The following table can be used in very fundamental ways and allows the game master to remove a lot of guess work from custom characters and abilities. It does this by prescribing how much a particular target number is worth in terms of probability, ability value, and experience. These attributes are created using a simple and easily interpretable system

Modeling All Possible Rolls

One of the hardest parts of the system was to try and figure out how to incorporate ability score improvements with the dice rolls. If the ability scores stayed with in the range of the dice rolls you could just assume that the modifiers modify the 3d6 roll only. That doesn’t work because many systems have a range of abilities that when combined with the dice roll for exceed that range. For AGE we have an approximate ability range of -4 to +15 (some AGE adversaries report a -4 ability score, a theoretical max of ability score of 12 plus a +3 focus). That range means there is a total range of -1 to 33. No way that neatly fits in 3 to 18 range.

The break through came when thinking about an optional rule in DnD 5e, where your proficiency modifier can be replaced with a proficiency die. This is an interesting idea where your dice roll is made from multiple sources (I know 3d6 is multiple sources but it is treated as a single type of roll). What if the proficiency was expanded to represent the whole range of static modifiers? The simplest roll is a uniform distribution (1dX) so let’s use that. To model the range of AGE modifiers we could use a 1d{-4..15} + 3d6 roll (https://anydice.com/program/1dbcc), however that would cause the the average of the roll to be not the same as an unmodified roll (16 versus 10.5). To maintain an average of 10.5 all we need to do is extend the lower end to be the negative of the maximum modifier which would be -15 in this case. The resulting distribution has the same average as the unmodified roll, and is still a plain 3d6 when there are no modifiers. There is no harm in lowering the theoretical minimum modifier as we will see later.

Model Each Target Number as the Geometric Distribution

The new “All Rolls” distribution isn’t enough to help us with all our issues. It only tells us the probability of rolling a target number (and beating it). What we need is how much effort it would take us (in this case how many tries) to beat the TN. For that we use the Geometric distribution which tells us for a given probability, how many failures will happen before the first success. The number of attempts is 1/probability, which is the mean of that distribution. For a 50% chance of success it is straight forward to imagine that it takes you about two tries to get a success. 1/0.5 = 2. As such we apply that formula to all the TNs in the “All Rolls” distribution to get effort needed to achieve success

Factoring in Ability Scaling

There is one more adjustment we need to make. Every roll adds part of the modifier to the damage roll. This means that for a TN 13 roll, its value should not only be from the geometric effort, but also the +2 that will be added to it. The total value of a TN is then 1/p + ability modifier. For the unmodified roll, the value will remain at 2

Creating XP Tables for Ability Scores

We haven’t diverged from the AGE too much yet, but that ends now. In AGE the leveling system awards one ability and one focus each level. The cost of each level roughly increases in terms of XP, but that cost does not reflect the value of the ability or focus chosen. If you improved from -2 to -1 at level 20, that ends of costing a lot of XP versus if you improved from a 4 to a 5 at level 3. That second improvement should cost way more.

We have to switch from a level system to more of a constant point buy system. The game still awards you XP, but you spend it specifically on ability improvements. Moving from -2 to -1 will cost you 55 XP while moving from 4 to 5 will cost you 155 XP. The XP cost is derived directly from the value calculated in the last section and in my case, multiplied by 10 and rounded to the nearest multiple of 5. Here is the final table for your enjoyment. The first sheet is formatted, but the calculations are one the second sheet. The “At Least” column is calculated using the “At Least” export from https://anydice.com/program/1dbd1

Next Gen Value and XP Table

https://docs.google.com/spreadsheets/d/1J_aXa6BpEMB47xeKs20jTflfuvq4pYyKIjpnXrqQP2w/edit?usp=sharing



Applications

How to price ability advancements less arbitrarily. What TN should a spell be? Calculate how much damage (or utility) your spell does. Find the largest TN where your spell is still under the maximum allowed value. That is the TN of the spell.

Future Work

Talents

Since I have thrown out the leveling system there needs to be another mechanism for awarding talents, class talents, and specializations. I think the simplest option to allow a new choice every time you purchase a new ability improvement. Since all talents and specializations have a minimum requirements their cost will already be taken into account with those requirements. I don’t see a problem with having to many talents. The current game already allows two dozen at max level. The GM just needs to award a number of available talent choices at the start of the game.

Starting Abilities

I am a big fan of point buy and this system is perfect for that. In AGE there are nine abilities and if you had a +0 modifier in every ability, the total cost would be 215 x 9 = 1935. I would use that as the point buy budget and let the players redistribute the points. The XP table would let the player reduce one ability to a -6 (215XP) allowing them to increase another ability to +2 (215 + 215 > 400). More likely they would trade a -2 for a +1, or two -1 for a +1.

Spell Design

The first attempts that used only the 3d6 probabilities suffered from TN18 spells being worth 216 value. While this had a small chance of happening, it is only small with a +0 modifier. The addition of the ability roll allows more diversity in TN values without such a high value. The table is truncated at the bottom because of negative values, but at the top as well since we only need to think about that +15 range. Yes a 33 can be rolled, but it is the new super rare roll and we only need to worry about the modifier range plus the average roll of 11.

The Cost of an Ability versus a Focus

AGE has grouped focuses under specific abilities. The ability improves many rolls but a focus only one. How do you use the XP table for that situation? I would charge the ability increase equal to the sum of equivalent focus increases. Let’s say you improve strength from zero to one, and strength has 5 related focuses. Then the cost is 85XP times 5 for a total of 425 XP.

Using Abilities versus Focuses

I combined the two together to make a single 1d{-15..15} modifier roll. You could definitely use any kind of roll that has the same range like 1d{-12..12} + 1d{-3..3}. This reinforces the current rules of a maximum of +12 for abilities and +3 for focuses. That is a bit of an arbitrary split and you could change it easily. +10 and +5 perhaps? Or something more equal like +8 and +7. Or create a completely custom range with a ceiling of +100! Create the roll on anydice reuse the spreadsheet. The +100 example isn’t recommended as it really flattens out the curve and each ability value (especially around +0) would not be noticeably different. I would probably lean in the +10 / +5 route, just to give a bit more room to really specialize. Keeping the ratio where there are more ability points than focus points available is going to force players to not exclusively buy focuses since they are more limited.