be out of bed. I assumed SIZ/STR/CON = 14 and DEX/APP = 10, to represent an 'average knight'. Hence, 'death' would come when one of these stats would drop to 3, which takes a loss score of 11 or 7, depending on which stat we are talking about here.
Death by age: [SIZ, STR, CON]-11 or [DEX,APP]-7
Mortality percentage in 10 years: 0.76%
Mortality percentage in 20 years: 17.85%
Mortality percentage in 30 years: 57.2%
Alright. So we have the significant fraction of 65 year old knights still able to get up and about (albeit with possibly very low scores). That's OK, they can totter along in their manors or offer advice to the Lord in his hall, even though they might not be such terrifying adversaries in duels.
But this took quite a lot of dice rolling, so would there be an easier way to get the approximately the same stat-loss distribution in tabletop games? After testing it out with a few options, I came up with this one:
Quick NPC aging system: Roll 1d3-1 per stat for statloss for each full 5 years after 35. So someone aged 42 would roll 1d3-1 for each stat and someone of 45 would roll 2d3-2 for each stat. (Alternatively, you could just give -1 / stat / 5 years and it would be close to the truth, but miss out the potential clumpiness. However, it can be argued that the active knights would already be self-selecting against people who have bad arthritis or other ailments (caused by one stat dropping more rapidly); those knights would stay at home, not adventure on the field or in tournaments where they might be met by the PKs in combat.)
Points lost in: years median mean std min max
Points lost in: 10 10.0 10.01 2.6 0 19
Points lost in: 20 20.0 20.02 3.62 7 34
Points lost in: 30 30.0 30.07 4.48 13 46
The mean is more or less where it should be... a bit too high, but we can rack that up to wounds in combat or adjust the stats upwards a bit if they creep close to 3 (or just +1 / lowest stat / 10 years, which would fix it, too). The std is lower, but that is OK, too. We are not trying to represent the whole distribution, just model the most common parts of it. So if you have a bunch of NPCs that you'd like to update to their decade older versions, here is one easy way to do it.
Of course, it wouldn't be hard to make something like an aging roller on the web. In fact, it would be dead easy. You'd only have to input the amount of years and it could then spit out the resulting stat loss per stat, based on the automated aging roll per year.
Comments and questions welcome as ever.
Taking 10000 knights, I aged them according to the rulebook rules first 10, then further 10 and then final 10 years for a total of 30 years (aged 65), recording their stat losses along the way. Then I took a look at the (mathematical) statistics of the stat loss.
Points lost in: years median mean std min max
Points lost in: 10 9.0 9.26 3.49 0 23
Points lost in: 20 18.0 18.56 4.92 4 43
Points lost in: 30 28.0 27.78 6.04 7 51
10 years, 0 loss: 14
Percentage of people with minimal stat loss:
Total of 2 or less points lost in 10 years: 1.63%
Total of 4 or less points lost in 20 years: 0.03%
So we see that about on average, the characters should lose about 9-10 points per decade of aging, total. We shouldn't see much difference from one decade to another, since Pendragon doesn't accelerate aging (nor does it need to). But we can also see that there is significant variation (std) in stat loss. For instance, the first 10 years gives an average (mean) of 9.26 points lost, with standard deviation of 3.49. What this means is that about two-thirds of the knights lost between 5.8 and 12.8 points (call it 6-13) during that decade. But there are still outliers, as can be seen by min and max; some knights would not lose any points while some unlucky sods might lose 23. 23 is probably a single occurence as it is many std steps away from mean; however, 0 is closer to the mean, and we can see that there were 14 lucky knights out of 10000, so 0.14%, who didn't lose any points during their first decade. Had I been rolling only 1000 knights, I would have been likely to see just one such a lucky knight.
Anyway, how does this translate to individual stat-loss?
Point-loss by stat: stat years median mean std min max
Point-loss by stat: SIZ 10 2.0 1.87 1.4 0 9
Point-loss by stat: DEX 10 2.0 1.86 1.41 0 10
Point-loss by stat: STR 10 2.0 1.85 1.39 0 10
Point-loss by stat: CON 10 2.0 1.82 1.38 0 11
Point-loss by stat: APP 10 2.0 1.86 1.4 0 9
Point-loss by stat: SIZ 20 4.0 3.71 1.97 0 16
Point-loss by stat: DEX 20 4.0 3.73 2.0 0 13
Point-loss by stat: STR 20 4.0 3.72 1.97 0 15
Point-loss by stat: CON 20 3.0 3.67 1.98 0 12
Point-loss by stat: APP 20 4.0 3.72 1.99 0 15
Again, since all stats have equal probability to get rolled up in the aging and thus reduced, they should be statistically the same (as evidenced by the mean and the std). But since it is possible that you just happen to miss rolling one particular stat, you get more 'clumpiness': some guys don't lose any from one or more stats, but then get hit several times into another stat. This is shown by the min/max, and also the huge proportional standard deviation (std) in the 10 year mean: 1.9+-1.4. Which is trying to say that while on average the knights lose around 2 points per stat, the actual odds are more like losing between 0 - 4 stat points.
I was curious to see just how clumpy this distribution would be, so I printed out another couple of statistics
Percentage of people with
2 or less points lost in each stat in 10 years: 21.61%
4 or less points lost in each stat in 20 years: 17.54%
That was quite sobering. It says that even if you take the averages, you are still only sampling about 20% of the population (and not even them, since you are overestimating the stat loss of those who lost less than 2 or 4 points in their stat). Thus, 80% of the knights do lose more in at least one stat.
Since death by aging in Pendragon comes when your stats collapse to 0, losing predominately from one stat can actually doom you while you might otherwise stay healthy. I put the threshold of 'death' in this case to 'bedridden', which is when your stat is 3 or less. So take death in this case to mean: not able to be out of bed. I assumed SIZ/STR/CON = 14 and DEX/APP = 10, to represent an 'average knight'. Hence, 'death' would come when one of these stats would drop to 3, which takes a loss score of 11 or 7, depending on which stat we are talking about here.
Death by age: [SIZ, STR, CON]-11 or [DEX,APP]-7
Mortality percentage in 10 years: 0.76%
Mortality percentage in 20 years: 17.85%
Mortality percentage in 30 years: 57.2%
Alright. So we have the significant fraction of 65 year old knights still able to get up and about (albeit with possibly very low scores). That's OK, they can totter along in their manors or offer advice to the Lord in his hall, even though they might not be such terrifying adversaries in duels.
But this took quite a lot of dice rolling, so would there be an easier way to get the approximately the same stat-loss distribution in tabletop games? After testing it out with a few options, I came up with this one:
Quick NPC aging system: Roll 1d3-1 per stat for statloss for each full 5 years after 35. So someone aged 42 would roll 1d3-1 for each stat and someone of 45 would roll 2d3-2 for each stat. (Alternatively, you could just give -1 / stat / 5 years and it would be close to the truth, but miss out the potential clumpiness. However, it can be argued that the active knights would already be self-selecting against people who have bad arthritis or other ailments (caused by one stat dropping more rapidly); those knights would stay at home, not adventure on the field or in tournaments where they might be met by the PKs in combat.)
Points lost in: years median mean std min max
Points lost in: 10 10.0 10.01 2.6 0 19
Points lost in: 20 20.0 20.02 3.62 7 34
Points lost in: 30 30.0 30.07 4.48 13 46
The mean is more or less where it should be... a bit too high, but we can rack that up to wounds in combat or adjust the stats upwards a bit if they creep close to 3 (or just +1 / lowest stat / 10 years, which would fix it, too). The std is lower, but that is OK, too. We are not trying to represent the whole distribution, just model the most common parts of it. So if you have a bunch of NPCs that you'd like to update to their decade older versions, here is one easy way to do it.
Of course, it wouldn't be hard to make something like an aging roller on the web. In fact, it would be dead easy. You'd only have to input the amount of years and it could then spit out the resulting stat loss per stat, based on the automated aging roll per year.
Comments and questions welcome as ever.